Recipes for writing Rascal programs.
These Rascal Recipes are a work-in-progress but will gradually evolve into a collection of basic Rascal language examples and use cases. It consists of the following parts:
-
Basic: Some basic, hello world-like, examples of Rascal programs.
-
Common: Solutions for some common tasks.
-
Languages: Definitions of several languages and their tools.
-
Metrics: Computing.
-
Visualization: Recipes for creating visualizations.
The following features are covered:
-
Basic language features.
-
Common tasks.
-
Fact extraction.
-
Language definition.
-
Syntax definition.
-
Parsing.
-
Transformation.
-
Code generation.
-
IDE extensions.
-
Visualization.
1. Basic
Some basic, hello world-like, examples of Rascal programs.
We discuss the following examples:
-
Hello: Variations on the ubiquitous Hello World example.
-
Factorial: Compute the factorial function.
-
Squares: Print a list of squares.
-
Bottles Of Beer: A Rascal version of a generator for the 99 Bottles of Beer song.
-
Bubble: Variout styles to write bubble sort.
-
Even: Produce a list of even numbers.
-
FizzBuzz: We solve a well-known job interview puzzle.
-
Quine: A self-reproducing program.
These programs illustrate various features of Rascal; they are not representative as use cases of the language.
1.1. Hello
Variations on the ubiquitous Hello World example.
1.1.1. hello on command line
We demonstrate hello via an interactive session with the Rascal system. First we get the prompt rascal> that shows that Rascal is ready for our input. Next, we import the library module IO since hello world requires printing. Rascal responds with the feedback ok so we know that all went well. Finally, we call println and proudly observe our first Rascal output!
rascal>import IO;
ok
rascal>println("Hello world, this is my first Rascal program");
Hello world, this is my first Rascal program
ok1.1.2. hello as function
A slightly more audacious approach is to wrap the print statement in a function and call it:
rascal>import IO;
ok
rascal>void hello() {
>>>>>>> println("Hello world, this is my first Rascal program");
>>>>>>>}
void (): function(|prompt:///|(0,76,<1,0>,<3,1>))When you type in a command and continue it on a new line the Rascal systems prompts you with >>>>>>> to indicate that more input is needed. Don’t get scared by the void (): void hello(); that you get back when typing in the hello function. The first
void () part says the result is a function that returns nothing, and the second part
void hello() summarizes its value (or would you prefer a hex dump?). Finally, we call the hello function and enjoy its output.
rascal>hello();
Hello world, this is my first Rascal program
ok1.1.3. hello as module
The summit of hello-engineering can be reached by placing all the above in a separate module:
module demo::basic::Hello
import IO;
void hello() {
println("Hello world, this is my first Rascal program");
}Using this Hello module is now simple:
rascal>import demo::basic::Hello;
ok
rascal>hello();
Hello world, this is my first Rascal program
okThe hello function is by default visible outside the Hello module. We could stress this by adding writing public void hello() { … }. Restricting visibility to the module itself can be achieved by adding the keyword private
to the definition of hello.
1.2. Factorial
Compute the factorial function.
The factorial
of a number N is defined as N * (N-1) * (N-2) * … * 1. Here is the Rascal version:
module demo::basic::Factorial
int fac(int N) = N <= 0 ? 1 : N * fac(N - 1); (1)
int fac2(0) = 1; (2)
default int fac2(int N) = N * fac2(N - 1); (3)
int fac3(int N) { (4)
if (N == 0)
return 1;
return N * fac3(N - 1);
}
// end::module[]
test bool tfac0() = fac(0) == 1;
test bool tfac1() = fac(1) == 1;
test bool tfac2() = fac(4) == 24;
test bool tfac47() = fac(47) == 258623241511168180642964355153611979969197632389120000000000;| 1 | fac is defined using a conditional expression to distinguish cases. |
| 2 | fac2 distinguishes cases using pattern-based dispatch (Rascal Functions). Here the case for 0 is defined. |
| 3 | Here all other cases for fac2 are defined (as indicated by the default keyword). |
| 4 | fac3 shows a more imperative implementation of factorial. |
Here is how to use fac:
rascal>import demo::basic::Factorial;
ok
rascal>fac(47);
int: 258623241511168180642964355153611979969197632389120000000000| Indeed, Rascal supports arbitrary length numbers. |
Here is an example of fac2:
rascal>fac2(47);
int: 2586232415111681806429643551536119799691976323891200000000001.3. Squares
Print a list of squares
How can we print a list of squares? Here is a solution:
module demo::basic::Squares
import IO; (1)
// Print a table of squares
void squares(int N){
println("Table of squares from 1 to <N>\n"); (2)
for(int I <- [1 .. N + 1])
println("<I> squared = <I * I>"); (3)
}
// a solution with a multi line string template:
str squaresTemplate(int N) (4)
= "Table of squares from 1 to <N>
'<for (int I <- [1 .. N + 1]) {>
' <I> squared = <I * I><}>";| 1 | The IO module is imported since we want to print things using println. |
| 2 | String interpolation is used several times. Here the value of N is inserted in the header message. |
| 3 | The values of I and I * I are inserted in each line that is printed. |
| 4 | Define an alternative implementation squareTemplate that is based on string templates and returns a string value instead of printing the results itself. |
Here is how square can be used:
rascal>import demo::basic::Squares;
ok
rascal>squares(9);
Table of squares from 1 to 9
1 squared = 1
2 squared = 4
3 squared = 9
4 squared = 16
5 squared = 25
6 squared = 36
7 squared = 49
8 squared = 64
9 squared = 81
oksquaresTemplate gives a similar result but now as a string:
rascal>squaresTemplate(9);
str: "Table of squares from 1 to 9\n\n 1 squared = 1\n 2 squared = 4\n 3 squared = 9\n 4 squared = 16\n 5 squared = 25\n 6 squared = 36\n 7 squared = 49\n 8 squared = 64\n 9 squared = 81"To get a truly identical result we have to import the IO module and print the value of squaresTemplate:
rascal>import IO;
ok
rascal>println(squaresTemplate(9));
Table of squares from 1 to 9
1 squared = 1
2 squared = 4
3 squared = 9
4 squared = 16
5 squared = 25
6 squared = 36
7 squared = 49
8 squared = 64
9 squared = 81
ok1.4. Bottles Of Beer
A Rascal version of a generator for the 99 Bottles of Beer song.
Programs that generate the lyrics for the song 99 Bottles of Beer are a popular way to compare programming languages. At 99-bottles-of-beer.net you can find versions in nearly 1500 different languages and the lyrics can be found here.
Here is our version:
module demo::basic::Bottles
import IO;
str bottles(0) = "no more bottles"; (1)
str bottles(1) = "1 bottle";
default str bottles(int n) = "<n> bottles"; (2)
void sing(){ (3)
for(n <- [99 .. 0]){
println("<bottles(n)> of beer on the wall, <bottles(n)> of beer.");
println("Take one down, pass it around, <bottles(n-1)> of beer on the wall.\n");
}
println("No more bottles of beer on the wall, no more bottles of beer.");
println("Go to the store and buy some more, 99 bottles of beer on the wall.");
}| 1 | We use an auxiliary function bottles that returns the word "bottle" adjusted for the actual number of bottles that is available. Observe how we use the patterns 0, 1 and int n in the definition of three variants of this function. |
| 2 | Pattern-directed invocation (see function declaration) will determine at the call site which function will be called. The general case is labeled with default to indicate that if the case for 0 and 1 do not match, this alternative should handle the other cases. |
| 3 | The main function is sing that iterates over the numbers 99 downto 1 (as described by the range [99 .. 1]) and prints appriopriate lyrics. Observe how the value of the bottles function is interpolated several times in the string. |
Here is the result:
rascal>import demo::basic::Bottles;
ok
rascal>sing();
99 bottles of beer on the wall, 99 bottles of beer.
Take one down, pass it around, 98 bottles of beer on the wall.
98 bottles of beer on the wall, 98 bottles of beer.
Take one down, pass it around, 97 bottles of beer on the wall.
97 bottles of beer on the wall, 97 bottles of beer.
Take one down, pass it around, 96 bottles of beer on the wall.
96 bottles of beer on the wall, 96 bottles of beer.
Take one down, pass it around, 95 bottles of beer on the wall.
95 bottles of beer on the wall, 95 bottles of beer.
Take one down, pass it around, 94 bottles of beer on the wall.
94 bottles of beer on the wall, 94 bottles of beer.
Take one down, pass it around, 93 bottles of beer on the wall.
93 bottles of beer on the wall, 93 bottles of beer.
Take one down, pass it around, 92 bottles of beer on the wall.
92 bottles of beer on the wall, 92 bottles of beer.
Take one down, pass it around, 91 bottles of beer on the wall.
91 bottles of beer on the wall, 91 bottles of beer.
Take one down, pass it around, 90 bottles of beer on the wall.
90 bottles of beer on the wall, 90 bottles of beer.
Take one down, pass it around, 89 bottles of beer on the wall.
89 bottles of beer on the wall, 89 bottles of beer.
Take one down, pass it around, 88 bottles of beer on the wall.
88 bottles of beer on the wall, 88 bottles of beer.
Take one down, pass it around, 87 bottles of beer on the wall.
87 bottles of beer on the wall, 87 bottles of beer.
Take one down, pass it around, 86 bottles of beer on the wall.
86 bottles of beer on the wall, 86 bottles of beer.
Take one down, pass it around, 85 bottles of beer on the wall.
85 bottles of beer on the wall, 85 bottles of beer.
Take one down, pass it around, 84 bottles of beer on the wall.
84 bottles of beer on the wall, 84 bottles of beer.
Take one down, pass it around, 83 bottles of beer on the wall.
83 bottles of beer on the wall, 83 bottles of beer.
Take one down, pass it around, 82 bottles of beer on the wall.
82 bottles of beer on the wall, 82 bottles of beer.
Take one down, pass it around, 81 bottles of beer on the wall.
81 bottles of beer on the wall, 81 bottles of beer.
Take one down, pass it around, 80 bottles of beer on the wall.
80 bottles of beer on the wall, 80 bottles of beer.
Take one down, pass it around, 79 bottles of beer on the wall.
79 bottles of beer on the wall, 79 bottles of beer.
Take one down, pass it around, 78 bottles of beer on the wall.
78 bottles of beer on the wall, 78 bottles of beer.
Take one down, pass it around, 77 bottles of beer on the wall.
77 bottles of beer on the wall, 77 bottles of beer.
Take one down, pass it around, 76 bottles of beer on the wall.
76 bottles of beer on the wall, 76 bottles of beer.
Take one down, pass it around, 75 bottles of beer on the wall.
75 bottles of beer on the wall, 75 bottles of beer.
Take one down, pass it around, 74 bottles of beer on the wall.
74 bottles of beer on the wall, 74 bottles of beer.
Take one down, pass it around, 73 bottles of beer on the wall.
73 bottles of beer on the wall, 73 bottles of beer.
Take one down, pass it around, 72 bottles of beer on the wall.
72 bottles of beer on the wall, 72 bottles of beer.
Take one down, pass it around, 71 bottles of beer on the wall.
71 bottles of beer on the wall, 71 bottles of beer.
Take one down, pass it around, 70 bottles of beer on the wall.
70 bottles of beer on the wall, 70 bottles of beer.
Take one down, pass it around, 69 bottles of beer on the wall.
69 bottles of beer on the wall, 69 bottles of beer.
Take one down, pass it around, 68 bottles of beer on the wall.
68 bottles of beer on the wall, 68 bottles of beer.
Take one down, pass it around, 67 bottles of beer on the wall.
67 bottles of beer on the wall, 67 bottles of beer.
Take one down, pass it around, 66 bottles of beer on the wall.
66 bottles of beer on the wall, 66 bottles of beer.
Take one down, pass it around, 65 bottles of beer on the wall.
65 bottles of beer on the wall, 65 bottles of beer.
Take one down, pass it around, 64 bottles of beer on the wall.
64 bottles of beer on the wall, 64 bottles of beer.
Take one down, pass it around, 63 bottles of beer on the wall.
63 bottles of beer on the wall, 63 bottles of beer.
Take one down, pass it around, 62 bottles of beer on the wall.
62 bottles of beer on the wall, 62 bottles of beer.
Take one down, pass it around, 61 bottles of beer on the wall.
61 bottles of beer on the wall, 61 bottles of beer.
Take one down, pass it around, 60 bottles of beer on the wall.
60 bottles of beer on the wall, 60 bottles of beer.
Take one down, pass it around, 59 bottles of beer on the wall.
59 bottles of beer on the wall, 59 bottles of beer.
Take one down, pass it around, 58 bottles of beer on the wall.
58 bottles of beer on the wall, 58 bottles of beer.
Take one down, pass it around, 57 bottles of beer on the wall.
57 bottles of beer on the wall, 57 bottles of beer.
Take one down, pass it around, 56 bottles of beer on the wall.
56 bottles of beer on the wall, 56 bottles of beer.
Take one down, pass it around, 55 bottles of beer on the wall.
55 bottles of beer on the wall, 55 bottles of beer.
Take one down, pass it around, 54 bottles of beer on the wall.
54 bottles of beer on the wall, 54 bottles of beer.
Take one down, pass it around, 53 bottles of beer on the wall.
53 bottles of beer on the wall, 53 bottles of beer.
Take one down, pass it around, 52 bottles of beer on the wall.
52 bottles of beer on the wall, 52 bottles of beer.
Take one down, pass it around, 51 bottles of beer on the wall.
51 bottles of beer on the wall, 51 bottles of beer.
Take one down, pass it around, 50 bottles of beer on the wall.
50 bottles of beer on the wall, 50 bottles of beer.
Take one down, pass it around, 49 bottles of beer on the wall.
49 bottles of beer on the wall, 49 bottles of beer.
Take one down, pass it around, 48 bottles of beer on the wall.
48 bottles of beer on the wall, 48 bottles of beer.
Take one down, pass it around, 47 bottles of beer on the wall.
47 bottles of beer on the wall, 47 bottles of beer.
Take one down, pass it around, 46 bottles of beer on the wall.
46 bottles of beer on the wall, 46 bottles of beer.
Take one down, pass it around, 45 bottles of beer on the wall.
45 bottles of beer on the wall, 45 bottles of beer.
Take one down, pass it around, 44 bottles of beer on the wall.
44 bottles of beer on the wall, 44 bottles of beer.
Take one down, pass it around, 43 bottles of beer on the wall.
43 bottles of beer on the wall, 43 bottles of beer.
Take one down, pass it around, 42 bottles of beer on the wall.
42 bottles of beer on the wall, 42 bottles of beer.
Take one down, pass it around, 41 bottles of beer on the wall.
41 bottles of beer on the wall, 41 bottles of beer.
Take one down, pass it around, 40 bottles of beer on the wall.
40 bottles of beer on the wall, 40 bottles of beer.
Take one down, pass it around, 39 bottles of beer on the wall.
39 bottles of beer on the wall, 39 bottles of beer.
Take one down, pass it around, 38 bottles of beer on the wall.
38 bottles of beer on the wall, 38 bottles of beer.
Take one down, pass it around, 37 bottles of beer on the wall.
37 bottles of beer on the wall, 37 bottles of beer.
Take one down, pass it around, 36 bottles of beer on the wall.
36 bottles of beer on the wall, 36 bottles of beer.
Take one down, pass it around, 35 bottles of beer on the wall.
35 bottles of beer on the wall, 35 bottles of beer.
Take one down, pass it around, 34 bottles of beer on the wall.
34 bottles of beer on the wall, 34 bottles of beer.
Take one down, pass it around, 33 bottles of beer on the wall.
33 bottles of beer on the wall, 33 bottles of beer.
Take one down, pass it around, 32 bottles of beer on the wall.
32 bottles of beer on the wall, 32 bottles of beer.
Take one down, pass it around, 31 bottles of beer on the wall.
31 bottles of beer on the wall, 31 bottles of beer.
Take one down, pass it around, 30 bottles of beer on the wall.
30 bottles of beer on the wall, 30 bottles of beer.
Take one down, pass it around, 29 bottles of beer on the wall.
29 bottles of beer on the wall, 29 bottles of beer.
Take one down, pass it around, 28 bottles of beer on the wall.
28 bottles of beer on the wall, 28 bottles of beer.
Take one down, pass it around, 27 bottles of beer on the wall.
27 bottles of beer on the wall, 27 bottles of beer.
Take one down, pass it around, 26 bottles of beer on the wall.
26 bottles of beer on the wall, 26 bottles of beer.
Take one down, pass it around, 25 bottles of beer on the wall.
25 bottles of beer on the wall, 25 bottles of beer.
Take one down, pass it around, 24 bottles of beer on the wall.
24 bottles of beer on the wall, 24 bottles of beer.
Take one down, pass it around, 23 bottles of beer on the wall.
23 bottles of beer on the wall, 23 bottles of beer.
Take one down, pass it around, 22 bottles of beer on the wall.
22 bottles of beer on the wall, 22 bottles of beer.
Take one down, pass it around, 21 bottles of beer on the wall.
21 bottles of beer on the wall, 21 bottles of beer.
Take one down, pass it around, 20 bottles of beer on the wall.
20 bottles of beer on the wall, 20 bottles of beer.
Take one down, pass it around, 19 bottles of beer on the wall.
19 bottles of beer on the wall, 19 bottles of beer.
Take one down, pass it around, 18 bottles of beer on the wall.
18 bottles of beer on the wall, 18 bottles of beer.
Take one down, pass it around, 17 bottles of beer on the wall.
17 bottles of beer on the wall, 17 bottles of beer.
Take one down, pass it around, 16 bottles of beer on the wall.
16 bottles of beer on the wall, 16 bottles of beer.
Take one down, pass it around, 15 bottles of beer on the wall.
15 bottles of beer on the wall, 15 bottles of beer.
Take one down, pass it around, 14 bottles of beer on the wall.
14 bottles of beer on the wall, 14 bottles of beer.
Take one down, pass it around, 13 bottles of beer on the wall.
13 bottles of beer on the wall, 13 bottles of beer.
Take one down, pass it around, 12 bottles of beer on the wall.
12 bottles of beer on the wall, 12 bottles of beer.
Take one down, pass it around, 11 bottles of beer on the wall.
11 bottles of beer on the wall, 11 bottles of beer.
Take one down, pass it around, 10 bottles of beer on the wall.
10 bottles of beer on the wall, 10 bottles of beer.
Take one down, pass it around, 9 bottles of beer on the wall.
9 bottles of beer on the wall, 9 bottles of beer.
Take one down, pass it around, 8 bottles of beer on the wall.
8 bottles of beer on the wall, 8 bottles of beer.
Take one down, pass it around, 7 bottles of beer on the wall.
7 bottles of beer on the wall, 7 bottles of beer.
Take one down, pass it around, 6 bottles of beer on the wall.
6 bottles of beer on the wall, 6 bottles of beer.
Take one down, pass it around, 5 bottles of beer on the wall.
5 bottles of beer on the wall, 5 bottles of beer.
Take one down, pass it around, 4 bottles of beer on the wall.
4 bottles of beer on the wall, 4 bottles of beer.
Take one down, pass it around, 3 bottles of beer on the wall.
3 bottles of beer on the wall, 3 bottles of beer.
Take one down, pass it around, 2 bottles of beer on the wall.
2 bottles of beer on the wall, 2 bottles of beer.
Take one down, pass it around, 1 bottle of beer on the wall.
1 bottle of beer on the wall, 1 bottle of beer.
Take one down, pass it around, no more bottles of beer on the wall.
No more bottles of beer on the wall, no more bottles of beer.
Go to the store and buy some more, 99 bottles of beer on the wall.
ok1.5. Bubble
Variout styles to write bubble sort.
Bubble sort is a classical (albeit not the most efficient) technique to sort lists of values. We present here several styles to implement bubble sort. Also see sort for a more efficient library function for sorting.
module demo::basic::Bubble
import List;
// Variations on Bubble sort
// sort1: uses list indexing and a for-loop
list[int] sort1(list[int] numbers) {
if (size(numbers) > 0) {
for (int i <- [0 .. size(numbers)-1]) {
if (numbers[i] > numbers[i+1]) {
<numbers[i], numbers[i+1]> = <numbers[i+1], numbers[i]>;
return sort1(numbers);
}
}
}
return numbers;
}
// sort2: uses list matching and switch
list[int] sort2(list[int] numbers) {
switch(numbers){
case [*int nums1, int p, int q, *int nums2]:
if (p > q) {
return sort2(nums1 + [q, p] + nums2);
} else {
fail;
}
default: return numbers;
}
}
// sort3: uses list matching and while
list[int] sort3(list[int] numbers) {
while ([*int nums1, int p, *int nums2, int q, *int nums3] := numbers && p > q)
numbers = nums1 + [q] + nums2 + [p] + nums3;
return numbers;
}
// sort4: using recursion instead of iteration, and splicing instead of concat
list[int] sort4([*int nums1, int p, *int nums2, int q, *int nums3]) {
if (p > q)
return sort4([*nums1, q, *nums2, p, *nums3]);
else
fail sort4;
}
default list[int] sort4(list[int] x) = x;
// sort5: inlines the condition into a when:
list[int] sort5([*int nums1, int p, *int nums2, int q, *int nums3])
= sort5([*nums1, q, *nums2, p, *nums3])
when p > q;
default list[int] sort5(list[int] x) = x;sort1 is a classic, imperative style, implementation of bubble sort: it iterates over consecutive pairs of elements and when a not-yet-sorted pair is encountered, the elements are exchanged, and sort1 is applied recursively to the whole list.
sort2 uses list matching and consists of a switch with two cases:
-
a case matching a list with two consecutive elements that are unsorted. Observe that when the pattern of a case matches, the case as a whole can still fail.
-
a default case.
sort3 also uses list matching but in a more declarative style: as long as there are unsorted elements in the list (possibly with intervening elements), exchange them.
sort4 is identical to sort3, except that the shorter *-notation for list variables is used and that the type declaration for the the non-list variables has been omitted.
sort5 uses tail recursion to reach a fixed point instead of a while loop. One alternative matches lists with out-of-order elements, while the default alternative returns the list if no out-of-order elements are found.
Let’s put them to the test:
rascal>import demo::basic::Bubble;
ok
rascal>L = [9,8,7,6,5,4,3,2,1];
list[int]: [9,8,7,6,5,4,3,2,1]
rascal>sort1(L);
list[int]: [1,2,3,4,5,6,7,8,9]
rascal>sort2(L);
list[int]: [1,2,3,4,5,6,7,8,9]
rascal>sort3(L);
list[int]: [1,2,3,4,5,6,7,8,9]
rascal>sort4(L);
list[int]: [1,2,3,4,5,6,7,8,9]
rascal>sort5(L);
list[int]: [1,2,3,4,5,6,7,8,9]1.6. Even
Produce a list of even numbers.
Let’s write a function that generates all the even numbers in a list up to a certain maximum. We will do it in a few alternative ways: from very imperative to very declarative and some steps in between.
rascal>list[int] even0(int max) {
>>>>>>> list[int] result = [];
>>>>>>> for (int i <- [0..max])
>>>>>>> if (i % 2 == 0)
>>>>>>> result += i;
>>>>>>> return result;
>>>>>>>}
list[int] (int): function(|prompt:///|(0,135,<1,0>,<7,1>))
rascal>even0(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]Now lets remove the temporary type declarations:
rascal>list[int] even1(int max) {
>>>>>>> result = [];
>>>>>>> for (i <- [0..max])
>>>>>>> if (i % 2 == 0)
>>>>>>> result += i;
>>>>>>> return result;
>>>>>>>}
list[int] (int): function(|prompt:///|(0,121,<1,0>,<7,1>))
rascal>even1(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]To make the code shorter, we can inline the condition in the for loop:
rascal>list[int] even2(int max) {
>>>>>>> result = [];
>>>>>>> for (i <- [0..max], i % 2 == 0)
>>>>>>> result += i;
>>>>>>> return result;
>>>>>>>}
list[int] (int): function(|prompt:///|(0,111,<1,0>,<6,1>))
rascal>even2(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]In fact, for loops may produce lists as values, using the append statement:
rascal>list[int] even3(int max) {
>>>>>>> result = for (i <- [0..max], i % 2 == 0)
>>>>>>> append i;
>>>>>>> return result;
>>>>>>>}
list[int] (int): function(|prompt:///|(0,102,<1,0>,<5,1>))
rascal>even3(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]So now, the result temporary is not necessary anymore:
rascal>list[int] even4(int max) {
>>>>>>> return for (i <- [0..max], i % 2 == 0)
>>>>>>> append i;
>>>>>>>}
list[int] (int): function(|prompt:///|(0,90,<1,0>,<4,1>))
rascal>even4(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]This code is actually very close to a list comprehension already:
rascal>list[int] even5(int max) {
>>>>>>> return [ i | i <- [0..max], i % 2 == 0];
>>>>>>>}
list[int] (int): function(|prompt:///|(0,71,<1,0>,<3,1>))
rascal>even5(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]And now we can just define even using an expression only:
rascal>list[int] even6(int max) = [i | i <- [0..max], i % 2 == 0];
list[int] (int): function(|prompt:///|(0,59,<1,0>,<1,59>))
rascal>even6(25);
list[int]: [0,2,4,6,8,10,12,14,16,18,20,22,24]Or, perhaps we prefer creating a set instead of a list:
rascal>set[int] even7(int max) = {i | i <- [0..max], i % 2 == 0};
set[int] (int): function(|prompt:///|(0,58,<1,0>,<1,58>))
rascal>even7(25);
set[int]: {10,16,8,14,20,2,4,6,24,12,22,18,0}-
You can program in for loops and use temporary variables if you like.
-
Comprehensions are shorter and more powerful.
-
There are comprehensions for lists, sets, and maps
-
Trainwreck alert: if you start putting too many conditions in a single for loop or comprehension the code may become unreadable.
1.7. FizzBuzz
We solve a well-known job interview puzzle.
FizzBuzz is a well-known puzzle that is used at job interviews. It is defined as follows:
Write a program that prints the numbers from 1 to 100. But for multiples of three print "Fizz" instead of the number and for the multiples of five print "Buzz". For numbers which are multiples of both three and five print "FizzBuzz".
Surprisingly, many candidates fail to pass this test. Solutions to FizzBuzz in various languages are available here.
Here are a few possible Rascal solutions:
module demo::basic::FizzBuzz
import IO;
void fizzbuzz() {
for (int n <- [1 .. 101]){
fb = ((n % 3 == 0) ? "Fizz" : "") + ((n % 5 == 0) ? "Buzz" : "");
println((fb == "") ?"<n>" : fb);
}
}
void fizzbuzz2() {
for (n <- [1..101])
switch(<n % 3 == 0, n % 5 == 0>) {
case <true,true> : println("FizzBuzz");
case <true,false> : println("Fizz");
case <false,true> : println("Buzz");
default: println(n);
}
}
void fizzbuzz3() {
for (n <- [1..101]) {
if (n % 3 == 0) print("Fizz");
if (n % 5 == 0) print("Buzz");
else if (n % 3 != 0) print(n);
println("");
}
}rascal>import demo::basic::FizzBuzz;
ok
rascal>fizzbuzz();
1
2
Fizz
4
Buzz
Fizz
7
8
Fizz
Buzz
11
Fizz
13
14
FizzBuzz
16
17
Fizz
19
Buzz
Fizz
22
23
Fizz
Buzz
26
Fizz
28
29
FizzBuzz
31
32
Fizz
34
Buzz
Fizz
37
38
Fizz
Buzz
41
Fizz
43
44
FizzBuzz
46
47
Fizz
49
Buzz
Fizz
52
53
Fizz
Buzz
56
Fizz
58
59
FizzBuzz
61
62
Fizz
64
Buzz
Fizz
67
68
Fizz
Buzz
71
Fizz
73
74
FizzBuzz
76
77
Fizz
79
Buzz
Fizz
82
83
Fizz
Buzz
86
Fizz
88
89
FizzBuzz
91
92
Fizz
94
Buzz
Fizz
97
98
Fizz
Buzz
ok1.8. Quine
A self-reproducing program.
A quine is a computer program that takes no input and produces a copy of its own source code. A quine is also called a self-replicating or self-reproducing program.
At the Quine Page you can find hundreds of quines in many different programming languages.
Learning about quines, is about learning how to quote and escape symbols in strings.
module demo::basic::Quine
import IO;
import String;
void quine(){
println(program); (3)
println("\"" + escape(program, ("\"" : "\\\"", "\\" : "\\\\")) + "\";"); (4)
}
str program = (1)
"module demo::basic::Quine
import IO;
import String;
void quine(){
println(program);
println(\"\\\"\" + escape(program, (\"\\\"\" : \"\\\\\\\"\", \"\\\\\" : \"\\\\\\\\\")) + \"\\\";\");
}
str program ="; (2)| 1 | A remarkable point in the code: the string variable program has as value the text of the module Quine upto here. |
| 2 | The definition of program ends here. This string has a mesmerizing amount of escapes to which we will come back in a moment. |
| 3 | The function quine prints the string program twice, here as is and this produces the program upto above. |
| 4 | Here the value of program is printed as a string (surrounded with string quotes) in order to reproduce the string value of program followed by a semi-colon (;). |
Now here is the catch: we have to be very carefull in handling special characters like quote (") and backslash (\) in strings.
Let’s do a simple experiment:
rascal>import IO;
ok
rascal>str greeting = "\"Good Morning, Dr. Watson\", said Holmes";
str: "\"Good Morning, Dr. Watson\", said Holmes"
rascal>println("\"" + greeting + "\"");
""Good Morning, Dr. Watson", said Holmes"
okAs you see the quotes inside the string are not escaped and the result is not a legal string. So what can we do? We escape all dangerous characters in the string before printing it using the [Rascal:escape] function. It takes a string and a map of characters to be escaped and returns a result in which all escaping has been carried out. Be aware that in the map, also escaping is needed! We want to say: escape " and replace it by \", but since both " and \ have to be escaped themselves we have to say: escape "\"" and replace it by "\\\"". The effect is as follows:
rascal>import String;
ok
rascal>println("\"" + escape(greeting, ("\"": "\\\"")) + "\"");
"\"Good Morning, Dr. Watson\", said Holmes"
okAnd indeed, the two quotes are now properly escaped.
This is exactly what happens at 
in the definition of quine:
println("\"" + escape(program, ("\"" : "\\\"", "\\" : "\\\\")) + "\";");We escape program and replace " by \", and \ by \\. The mesmerizing amount of \ characters can be explained due to escaping " and \.
Now let’s put quine to the test.
rascal>import demo::basic::Quine;
ok
rascal>quine();
module demo::basic::Quine
import IO;
import String;
void quine(){
println(program);
println("\"" + escape(program, ("\"" : "\\\"", "\\" : "\\\\")) + "\";");
}
str program =
"module demo::basic::Quine
import IO;
import String;
void quine(){
println(program);
println(\"\\\"\" + escape(program, (\"\\\"\" : \"\\\\\\\"\", \"\\\\\" : \"\\\\\\\\\")) + \"\\\";\");
}
str program =";
okIf you follow this output line-by-line you will see that it is identical to the original source code of module Quine.
2. Common
Solutions for some common tasks.
We discuss the following tasks:
-
Ad Hoc Data Exploration: Using Rascal to explore an interesting data space.
-
Call Analysis: Analyzing the call structure of an application.
-
Call Lifting: Lift procedure calls to component calls.
-
Colored Trees: Computations on binary trees.
-
Count Constructors: Generic function that can count constructors in a value of any algebraic data type.
-
Derivative: Symbolic differentiation.
-
String Template: Using string templates to generate code.
-
Word Count: Counting words in strings.
-
CountInLine1: Count words in a line.
-
CountInLine2: Count words in a line.
-
CountInLine3: Count words in a line.
-
Jabberwocky: Lewis Carroll’s well-known poem.
-
-
Word Replacement: Replace words in a string.
2.1. Ad Hoc Data Exploration
Using Rascal to explore an interesting data space.
The problem we will look at comes from mathematics, and has a precise analytical solution, but let’s use Rascal to explore the state space, and see how it can help us to build intuition.
As you know, Rascal supports arbitrarily large numbers cleanly and simply, unlike more traditional languages like C or Java. For example, if you want to compute 1000!, then it’s a simple matter of calling fact(1000) at the command line. Let’s use this definition of factorial:
public int fact (int n) {
if (n <= 1) {
return 1;
} else {
return n * fact (n-1);
}
}If you compute fact(1000) at the Rascal command line, you get a large number, on the order of 4.02 x 102567. This is much, much bigger than, say a google, which is a mere 10<>100. (If Rascal runs out stack space, try computing 100!, then 200!, then … then 1000!; the run-time will allocate more stack space incrementally and automatically if you sneak up to where you want to go).
rascal> fact(1000);
int: 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000Now copy the numerical result above and paste it into an edit window to have a good look at it. Notice anything interesting? The last 249 digits are all zeros. How did this happen and what does it mean?
To be honest, when I did this calculation for the first time, I thought I’d found a bug. So I looked at the values of N! for N in the range 900 to 1000 and discovered that the zeros accumulate on the end of N! as N gets bigger. Let’s think about it for a bit: N! is a cumulative product, so once a zero has appeared on the end there is no way to get rid of it by multiplying by a positive integer.
How do the zeros appear? Well, this isn’t to hard to figure out. Obviously, each time you reach a multiple of 10, you will add (at least) one more zero to the cumulative product. But what about multiples of 5? Well, you would add one more zero if you can match the 5 to a 2 within the factors, and there are lots of lonely 2s in that list. So, to summarize, each time N is a multiple of 5, you add at least one zero onto the cumulative product N!.
So here’s the question we’re going to solve: For an arbitrary N, can you predict exactly how many trailing zeros there will be in N!?
Again, this can be solved analytically (and if you go looking on the web, you will discover that this is an old chestnut of a math problem that’s sometimes used in job interviews to test analytical ability), but what I want to do here is to show how we can use Rascal to play around with the problem space a bit to help us build up our intuition. This is very much like what we do in empirical software engineering, when we have lots of data to analyze, and we’re trying to look for patterns that might explain behaviours, such as why some functions are more likely to be associated with bugs than others. In that kind of situation, we typically go through two stages: first, we wade through the data, exploring relationships, looking for unusual lumps or recognizable patters; second, we build theories of how the world works, and test them out using the data. In both stages, we not only look at the data, we play with it. We build little tools to help answer our questions, see where our hunches lead us. We use this "play" to improve our understanding of the problem space, and build intuition about how it works as testable theories. In empirical software engineering, as in most other sciences, we usually don’t get concrete proof of a theory; rather, we gather evidence towards ultimately accepting or rejecting the theories (tho often, we may choose to use this evidence to refine the theories and try again).
In this case, however, there is a precise analytical solution, a proof, a "ground truth". But that doesn’t mean that we can’t use the empirical approach to help build our intuition about the problem space, and ultimately devise a theory about how to calculate the number of trailing zeros in N!. Solving analytical problems is about having enough intuition to see possible solutions. And using this empirical approach is one way to build intuition.
So let’s define a few helper functions and see where that leads us:
public int countZeros (int n) {
if (n < 10) {
return 0;
} else if (n % 10 == 0) {
return 1 + countZeros (n / 10);
} else {
return countZeros (n / 10);
}
}
rascal> int i = fact(1000);
int: 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
rascal> countZeros(i);
int: 472This was my first try at the solution (really!), and there’s a problem: 1000! has exactly 249 trailing zeros, not 472.
What did I do wrong? Oh, right, trailing zeros, and the above function counts all of the zeros. Let’s try again:
public int countTrailingZeros (int n) {
if (n < 10) {
return 0;
} else if (n % 10 == 0) {
return 1 + countTrailingZeros (n / 10);
} else {
return 0 ;
}
}
rascal> countTrailingZeros(i);
int: 249OK, so we’re making progress. Let’s define another function to help us explore the data space:
public void printLastTwenty (int n){
for(int i <- [n-19..n+1]) {
println ("<i>! has <countTrailingZeros(fact(i))> trailing zeros.");
}
}
rascal>printLastTwenty(1000);
981! has 243 trailing zeros.
982! has 243 trailing zeros.
983! has 243 trailing zeros.
984! has 243 trailing zeros.
985! has 244 trailing zeros.
986! has 244 trailing zeros.
987! has 244 trailing zeros.
988! has 244 trailing zeros.
989! has 244 trailing zeros.
990! has 245 trailing zeros.
991! has 245 trailing zeros.
992! has 245 trailing zeros.
993! has 245 trailing zeros.
994! has 245 trailing zeros.
995! has 246 trailing zeros.
996! has 246 trailing zeros.
997! has 246 trailing zeros.
998! has 246 trailing zeros.
999! has 246 trailing zeros.
1000! has 249 trailing zeros.
okSo the pattern I see arising (confirmed by more playing that I won’t show you) is that you add a zero every time N is divisible by 5. But sometimes you add more than one zero: 1000! adds three zeros.
We defined one function above to help us look at the data more compactly; now let’s create another function to look for lumps in the data:
// Printout all i in [0..n] where i! has more trailing zeros than (i-1)!
public void findLumps (int n) {
int iMinusOneFactZeros = 0;
for (int i <- [1..n+1]) {
int iFactZeros = countTrailingZeros(fact(i));
int diff = iFactZeros - iMinusOneFactZeros ;
if (diff >= 1) {
println ("<diff> more zeros at <i>!");
}
iMinusOneFactZeros = iFactZeros;
}
}
rascal>findLumps(1000);
1 more zeros at 5!
1 more zeros at 10!
1 more zeros at 15!
1 more zeros at 20!
2 more zeros at 25!
1 more zeros at 30!
1 more zeros at 35!
1 more zeros at 40!
1 more zeros at 45!
2 more zeros at 50!
1 more zeros at 55!
1 more zeros at 60!
1 more zeros at 65!
1 more zeros at 70!
2 more zeros at 75!
1 more zeros at 80!
1 more zeros at 85!
1 more zeros at 90!
1 more zeros at 95!
2 more zeros at 100!
1 more zeros at 105!
1 more zeros at 110!
1 more zeros at 115!
1 more zeros at 120!
3 more zeros at 125!
1 more zeros at 130!
...
1 more zeros at 245!
3 more zeros at 250!
1 more zeros at 255!
1 more zeros at 495!
3 more zeros at 500!
1 more zeros at 505!
...
1 more zeros at 620!
4 more zeros at 625!
1 more zeros at 630!
...
1 more zeros at 985!
1 more zeros at 990!
1 more zeros at 995!
3 more zeros at 1000!
okSo probably we’re noticing some patterns here already, and maybe forming some intuition. But let’s first revise our lump-finding function to produce even more concise output:
// We can parameterize the threshold to look for jumps of 2, 3, or 4 zeros
public void findLumps2 (int n, int tao) {
int iMinusOneFactZeros = 0;
for (int i <- [1..n+1]) {
int iFactZeros = countTrailingZeros(fact(i));
int diff = iFactZeros - iMinusOneFactZeros ;
if (diff >= tao) {
println ("<diff> more zeros at <i>!");
}
iMinusOneFactZeros = iFactZeros;
}
}
rascal>findLumps2(1000,2);
2 more zeros at 25!
2 more zeros at 50!
2 more zeros at 75!
2 more zeros at 100!
3 more zeros at 125!
2 more zeros at 150!
2 more zeros at 175!
2 more zeros at 200!
2 more zeros at 225!
3 more zeros at 250!
2 more zeros at 275!
...
2 more zeros at 950!
2 more zeros at 975!
3 more zeros at 1000!
ok
rascal>findLumps2(1000,3);
3 more zeros at 125!
3 more zeros at 250!
3 more zeros at 375!
3 more zeros at 500!
4 more zeros at 625!
3 more zeros at 750!
3 more zeros at 875!
3 more zeros at 1000!
ok
rascal>findLumps2(1000,4);
4 more zeros at 625!
okNotice anything yet? Here are some fun math facts to consider:
-
50 = 1
-
51 = 5
-
5 2 = 25
-
53 = 125
-
54 = 625
-
55 = 3125
So here’s the solution:
Let N be a positive integer.
Let k = floor (log5 N)
Start a counter at zero, call it nz
We want to examine i ← [1..N+1]
-
If i is not divisible by 5, ignore it
-
If i is divisible by 5, add 1 to nz
-
If i is also divisible by 25, add 1 more
-
…
-
If i is also divisible by 2k, add 1 more
We can write this in Rascal as:
public int predictZeros (int N) {
int k = floorLogBase(N, 5); // I wrote this
int nz = 0;
for (int i <- [1..N+1] ){
int p5 = 1;
for (int j <- [1..k+1]) {
p5 *= 5;
if (i % p5 == 0) {
nz += 1;
} else {
break;
}
}
}
return nz;
}Now a little hand validation might convince you that this should work, but let’s write a little verifier function to be sure:
public void verifyTheory (int N) {
int checkInterval = 100; // for printing
bool failed = false;
for (int i <- [1..N+1]) {
ifact=fact(i);
int p = predictZeros(i);
int c = countTrailingZeros(ifact);
if (p != c) {
failed = true;
println ("Found a counter example at i=<i>");
break;
} else {
if (i % checkInterval == 0) {
println ("<i>! has <p> trailing zeros");
}
}
}
if (!failed) {
println ("The theory works for i: 1..<N>");
}
}
rascal>verifyTheory(10);
The theory works for i: 1..10
ok
rascal>verifyTheory(100);
100! has 24 trailing zeros
The theory works for i: 1..100
ok
rascal>verifyTheory(1000);
100! has 24 trailing zeros
200! has 49 trailing zeros
300! has 74 trailing zeros
400! has 99 trailing zeros
500! has 124 trailing zeros
600! has 148 trailing zeros
Found a counter example at i=625
predicted zeros = 155
observed zeros = 156
okYikes, what do we do? Well, first let’s look under the hood at the engine. The function predictZeros is actually correct, assuming that the functions is calls are correct. So let’s look at the auxiliary functions I wrote (but haven’t shown you yet):
// Log for an arbitrary base
public real logB(real a, real base) {
return log(a) / log(base);
}
public real floor (real a) {
return toReal(round (a - 0.5));
}
public int floorLogBase (int a, int b) {
return toInt(floor(logB(toReal(a), toReal(b))));
}
rascal>floorLogBase(625,5);
int: 3
rascal>logB(625.0,5.0);
real: 3.9999999999999998757330130880776320985295476764801684...Oh right, real numbers are prone to round off error. What should we do?
Well, here’s a bad solution (that "works"):
public real floor (real a) {
return toReal(round (a - 0.5 + 0.00001));
}But how can I be sure that that’s enought decimal places? What if someone likes my floor function and sticks it into the Rascal library, where it is subsequently used by the Eurpoean Space Agency for its next generation of flight control software?
Sometimes, the answer is to do a lot of homework. Lucky for us, here there is a fairly efficient exact solution using repeated integer division:
// Also change predictZeros to call this version
public int floorLogBase2 (int a, int b) {
int remaining = a;
int ans = 0;
while (remaining >= b) {
ans += 1;
remaining /= b;
}
return ans;
}
rascal>verifyTheory(1000);
100! has 24 trailing zeros
200! has 49 trailing zeros
300! has 74 trailing zeros
400! has 99 trailing zeros
500! has 124 trailing zeros
600! has 148 trailing zeros
700! has 174 trailing zeros
800! has 199 trailing zeros
900! has 224 trailing zeros
1000! has 249 trailing zeros
The theory works for i: 1..1000
okAnd we’re done. But what did we learn here? Here’s what I think:
-
Explore the terrain, take notes, build intuition, develop theories, test them.
-
Refine and repeat
-
Double check!
-
-
Build infrastructure with natural "break points"
-
Understandable is better than fast, esp. in the beginning
-
The correct way is better than the easy way
-
The correct way may be pretty easy too
-
-
-
Document and later challenge your assumptions
-
Are you measuring what you think you are measuring? How do you know?
-
2.2. Call Analysis
Analyzing the call structure of an application.
Suppose a mystery box ends up on your desk. When you open it, it contains a huge software system with several questions attached to it:
-
How many procedure calls occur in this system?
-
How many procedures does it contains?
-
What are the entry points for this system, i.e., procedures that call others but are not called themselves?
-
What are the leaves of this application, i.e., procedures that are called but do not make any calls themselves?
-
Which procedures call each other indirectly?
-
Which procedures are called directly or indirectly from each entry point?
-
Which procedures are called from all entry points?
Let’s see how these questions can be answered using Rascal.
Consider the following call graph (a box represents a procedure and an arrow represents a call from one procedure to another procedure):
rascal>import Set;
ok
rascal>import Relation;
ok
rascal>import analysis::graphs::Graph;
okRascal supports basic data types like integers and strings which are sufficient to formulate and answer the questions at hand. However, we can gain readability by introducing separately named types for the items we are describing. First, we introduce therefore a new type Proc (an alias for strings) to denote procedures:
rascal>alias Proc = str;
okNext, we have to represent the call relation as a Rascal datatype, and the relation is the most appropriate for it. As preparation, we also import the libraries [$Rascal:Prelude/Set], [$Rascal:Prelude/Relation] and [$Rascal:Libraries/analysis/graphs/Graph] that will come in handy.
rascal>rel[Proc, Proc] Calls = {<"a", "b">, <"b", "c">, <"b", "d">, <"d", "c">,
>>>>>>> <"d", "e">, <"f", "e">, <"f", "g">, <"g", "e">};
rel[str,str]: {
<"a","b">,
<"g","e">,
<"b","c">,
<"b","d">,
<"d","c">,
<"d","e">,
<"f","e">,
<"f","g">
}Now we are in a good position to start asking some questions.
How many calls occur in this system?
We use the function [Rascal:Set/size] to determine the number of elements in a set or relation. Since each tuple in the Calls relation represents a call between procedures, the number of tuples is equal to the number of calls.
rascal>size(Calls);
int: 8How many procedures occur in this system? This question is more subtle, since a procedure may call (or be called) by several others and the number of tuples is therefore not indicative. What we need are the set of procedures that occur (as first or second element) in any tuple. This is precisely what the function [$Rascal:Libraries/Prelude/Relation/carrier] gives us:
rascal>carrier(Calls);
set[str]: {"a","b","c","d","e","f","g"}and computing the number of procedures is now easy:
rascal>size(carrier(Calls));
int: 7As an aside, functions [$Rascal:Prelude/Relation/domain] and [$Rascal:Prelude/Relation/range] do the same for the first, respectively, second element of the pairs in a relation:
rascal>domain(Calls);
set[str]: {"a","b","d","f","g"}
rascal>range(Calls);
set[str]: {"b","c","d","e","g"}What are the entry points for this system?
The next step in the analysis is to determine which entry points this application has, i.e., procedures which call others but are not called themselves. Entry points are useful since they define the external interface of a system and may also be used as guidance to split a system in parts. The top of a relation contains those left-hand sides of tuples in a relation that do not occur in any right-hand side. When a relation is viewed as a graph, its top corresponds to the root nodes of that graph. Similarly, the bottom of a relation corresponds to the leaf nodes of the graph. See the section called [$Rascal:Libraries/analysis/graphs/Graph] for more details. Using this knowledge, the entry points can be computed by determining the top of the Calls relation:
rascal>top(Calls);
set[str]: {"a","f"}What are the leaves of this application?
In a similar spirit, we can determine the leaves of this application, i.e., procedures that are being called but do not make any calls themselves:
rascal>bottom(Calls);
set[str]: {"c","e"}Which procedures call each other indirectly?
We can also determine the indirect calls between procedures, by taking the transitive closure of the Calls relation, written as Calls+. Observe that the transitive closure will contain both the direct and the indirect calls.
rascal>closureCalls = Calls+;
rel[str,str]: {
<"g","e">,
<"a","b">,
<"a","c">,
<"a","d">,
<"a","e">,
<"b","c">,
<"b","d">,
<"b","e">,
<"d","c">,
<"d","e">,
<"f","e">,
<"f","g">
}Which procedures are called directly or indirectly from each entry point?
We now know the entry points for this application ("a" and "f") and the indirect call relations. Combining this information, we can determine which procedures are called from each entry point. This is done by indexing closureCalls with appropriate procedure name. The index operator yields all right-hand sides of tuples that have a given value as left-hand side. This gives the following:
rascal>calledFromA = closureCalls["a"];
set[str]: {"b","c","d","e"}
rascal>calledFromF = closureCalls["f"];
set[str]: {"e","g"}Which procedures are called from all entry points?
Finally, we can determine which procedures are called from both entry points by taking the intersection of the two sets
calledFromA and calledFromF:
rascal>calledFromA & calledFromF;
set[str]: {"e"}or if your prefer to write all of the above as a one-liner using a [$Rascal:Expressions/Reducer] expression:
rascal>(carrier(Calls) | it & (Calls+)[p] | p <- top(Calls));
set[str]: {"e"}The reducer is initialized with all procedures (carrier(Calls)) and iterates over all entry points (p ← top(Calls)). At each iteration the current value of the reducer (it) is intersected (&) with the procedures called directly or indirectly from that entry point ((Calls+)[p]).
-
In small examples, the above results can be easily obtained by a visual inspection of the call graph. Such a visual inspection does not scale very well to large graphs and this makes the above form of analysis particularly suited for studying large systems.
-
We discuss call analysis in a, intentionally, simplistic fashion that does not take into account how the call relation is extracted from actual source code. The above principles are, however, applicable to real cases as well.
2.3. Call Lifting
Lift procedure calls to component calls.
A frequently occurring problem is that we know the call relation of a system but that we want to understand it at the component level rather than at the procedure level. If it is known to which component each procedure belongs, it is possible to lift the call relation to the component level. Actual lifting amounts to translating each call between procedures by a call between components.
Consider the following figure:
(a) Shows the calls between procedures; (b) shows how procedures are part of a system component. (c) shows how the call relation given in (a) can be lifted to the component level.
The situation can be characterized by:
-
A call relation between procedures
-
A partOf relation between procedures and components
The problem is now to lift the call relation using the information in the partOf relation. In other words: a call between two procedures will be lifted to a call between the components to which each procedure belongs.
Here is a solution:
module demo::common::Lift
alias proc = str;
alias comp = str;
rel[comp,comp] lift(rel[proc,proc] aCalls, rel[proc,comp] aPartOf){
return { <C1, C2> | <proc P1, proc P2> <- aCalls,
<comp C1, comp C2> <- aPartOf[P1] * aPartOf[P2] };
}
// Test set-up
rel[proc,proc] Calls = {<"main", "a">, <"main", "b">, <"a", "b">, <"a", "c">, <"a", "d">,
<"b", "d">};
rel[proc, comp] PartOf = {<"main", "Appl">, <"a", "Appl">, <"b", "DB">,
<"c", "Lib">, <"d", "Lib">};
rel[comp,comp] ComponentCalls = lift(Calls, PartOf);And we can use it as follows:
rascal>import demo::common::Lift;
okEncode the call relation and partOf relation:
rascal>calls = {<"main", "a">, <"main", "b">, <"a", "b">, <"a", "c">, <"a", "d">, <"b", "d">};
rel[str,str]: {
<"b","d">,
<"a","b">,
<"a","c">,
<"a","d">,
<"main","a">,
<"main","b">
}
rascal>partOf = {<"main", "Appl">, <"a", "Appl">, <"b", "DB">, <"c", "Lib">, <"d", "Lib">};
rel[str,str]: {
<"a","Appl">,
<"b","DB">,
<"c","Lib">,
<"d","Lib">,
<"main","Appl">
}and do the lifting:
rascal>lift(calls, partOf);
rel[str,str]: {
<"DB","Lib">,
<"Appl","Lib">,
<"Appl","Appl">,
<"Appl","DB">
}Please verify that this corresponds exactly to (c) in the figure above.
2.4. Colored Trees
Computations on binary trees.
We consider binary trees---trees with exactly two children---that have integers as their leaves. Our trees can have red and black nodes and we want to perform the following operations on them:
-
Count the number of red nodes.
-
Compute the sum of all the integers that occur in the leaves.
-
Extend the tree data type with green nodes.
-
Replace all red nodes by green ones.
The definition of ColoredTrees is as follows:
module demo::common::ColoredTrees
// Define ColoredTrees with red and black nodes and integer leaves
data ColoredTree = leaf(int N) (1)
| red(ColoredTree left, ColoredTree right)
| black(ColoredTree left, ColoredTree right);
public ColoredTree rb = red(black(leaf(1), red(leaf(2),leaf(3))), black(leaf(3), leaf(4)));
// Count the number of red nodes
int cntRed(ColoredTree t) {
int c = 0;
visit(t) {
case red(_,_): c = c + 1; (2)
};
return c;
}
test bool tstCntRed() = cntRed(rb) == 2;
// Compute the sum of all integer leaves
int addLeaves(ColoredTree t) {
int c = 0;
visit(t) {
case leaf(int N): c = c + N; (3)
};
return c;
}
test bool tstAddLeaves() = addLeaves(rb) == 13;
// Add green nodes to ColoredTree
data ColoredTree = green(ColoredTree left, ColoredTree right); (4)
// Transform red nodes into green nodes
ColoredTree makeGreen(ColoredTree t) {
return visit(t) {
case red(l, r) => green(l, r) (5)
};
}| 1 | We define the data type of ColoredTrees with constructors leaf, red and black. |
| 2 | cntRed counts all red nodes by visiting all nodes and incrementing the counter c for each red one. |
| 3 | addLeaves visits all nodes and adds the integers in each leaf node. |
| 4 | coloredTrees are extended with a new constructor green. |
| 5 | makeGreen visits all nodes and turns red nodes in green ones. |
We can now explore ColoredTrees:
rascal>import demo::common::ColoredTrees;
ok
rascal>rb = red(black(leaf(1), red(leaf(2),leaf(3))), black(leaf(3), leaf(4)));
ColoredTree: red(
black(
leaf(1),
red(
leaf(2),
leaf(3))),
black(
leaf(3),
leaf(4)))Count the red nodes in rb:
rascal>cntRed(rb);
int: 2and compute the sum of all leaves:
rascal>addLeaves(rb);
int: 13Finally, we convert all red nodes:
rascal>makeGreen(rb);
ColoredTree: green(
black(
leaf(1),
green(
leaf(2),
leaf(3))),
black(
leaf(3),
leaf(4)))This example illustrates the fully automatic visiting of the elements of a structured data type. Compare this with the traditional programming style in which a switch statement is used to determine the constructor and recursion is used to visit substructures. This style becomes particularly cumbersome for data types with large numbers of constructors such as, for instance, abstract syntax trees for real programming languages.
The visit statement is based on a new paradigm one has to learn.
2.5. Count Constructors
Generic function that can count constructors in a value of any algebraic data type.
In [ColoredTrees], we have seen a function that can count the number of red nodes in a ColoredTree. Is it possible to define a function that can count constructors in a value of any algerbaic data type?
We exploit the subtype relation (see Static Typing) between algebraic data typess and the type node to achieve this.
In real applications this becomes relevant when counting, for instance, statement types in programs.
module demo::common::CountConstructors
import Node;
import Map;
// Define a ColoredTree data type
data ColoredTree = leaf(int N)
| red(ColoredTree left, ColoredTree right)
| black(ColoredTree left, ColoredTree right);
public ColoredTree CT = red(black(leaf(1), red(leaf(2),leaf(3))), black(leaf(3), leaf(4)));
// Define a Card data type.
data Suite = hearts() | diamonds() | clubs() | spades();
data Card = two(Suite s) | three(Suite s) | four(Suite s) | five(Suite s) |
six(Suite s) | seven(Suite s) | eight(Suite s) | nine(Suite s) | ten(Suite s) |
jack(Suite s) | queen(Suite s) | king(Suite s) | ace(Suite s);
data Hand = hand(list[Card] cards);
public Hand H = hand([two(hearts()), jack(diamonds()), six(hearts()), ace(spades())]);
// Count frequencies of constructors
map[str,int] count(node N){ (1)
freq = (); (2)
visit(N){ (3)
case node M: { name = getName(M); (4)
freq[name] ? 0 += 1;
}
}
return freq; (5)
}
map[str,int] countRelevant(node N, set[str] relevant) = domainR(count(N), relevant); (6)Two data types are introduced ColoredTree and Hand together with an example value of each (CT, respectively, H).
| 1 | The function count is defined. |
| 2 | Introduces an empty map to maintain the frequencies. |
| 3 | Defines a visit of argument N; it traverses the complete value of N. |
| 4 | Defines the case that we encounter a node and we update its frequency count. First the name of the constructor is retrieved (using getName) and then the frequency is updated. The isDefined operator is used to provide a default value of 0 when the name was not yet in the map. |
| 5 | The map freq is returned as result. |
| 6 | Defines a variant countRelevant; it gets is an extra argument of relevant constructors names that is used to filter the map that is returned by count using domainR. |
rascal>import demo::common::CountConstructors;
ok
rascal>count(CT);
map[str, int]: ("red":2,"leaf":5,"black":2)
rascal>count(H);
map[str, int]: ("six":1,"ace":1,"two":1,"hearts":2,"spades":1,"hand":1,"diamonds":1,"jack":1)
rascal>countRelevant(H, {"hearts", "spades"});
map[str, int]: ("hearts":2,"spades":1)2.6. Derivative
Symbolic differentiation.
Computing the derivative of an expression with respect to some variable is a classical calculus problem. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object’s instantaneous velocity.
We present here rules for determining the derivative dE/dX of simple expressions E for a given variable X. Recall that for number N, variables X and Y, and expressions E1 and E2 the following rules apply:
-
dN / dX = 0. -
dX / dX = 1. -
dX / dY = 0, whenX != Y. -
d(E1 + E2) /dX = dE1 / dX + d E2 /dX. -
d(E1 * E2) / dX = (d E1 / dX * E2) + (E1 * d E2 /dX).
Here is our solution followed by a list of explanations:
module demo::common::Derivative
data Exp = con(int n) (1)
| var(str name)
| mul(Exp e1, Exp e2)
| add(Exp e1, Exp e2)
;
public Exp E = add(mul(con(3), var("y")), mul(con(5), var("x"))); (2)
Exp dd(con(n), var(V)) = con(0); (3)
Exp dd(var(V1), var(V2)) = con((V1 == V2) ? 1 : 0);
Exp dd(add(Exp e1, Exp e2), var(V)) = add(dd(e1, var(V)), dd(e2, var(V)));
Exp dd(mul(Exp e1, Exp e2), var(V)) = add(mul(dd(e1, var(V)), e2), mul(e1, dd(e2, var(V))));
Exp simp(add(con(n), con(m))) = con(n + m); (4)
Exp simp(mul(con(n), con(m))) = con(n * m);
Exp simp(mul(con(1), Exp e)) = e;
Exp simp(mul(Exp e, con(1))) = e;
Exp simp(mul(con(0), Exp e)) = con(0);
Exp simp(mul(Exp e, con(0))) = con(0);
Exp simp(add(con(0), Exp e)) = e;
Exp simp(add(Exp e, con(0))) = e;
default Exp simp(Exp e) = e; (5)
Exp simplify(Exp e){ (6)
return bottom-up visit(e){
case Exp e1 => simp(e1)
}
}| 1 | Define a data type Exp to represent expressions. |
| 2 | Introduce an example expression E for later use. |
| 3 | Define the actual differentiation function dd. Observe that this definition depends on the use of patterns in function declarations, see [Rascal:Function]. |
| 4 | Define simplification rules. |
| 5 | A default rule is give for the case that no simplification applies. |
| 6 | Define the actual simplication function simplify that performs a bottom up traversal of the expression, application simplification rules on the the up. |
Let’s differentiate the example expression E:
rascal>import demo::common::Derivative;
ok
rascal>dd(E, var("x"));
Exp: add(
add(
mul(
con(0),
var("y")),
mul(
con(3),
con(0))),
add(
mul(
con(0),
var("x")),
mul(
con(5),
con(1))))As you can see, we managed to compute a derivative, but the result is far more complex than we would like. This is where simplification comes in. First try a simple case:
rascal>simplify(mul(var("x"), add(con(3), con(5))));
Exp: mul(
var("x"),
con(8))Now apply simplification to the result of differentiation:
rascal>simplify(dd(E, var("x")));
Exp: con(5)2.7. String Template
Using string templates to generate code.
Many websites and code generators use template-based code generation. They start from a text template that contains embedded variables and code. The template is "executed" by replacing the embedded variables and code by their string value. Languages like PHP and Ruby are popular for this feature. Let’s see how we can do this in Rascal.
Rascal provides string templates that rival what is provided in Ruby, PHP or ANTLR. They are fully described in string values.
The problem we want to solve is as follows: given a number of fields (with a name and a type) how can we generate a Java class with getters and setters for those fields?
Here is a solution:
module demo::common::StringTemplate
import String;
import List;
// Capitalize the first character of a string
str capitalize(str s) { (1)
return toUpperCase(substring(s, 0, 1)) + substring(s, 1);
}
// Helper function to generate a setter
private str genSetter(map[str,str] fields, str x) {
return "public void set<capitalize(x)>(<fields[x]> <x>) {
' this.<x> = <x>;
'}";
}
// Helper function to generate a getter
private str genGetter(map[str,str] fields, str x) {
return "public <fields[x]> get<capitalize(x)>() {
' return <x>;
'}";
}
// Generate a class with given name and fields.
// The field names are processed in sorted order.
str genClass(str name, map[str,str] fields) { (2)
return
"public class <name> {
' <for (x <- sort([f | f <- fields])) {>
' private <fields[x]> <x>;
' <genSetter(fields, x)>
' <genGetter(fields, x)><}>
'}";
}
map[str, str] fields = (
"name" : "String",
"age" : "Integer",
"address" : "String"
);
str cperson =
// Do not change a single space in the string below!
"public class Person {
'
' private String address;
' public void setAddress(String address) {
' this.address = address;
' }
' public String getAddress() {
' return address;
' }
' private Integer age;
' public void setAge(Integer age) {
' this.age = age;
' }
' public Integer getAge() {
' return age;
' }
' private String name;
' public void setName(String name) {
' this.name = name;
' }
' public String getName() {
' return name;
' }
'}";| 1 | An auxiliary function capitalize is defined to capitalize the first character of a string. |
| 2 | Here is the heavy lifting done: genClass is defined that takes as arguments:
|
Function genClass returns a string that contains several string interpolations delimited by < and >. Let’s discuss some of them:
-
In each line, only the text following
'is contributed to the output. The text before (and including)'can be used to properly indent the string. -
The output of each interpolated call, like to
genMethodis auto-indented. -
public class <name>: insert the desired class name in the result. -
<for x←fields){>…<}>: loops over the fields and contributes the text produced by its body to the result. -
private <fields[x]> <x>;: finds for the current fieldxits type and produces an appropriate private field declaration. -
public void set<capitalize(x)>(<fields[x]> <x>): method header for the setter for fieldx.
Let’s see how this works out on actual data:
rascal>import demo::common::StringTemplate;
ok
rascal>import IO;
ok
rascal>fields = (
>>>>>>> "name" : "String",
>>>>>>> "age" : "Integer",
>>>>>>> "address" : "String"
>>>>>>> );
map[str, str]: ("name":"String","address":"String","age":"Integer")
rascal>println(genClass("Person", fields));
public class Person {
private String address;
public void setAddress(String address) {
this.address = address;
}
public String getAddress() {
return address;
}
private Integer age;
public void setAge(Integer age) {
this.age = age;
}
public Integer getAge() {
return age;
}
private String name;
public void setName(String name) {
this.name = name;
}
public String getName() {
return name;
}
}
ok-
String templates are ideal to generate arbitrary output. In particular, no grammar is needed to describe this output.
-
Auto-indent helps to be able to compose templates from reusable parts.
-
Since no grammar is used to control output, errors in generated code can only be detected by a downstream processor such as a compiler for the generated code.
-
In more complex cases, it can be better to introduce an abstract datatype to represent the desired code and to use string templates to produce the actual textual representation of that code.
2.8. Word Count
Counting words in strings.
The purpose of WordCount is to count the number of words in a list of lines (strings). A word is here defined as one or more letters (lowercase or uppercase), digits and the underscore character (_).
We split the problem in two parts:
-
Count the words in a single line. We explore three ways to do this in an imperative (CountInLine1], CountInLine2) and a functional style (CountInLine3).
-
Next we apply the single line counter to all the lines.
wordCount is a function with two arguments: * A list of lines. * A function that returns the number of words in a line.
The main task of wordCount is to loop over all lines and to add the word counts per line.
module demo::common::WordCount::WordCount
import demo::common::WordCount::CountInLine1;
import demo::common::WordCount::CountInLine2;
import demo::common::WordCount::CountInLine3;
import demo::common::WordCount::Jabberwocky;
import String;
// wordCount takes a list of strings and a count function
// that is applied to each line. The total number of words is returned
int wordCount(list[str] input, int (str s) countInLine)
{
count = 0;
for(str line <- input){ (1)
count += countInLine(line); (2)
}
return count;
}| 1 | An enumerator is used to generated all the lines in the list of lines. |
| 2 | The argument function countInLine is applied to count the number of words in each line. |
Let’s now do some experiments using the Jabberwocky poem by Lewis Carrol as input.
rascal>import demo::common::WordCount::WordCount;
ok
rascal>import demo::common::WordCount::CountInLine1;
ok
rascal>import demo::common::WordCount::CountInLine2;
ok
rascal>import demo::common::WordCount::CountInLine3;
ok
rascal>import demo::common::WordCount::Jabberwocky;
ok
rascal>wordCount(Jabberwocky, countInLine1);
int: 216
rascal>wordCount(Jabberwocky, countInLine2);
int: 216
rascal>wordCount(Jabberwocky, countInLine3);
int: 216It is satisfactory that the three ways of counting words all yield the same result.
If you are into one-liners, we can include everything you learned from this example in the following alternative wordCount2 function:
rascal>int wordCount2(list[str] lines) = (0 | it + (0 | it + 1 | /\w+/ := line) | str line <- lines);
int (list[str]): function(|prompt:///|(0,94,<1,0>,<1,94>))
rascal>wordCount2(Jabberwocky);
int: 216Explain what is going on in this function.
2.8.1. CountInLine1
Count words in a line.
We count words using a regular expression match in a for loop. Each time that the pattern /[a-zA-Z0-9_]+/ matches, the body of the loop is executed and count is incremented.
module demo::common::WordCount::CountInLine1
int countInLine1(str S){
int count = 0;
for(/[a-zA-Z0-9_]+/ := S){
count += 1;
}
return count;
}Let’s try it:
rascal>import demo::common::WordCount::CountInLine1;
ok
rascal>countInLine1("Jabberwocky by Lewis Carroll");
int: 42.8.2. CountInLine2
Count words in a line.
A slighly more involved manner of using regular matching in a loop.
module demo::common::WordCount::CountInLine2
int countInLine2(str S){
int count = 0;
// \w matches any word character
// \W matches any non-word character
// <...> are groups and should appear at the top level.
while (/^\W*\w+<rest:.*$>/ := S) {
count += 1;
S = rest;
}
return count;
}The pattern /^\W*<word:\w+><rest:.*$>/ can be understood as follows:
-
The
^makes it anchored, only matches at the begin of the substringS. -
\W*matches zero or more non-word characters. -
<word:\w+>matches one or more word characters and assigns the result to the variableword. -
<rest:.*$>matches the remaining part ofS.
Inside the loop count is incremented and the new value of S becomes the remainder of the current match. To summarize: each iteration removes the first word from S and counts it.
Here is countInLine2 in action:
rascal>import demo::common::WordCount::CountInLine2;
ok
rascal>countInLine2("Jabberwocky by Lewis Carroll");
int: 42.8.3. CountInLine3
Count words in a line.
Here is a clever, albeit rather dense, solution that illustrates several Rascal concepts.
module demo::common::WordCount::CountInLine3
int countInLine3(str S){
return (0 | it + 1 | /\w+/ := S);
}We use a reducer that is a recipe to reduce the values produced by one or more generators to a single value:
-
0is the initial value of the reducer -
The pattern match
/\w+/ := Smatches all words inS. -
Reduction is done by
it + 1. In the latteritis a keyword that refers to the value that has been reduced sofar. Effectively, the matches are reduced to a match count.
Let’s try it:
rascal>import demo::common::WordCount::CountInLine3;
ok
rascal>countInLine3("Jabberwocky by Lewis Carroll");
int: 42.8.4. Jabberwocky
Lewis Carroll’s well-known poem.
module demo::common::WordCount::Jabberwocky
public list[str] Jabberwocky = [
"Jabberwocky by Lewis Carroll",
"",
"\'Twas brillig, and the slithy toves",
"Did gyre and gimble in the wabe;",
"All mimsy were the borogoves,",
"And the mome raths outgrabe.",
"",
"\"Beware the Jabberwock, my son!",
"The jaws that bite, the claws that catch!",
"Beware the Jubjub bird, and shun",
"The frumious Bandersnatch!\"",
"",
"\'Twas brillig, and the slithy toves",
"Did gyre and gimble in the wabe;",
"All mimsy were the borogoves,",
"And the mome raths outgrabe.",
"",
"\"Beware the Jabberwock, my son!",
"The jaws that bite, the claws that catch!",
"Beware the Jubjub bird, and shun",
"The frumious Bandersnatch!\"",
"",
"He took his vorpal sword in hand:",
"Long time the manxome foe he sought.",
"So rested he by the Tumtum tree,",
"And stood awhile in thought.",
"",
"And as in uffish thought he stood,",
"The Jabberwock, with eyes of flame,",
"Came whiffling through the tulgey wood",
"And burbled as it came!",
"",
"One, two! One, two! and through and through",
"The vorpal blade went snicker-snack!",
"He left it dead, and with its head",
"He went galumphing back.",
"",
"\"And hast thou slain the Jabberwock?",
"Come to my arms, my beamish boy!",
"O frabjous day! Callooh! Callay!",
"He chortled in his joy.",
"",
"\'Twas brillig, and the slithy toves",
"Did gyre and gimble in the wabe;",
"All mimsy were the borogoves,",
"And the mome raths outgrabe."
];2.9. Word Replacement
Replace words in a string.
Suppose you are a book editor and want to ensure that all chapter and section titles are properly capitalized. Here is how to do this.
module demo::common::WordReplacement
import String;
// capitalize: convert first letter of a word to uppercase
str capitalize(str word) (1)
{
if(/^<letter:[a-z]><rest:.*$>/ := word){
return toUpperCase(letter) + rest;
} else {
return word;
}
}
test bool capitalize1() = capitalize("1") == "1";
test bool capitalize2() = capitalize("rascal") == "Rascal";
// Capitalize all words in a string
// Version 1: capAll1: using a while loop
str capAll1(str S) (2)
{
result = "";
while (/^<before:\W*><word:\w+><after:.*$>/ := S) {
result = result + before + capitalize(word);
S = after;
}
return result;
}
test bool tstCapAll1() = capAll1("turn this into a title") == "Turn This Into A Title";
// Version 2: capAll2: using visit
str capAll2(str S) (3)
{
return visit(S){
case /^<word:\w+>/i => capitalize(word)
};
}| 1 | We start by introducing a helper function capitalize that does the actual capitalization of a single word. See Regular Pattern for details about regular expression patterns. Next we give two versions of a capitalization functions for a sentence: |
| 2 | capAll1 uses a while loop to find subsequent words and to replace them by a capitalized version. |
| 3 | capAll2 uses a [Rascal:Visit] to visit all words in the sentence and replace them by a capitalized version. |
Here are some examples:
rascal>import demo::common::WordReplacement;
ok
rascal>capitalize("rascal");
str: "Rascal"
rascal>capAll1("turn this into a capitalized title")
str: "Turn This Into A Capitalized Title"
rascal>capAll2("turn this into a capitalized title")
str: "Turn This Into A Capitalized Title"3. Languages
Definitions of several languages and their tools.
Examples of several languages and the implementation of tools like interpreters and compilers:
-
Exp: The hello world of syntax definition and language definition.
-
Func: Func is a tiny functional language; we present several interpreters for it.
-
Abstract Syntax: The abstract syntax for Func.
-
Concrete Syntax: The concrete syntax of Func.
-
Eval0: A Func interpreter that does not support let-expressions and pointers.
-
Load AST: Parse Func program from string or file and convert to an abstract syntax tree.
-
Parse: Parse a Func program from a string or a file.
-
-
Lisra: A lisp interpreter in Rascal.
-
Pico: The classical toy language, including a specialized IDE.
-
Abstract: Abstract syntax for Pico.
-
Assembly: Assembly language for Pico.
-
Compile: Compile a Pico program to assembly language.
-
ControlFlow: Compute the control flow graph for a Pico program.
-
Evaluate: Evaluate a Pico program.
-
IDE: An Integrated Development Environment for Pico.
-
Load: Convert a Pico parse tree into a Pico abstract syntax tree.
-
Syntax: Concrete syntax for Pico.
-
Typecheck: Typechecker a Pico program.
-
Uninit: Find unitialized variables in a Pico program.
-
UseDef: Compute use-def information for the variables in a Pico program.
-
Visualize: Visualize Pico Control Flow Graphs.
-
Other languages that we are considering (but are not yet described):
-
Oberon0: a scaled down version of the Oberon language.
-
MissGrant: a state machine language.
3.1. Exp
The hello world of syntax definition and language definition. It illustrates how to define concrete and abstract syntax and how to use concrete and abstract patterns to evaluate expressions.
Our sample language Exp contains the following elements:
-
Integer constants, e.g.,
123. -
A multiplication operator, e.g.,
3*4. -
An addition operator, e.g.,
3+4. -
Multiplication is left-associative and has precedence over addition.
-
Addition is left-associative.
-
Parentheses can be used to override the precedence of the operators.
-
123 -
2+3+4 -
2+3*4 -
(2+3)*4
3.1.1. Abstract
A version of Exp based on abstract syntax.
The abstract syntax for a language is a data type that is used to represent programs in the language in an abstract form. Abstract syntax has the following properties:
-
It is "abstract" in the sense that it does not contain textual details such as parentheses, layout, and the like.
-
While a language has one grammar (also known as, concrete syntax) it may have several abstract syntaxes for different purposes: type analysis, code generation, etc.
The abstract syntax for Exp looks like this:
module demo::lang::Exp::Abstract::Syntax
data Exp = con(int n) (1)
| mul(Exp e1, Exp e2) (2)
| add(Exp e1, Exp e2) (3)
;| 1 | Defines integer constants, e.g., con(123). |
| 2 | Defines multiplication, e.g., mul(con(2),con(3)). |
| 3 | Defines addition, e.g., add(con(2),con(3)). |
Given the abstract syntax for Exp, we can define an interpreter that evaluates expressions:
module demo::lang::Exp::Abstract::Eval
import demo::lang::Exp::Abstract::Syntax;
int eval(con(int n)) = n; (1)
int eval(mul(Exp e1, Exp e2)) = eval(e1) * eval(e2); (2)
int eval(add(Exp e1, Exp e2)) = eval(e1) + eval(e2); (3)Here we see Rascal’s pattern-directed invocation in action (see Function Declaration). The essence is this: in other languages the formal parameters in a function declaration are just that: formal parameters, i.e., single names that can be used inside the function and that are bound when the function is called. In Rascal, however, the formal parameters are actually a pattern and functions can have arbitrarily complex patterns as (single) formal parameter. These patterns may bind variables and thus introduce variables that can be used in tthe function body.
The big advantage of pattern-directed invocation is modularity and extensibility:
-
The treatment of the cases in the abstract syntax is decoupled.
-
If the abstract is extended later on with new cases, the functions for the old cases can be reused.
In this example we use this mechanism to define separate functions for each case in the abstract syntax.
| 1 | Defines the case for evaluating integer constants: they evaluate to themselves. |
| 2 | Defines the case for evaluating multiplication: first evaluate the arguments e1 and e2
and return the multiplication of their values. |
| 3 | Defines the case for evaluating addition: first evaluate the arguments e1 and e2
and return the addition of their values. |
rascal>import demo::lang::Exp::Abstract::Syntax;
ok
rascal>import demo::lang::Exp::Abstract::Eval;
ok
rascal>eval(mul(con(7), con(3)));
int: 21
rascal>eval(add(con(3), mul(con(4), con(5))));
int: 23Entering expressions in abstract syntax form is no fun, and this is where concrete syntax comes to the rescue.
3.1.2. Combined
Combine concrete syntax with abstract syntax.
Concrete syntax gives full control over the textual appearance of a language and leads to parse trees in a standard format (i.e., values of type Tree).
Abstract syntax can be designed by the Rascal programmer according to his/her needs regarding the type checking, code generation, transformation, or optimization to be done on the abstract syntax trees.
How can we bridge this gap? We discuss two approaches:
Automatic
Use implode to translate an Exp parse tree to an abstract syntax tree.
implode is a function that automates the mapping between parse trees and abstract syntax trees. It takes two arguments:
-
The reified type of the desired abstract syntax. (In Rascal, types can not be used freely as values. A reified type, is a type that is wrapped in such a way that it can be passed as an argument to a function.)
-
The parse tree to be converted.
implode is smart in trying to find a mapping, but it needs some guidance. A necessary step is therefore to label the rules in the grammar with the name of the constructor to which it has to be mapped.
Let’s first label the syntax rules of the Exp grammar with constructor names:
module demo::lang::Exp::Combined::Automatic::Syntax
lexical LAYOUT = [\t-\n\r\ ];
layout LAYOUTLIST = LAYOUT* !>> [\t-\n\r\ ] ;
lexical IntegerLiteral = [0-9]+;
start syntax Exp =
con: IntegerLiteral (1)
| bracket "(" Exp ")"
> left mul: Exp "*" Exp (2)
> left add: Exp "+" Exp (3)
;Observe that at 
, 
and 
these labels have been added.
It is good practice to introduce separate modules for parsing and for the conversion itself:
-
A
Parsemodule defines a parse function and returns a parse tree. It imports only the concrete syntax. -
A
Loadmodule defines a load function that first calls the aboveparsefunction and then appliesimplodeto it. This is the only module that imports both concrete and abstract syntax at the same time and is therefore the only place to be concerned about name clashes. (If I mentionExp, do you know which one I mean?).
Here is the Parse module for Exp …
module demo::lang::Exp::Combined::Automatic::Parse
import demo::lang::Exp::Combined::Automatic::Syntax;
import ParseTree;
Tree parseExp(str txt) = parse(#Exp, txt);and this is how it works:
rascal>import demo::lang::Exp::Combined::Automatic::Parse;
ok
rascal>parseExp("2+3*4");
warning, ambiguity predicted: add: Exp "+" Exp lacks left or right associativity
warning, ambiguity predicted: mul: Exp "*" Exp lacks left or right associativity
Tree: appl(
prod(
label(
"add",
sort("Exp")),
[
sort("Exp"),
layouts("LAYOUTLIST"),
lit("+"),
layouts("LAYOUTLIST"),
sort("Exp")
],
{}),
[appl(
prod(
label(
"con",
sort("Exp")),
[lex("IntegerLiteral")],
{}),
[appl(
prod(
lex("IntegerLiteral"),
[iter(\char-class([range(48,57)]))],
{}),
[appl(
regular(iter(\char-class([range(48,57)]))),
[char(50)],
src=|unknown:///|(0,1,<1,0>,<1,1>))],
src=|unknown:///|(0,1,<1,0>,<1,1>))],
src=|unknown:///|(0,1,<1,0>,<1,1>)),appl(
prod(
layouts("LAYOUTLIST"),
[conditional(
\iter-star(lex("LAYOUT")),
{\not-follow(\char-class([
range(9,10),
range(13,13),
range(32,32)
]))})],
{}),
[appl(
regular(\iter-star(lex("LAYOUT"))),
[],
src=|unknown:///|(1,0,<1,1>,<1,1>))],
src=|unknown:///|(1,0,<1,1>,<1,1>)),appl(
prod(
lit("+"),
[\char-class([range(43,43)])],
{}),
[char(43)]),appl(
prod(
layouts("LAYOUTLIST"),
[conditional(
\iter-star(lex("LAYOUT")),
{\not-follow(\char-class([
range(9,10),
range(13,13),
range(32,32)
]))})],
{}),
[appl(
regular(\iter-star(lex("LAYOUT"))),
[],
src=|unknown:///|(2,0,<1,2>,<1,2>))],
src=|unknown:///|(2,0,<1,2>,<1,2>)),appl(
prod(
label(
"mul",
sort("Exp")),
[
sort("Exp"),
layouts("LAYOUTLIST"),
lit("*"),
layouts("LAYOUTLIST"),
sort("Exp")
],
{}),
[appl(
prod(
label(
"con",
sort("Exp")),
[lex("IntegerLiteral")],
{}),
[appl(
prod(
lex("IntegerLiteral"),
[iter(\char-class([range(48,57)]))],
{}),
[appl(
regular(iter(\char-class([range(48,57)]))),
[char(51)],
src=|unknown:///|(2,1,<1,2>,<1,3>))],
src=|unknown:///|(2,1,<1,2>,<1,3>))],
src=|unknown:///|(2,1,<1,2>,<1,3>)),appl(
prod(
layouts("LAYOUTLIST"),
[conditional(
\iter-star(lex("LAYOUT")),
{\not-follow(\char-class([
range(9,10),
range(13,13),
range(32,32)
]))})],
{}),
[appl(
regular(\iter-star(lex("LAYOUT"))),
[],
src=|unknown:///|(3,0,<1,3>,<1,3>))],
src=|unknown:///|(3,0,<1,3>,<1,3>)),appl(
prod(
lit("*"),
[\char-class([range(42,42)])],
{}),
[char(42)]),appl(
prod(
layouts("LAYOUTLIST"),
[conditional(
\iter-star(lex("LAYOUT")),
{\not-follow(\char-class([
range(9,10),
range(13,13),
range(32,32)
]))})],
{}),
[appl(
regular(\iter-star(lex("LAYOUT"))),
[],
src=|unknown:///|(4,0,<1,4>,<1,4>))],
src=|unknown:///|(4,0,<1,4>,<1,4>)),appl(
prod(
label(
"con",
sort("Exp")),
[lex("IntegerLiteral")],
{}),
[appl(
prod(
lex("IntegerLiteral"),
[iter(\char-class([range(48,57)]))],
{}),
[appl(
regular(iter(\char-class…WARNING: unexpected errors in the above SHELL example. Documentation author please fix!
We can use parse to define load:
module demo::lang::Exp::Combined::Automatic::Load
import demo::lang::Exp::Combined::Automatic::Parse; (1)
import demo::lang::Exp::Abstract::Syntax; (2)
import ParseTree; (3)
Exp load(str txt) = implode(#Exp, parseExp(txt));Notes:
| 1 | We also need the parse function, as defined above. |
| 2 | We also need the abstract syntax as already defined earlier in [Exp/Abstract]. |
| 3 | We need [Rascal:ParseTree] since it provides the [Rascal:implode] function. |
Let’s try it:
rascal>import demo::lang::Exp::Combined::Automatic::Load;
ok
rascal>load("2+3*4");
Exp: add(
con(
2,
location=|unknown:///|(0,1,<1,0>,<1,1>),
comments=()),
mul(
con(
3,
location=|unknown:///|(2,1,<1,2>,<1,3>),
comments=()),
con(
4,
location=|unknown:///|(4,1,<1,4>,<1,5>),
comments=()),
location=|unknown:///|(2,3,<1,2>,<1,5>),
comments=()),
location=|unknown:///|(0,5,<1,0>,<1,5>),
comments=())Remains the definition of the eval function:
module demo::lang::Exp::Combined::Automatic::Eval
import demo::lang::Exp::Abstract::Eval;
import demo::lang::Exp::Combined::Automatic::Load;
int eval(str txt) = eval(load(txt));Here is the end result:
rascal>import demo::lang::Exp::Combined::Automatic::Eval;
ok
rascal>eval("2+3*4");
int: 14Manual
An Exp evaluator that uses a manually written conversion from parse tree to abstract syntax tree.
First we define a parse function for Exp:
module demo::lang::Exp::Combined::Manual::Parse
import demo::lang::Exp::Concrete::WithLayout::Syntax;
import ParseTree;
demo::lang::Exp::Concrete::WithLayout::Syntax::Exp
parseExp(str txt) = parse(#Exp, txt);and test it:
rascal>import demo::lang::Exp::Combined::Manual::Parse;
ok
rascal>parseExp("2+3");
warning, ambiguity predicted: Exp "+" Exp lacks left or right associativity
warning, ambiguity predicted: Exp "*" Exp lacks left or right associativity
Exp: (Exp) `2+3`WARNING: unexpected errors in the above SHELL example. Documentation author please fix!
Next, we define a load function:
module demo::lang::Exp::Combined::Manual::Load
import demo::lang::Exp::Concrete::WithLayout::Syntax; (1)
import demo::lang::Exp::Abstract::Syntax; (2)
import demo::lang::Exp::Combined::Manual::Parse; (3)
import String;
demo::lang::Exp::Abstract::Syntax::Exp loadExp(str txt) = load(parseExp(txt)); (4)
demo::lang::Exp::Abstract::Syntax::Exp load((Exp)`<IntegerLiteral l>`) (5)
= con(toInt("<l>"));
demo::lang::Exp::Abstract::Syntax::Exp load((Exp)`<Exp e1> * <Exp e2>`)
= mul(load(e1), load(e2));
demo::lang::Exp::Abstract::Syntax::Exp load((Exp)`<Exp e1> + <Exp e2>`)
= add(load(e1), load(e2));
demo::lang::Exp::Abstract::Syntax::Exp load((Exp)`( <Exp e> )`)
= load(e);Some comments:
| 1 | We reuse the previously defined concrete syntax with layout. |
| 2 | We also reuse the previously defined abstract syntax. |
| 3 | Import the Parse module defined above. |
| 4 | The top level load function that converts a string to an abstract syntax tree. |
| 5 | The conversion from parse tree to abstract syntax tree start here. Note that we explicitly use demo::lang::Exp::Concrete::WithLayout::Syntax::Exp in these rules to distinguish from demo::lang::Exp::Abstract::Syntax::Exp. |
Let’s try it:
rascal>import demo::lang::Exp::Combined::Manual::Load;
warning, ambiguity predicted: Exp "+" Exp lacks left or right associativity
warning, ambiguity predicted: Exp "*" Exp lacks left or right associativity
ok
rascal>loadExp("2+3");
Exp: add(
con(2),
con(3))WARNING: unexpected errors in the above SHELL example. Documentation author please fix!
What remains is to write the interpreter using the above components:
module demo::lang::Exp::Combined::Manual::Eval
import demo::lang::Exp::Abstract::Eval;
import demo::lang::Exp::Combined::Manual::Load;
public int eval(str txt) = eval(loadExp(txt));Here is how it works:
rascal>import demo::lang::Exp::Combined::Manual::Eval;
ok
rascal>eval("2+3");
int: 53.1.3. Concrete
Various versions of Exp based on concrete syntax.
We discuss several versions of Exp based on concrete syntax:
-
No Layout: is the simplest version that does not consider layout symbols in expressions.
-
With Layout: adds layout information to Exp’s synax definition.
No Layout
A version of Exp based on concrete syntax.
We describe howto write a grammar for Exp and how to use it to implement an evaluator.
Here is the grammar for Exp:
module demo::lang::Exp::Concrete::NoLayout::Syntax
lexical IntegerLiteral = [0-9]+; (1)
start syntax Exp (2)
= IntegerLiteral (3)
| bracket "(" Exp ")" (4)
> left Exp "*" Exp (5)
> left Exp "+" Exp (6)
;Notes:
| 1 | Defines a lexical syntax rule for IntegerLiterals; they consist of one or more digits. |
| 2 | Defines the alternatives for Exp. The keyword start means that this is a start symbol of the grammar. |
| 3 | Defines alternative #1: an IntegerLiteral. |
| 4 | Defines alternative #2: parentheses. The | says that this alternative has the same priority as the previous one. The keyword bracket marks this as an alternative that defines parentheses. |
| 5 | Defines alternative #3: multiplication. The > says that the previous rule has a higher priority than the current one. The keyword left marks this as a left-associative rule. |
| 6 | Defines alternative #4: addition. The > says again that the previous rule has a higher priority than the current one. The keyword left marks this as a left-associative rule. |
Now that the grammar is in place we want to use it to build an evaluator. Here is how:
module demo::lang::Exp::Concrete::NoLayout::Eval
import demo::lang::Exp::Concrete::NoLayout::Syntax;
import String;
import ParseTree; (1)
int eval(str txt) = eval(parse(#Exp, txt)); (2)
int eval((Exp)`<IntegerLiteral l>`) = toInt("<l>"); (3)
int eval((Exp)`<Exp e1>*<Exp e2>`) = eval(e1) * eval(e2); (4)
int eval((Exp)`<Exp e1>+<Exp e2>`) = eval(e1) + eval(e2); (5)
int eval((Exp)`(<Exp e>)`) = eval(e); (6)Notes:
| 1 | We import [Rascal:ParseTree] because we will need the parse function below. |
| 2 | The main function eval that evaluates an expression as string to an integer. It proceeds in two steps:
|
| 3 | Converts an IntegerLiteral to an integer. Let’s dissect this further:
|
| 4 | Handle the multiplication case. |
| 5 | Handle the addition case. |
| 6 | Handles the case of parentheses. |
What remains, is to check that eval works as expected.
rascal>import demo::lang::Exp::Concrete::NoLayout::Syntax;
ok
rascal>import ParseTree;
okJust checking that parse returns a sort of parse tree:
rascal>parse(#Exp, "2+3");
warning, ambiguity predicted: Exp "*" Exp lacks left or right associativity
warning, ambiguity predicted: Exp "+" Exp lacks left or right associativity
Exp: (Exp) `2+3`WARNING: unexpected errors in the above SHELL example. Documentation author please fix! You will see such parse trees only once, unless you are a researcher in parsing ;-) Here is a demonstration of eval:
rascal>import demo::lang::Exp::Concrete::NoLayout::Eval;
warning, ambiguity predicted: Exp "*" Exp lacks left or right associativity
warning, ambiguity predicted: Exp "+" Exp lacks left or right associativity
ok
rascal>eval("2+3");
int: 5
rascal>eval("2+3*4");
int: 14
rascal>eval("(2+3)*4");
int: 20WARNING: unexpected errors in the above SHELL example. Documentation author please fix!
With Layout
Defines a concrete syntax for Exp with layout.
In Rascal, the major difference between lexical syntax and non-lexical syntax is that:
-
Strings that are parsed according to the lexical syntax do not contain additional layout characters such as spaces, new lines, and source code comments.
-
Strings that are parsed according to the normal (non-lexical) syntax can contain layout characters between each element.
-
Which 'layout' (whitespace and/or source code comments) will be accepted has to be defined explicitly by the grammar writer.
The following example extends the grammar for Exp in No Layout with a layout definition:
module demo::lang::Exp::Concrete::WithLayout::Syntax
layout Whitespace = [\t-\n\r\ ]*; (1)
lexical IntegerLiteral = [0-9]+;
start syntax Exp
= IntegerLiteral
| bracket "(" Exp ")"
> left Exp "*" Exp
> left Exp "+" Exp
;| 1 | Using the layout definition, we defcoine that the Whitespace non-terminal is used in between every symbol of the syntax productions in the current module. |
And now we can use spaces in our definition of the eval function as well:
module demo::lang::Exp::Concrete::WithLayout::Eval
import demo::lang::Exp::Concrete::WithLayout::Syntax;
import String;
import ParseTree;
int eval(str txt) = eval(parse(#start[Exp], txt).top);
int eval((Exp)`<IntegerLiteral l>`) = toInt("<l>");
int eval((Exp)`<Exp e1> * <Exp e2>`) = eval(e1) * eval(e2);
int eval((Exp)`<Exp e1> + <Exp e2>`) = eval(e1) + eval(e2);
int eval((Exp)`( <Exp e> )`) = eval(e);Note that Pattern Matching will ignore all trees in layout positions, such that the parse tree of "1 + \\n1" will match against <Exp e1> + <Exp e2>. The same goes for equality on parse trees.
For the above example Rascal will insert the Whitespace non-terminal between every element of the syntax rules for Exp. Moreover, for the start production (See No Layout) Whitespace will be added before and after the Exp.
The effect of the layout definition is that before parser generation the following grammar is derived for Exp:
syntax Exp
= IntegerLiteral
| bracket "(" Whitespace Exp Whitespace ")"
> left Exp Whitespace "*" Whitespace Exp
> left Exp Whitespace "+" Whitespace Exp
;
syntax start[Exp] = Whitespace Exp top Whitespace;To put this all to the test:
rascal>import demo::lang::Exp::Concrete::WithLayout::Syntax;
ok
rascal>import demo::lang::Exp::Concrete::WithLayout::Eval;
warning, ambiguity predicted: Exp "+" Exp lacks left or right associativity
warning, ambiguity predicted: Exp "*" Exp lacks left or right associativity
ok
rascal>eval("2 + 3");
int: 5
rascal>eval("2 + 3*4");
int: 14
rascal>eval("( 2+3 )* 4");
int: 20WARNING: unexpected errors in the above SHELL example. Documentation author please fix! .Benefits
-
If the grammar for
Expwould contain an optional symbol, as insyntax Exp = Exp "+"? Exp, then it would be ambiguous. Does a space in "1 1", belong to theWhitespacebefore or after the missing+? To disambiguate thelayoutdefinition should be changed tolayout Whitespace = [\ \t\n\r]* !>> [\ \t\n\r]. That will make sure the space goes with the first Whitespace, because even an empty Whitespace list must never be followed immediately by a space.
3.2. Func
Func is a tiny functional language; we present several interpreters for it.
Func is a functional language with the following features:
-
A program consists of a number of function declarations.
-
A function declaration consists of a name, zero or more formal parameter names and an expression.
-
An expression can be one of:
-
an integer constant.
-
a variable.
-
arithmetic operators
+,-,*and/. -
comparison operators
<,⇐,>and>=. -
a call of a function.
-
an
ifexpression. -
a sequence of expressions (
;). -
an assignment (
:=). -
a
letexpression to introduce new bindings for local variables. -
an address of a variables (denoted by
&). -
derefence of a variable (denoted by
*).
-
Some features add more complexity to an interpreter, therefore we present four interpreters Eval0, Eval1, Eval2 and Eval2 that implement increasingly complex features:
| Feature | Eval0 | Eval1 | Eval2 | Eval3 |
|---|---|---|---|---|
function declaration |
y |
y |
y |
y |
integer constant |
y |
y |
y |
y |
variable |
y |
y |
y |
y |
arithmetic operators |
y |
y |
y |
y |
comparison operators |
y |
y |
y |
y |
call |
y |
y |
y |
y |
if |
y |
y |
y |
y |
let |
y |
y |
y |
|
sequence |
y |
y |
||
assignment |
y |
y |
||
address operator |
y |
|||
dereference operator |
y |
Here are several versions of the factorial function that use more and more features of the Func language:
F0.func:
fact(n) = if n <= 1 then
1
else
n * fact(n-1)
endF1.func:
fact(n) = let
x = n
in
if x <= 1 then
x
else
x * fact(x-1)
end
endF2.func:
fact(n) = if n <= 1 then
n := 1
else
n := n * fact(n-1)
end;
nF3.func:
swap(a, b) =
let
temp = *a
in
*a := *b;
*b := temp
end
fact(n) = let
x = 1,
y = 0
in
if n <= 1 then
x := 1
else
x := n * fact(n-1)
end;
swap(&x, &y);
y
endFor convenience, we use two versions of these examples for each Fi:
-
A file Fi`.func` that contains the code as shown above.
-
A file Fi`.rsc` a Rascal file that declares a string variable Fi with the same content.
For instance, F0.rsc looks like this
module demo::lang::Func::programs::F0
public str F0 =
"fact(n) = if n \<= 1 then
1
else
n * fact(n-1)
end";
Note the escaped < character in \<=. This is necessary since < and > are used in strings to enclose interpolations (insertion of the value of a Rascal expression). Both symbols need to be escaped when used as literal symbol and not as interpolation.
|
3.2.1. Abstract Syntax
The abstract syntax for Func.
Here is the abstract syntax for Func:
module demo::lang::Func::AST
data Prog = prog(list[Func] funcs);
data Func = func(str name, list[str] formals, Exp body);
data Exp = let(list[Binding] bindings, Exp exp)
| cond(Exp cond, Exp then, Exp otherwise)
| var(str name)
| nat(int nat)
| call(str name, list[Exp] args)
| address(str var)
| deref(Exp exp)
| mul(Exp lhs, Exp rhs)
| div(Exp lhs, Exp rhs)
| add(Exp lhs, Exp rhs)
| sub(Exp lhs, Exp rhs)
| gt(Exp lhs, Exp rhs)
| lt(Exp lhs, Exp rhs)
| geq(Exp lhs, Exp rhs)
| leq(Exp lhs, Exp rhs)
| seq(Exp lhs, Exp rhs)
| assign(Exp lhs, Exp rhs);
data Binding = binding(str var, Exp exp);Observe that the abstract syntax follows the structur of the Concrete Syntax but omits details such as operator priorities, parentheses, and the like.
3.2.2. Concrete Syntax
The concrete syntax of Func.
module demo::lang::Func::Func
lexical Ident = [a-zA-Z][a-zA-Z0-9]* !>> [a-zA-Z0-9];
lexical Natural = [0-9]+ !>> [0-9];
lexical LAYOUT = [\t-\n\r\ ];
layout LAYOUTLIST = LAYOUT* !>> [\t-\n\r\ ] ;
start syntax Prog = prog: Func* ;
syntax Func = func: Ident name "(" {Ident ","}* ")" "=" Exp;
syntax Exp = let: "let" {Binding ","}* "in" Exp "end"
| cond: "if" Exp "then" Exp "else" Exp "end"
| bracket "(" Exp ")"
| var: Ident
| nat: Natural
| call: Ident "(" {Exp ","}* ")"
| address: "&" Ident
> deref: "*" Exp
> non-assoc (
left mul: Exp "*" Exp
| non-assoc div: Exp "/" Exp
)
> left (
left add: Exp "+" Exp
| left sub: Exp "-" Exp
)
>
non-assoc (
non-assoc gt: Exp "\>" Exp
| non-assoc lt: Exp "\<" Exp
| non-assoc geq: Exp "\>=" Exp
| non-assoc leq: Exp "\<=" Exp
)
>
right assign: Exp ":=" Exp
>
right seq: Exp ";" Exp;
syntax Binding = binding: Ident "=" Exp;The concrete syntax of Func uses many features of Rascal’s syntax definitions. Some notes:
-
The definition of lexical syntax follows the pattern:
-
Define lexical symbols (
Ident,Natural). -
Define rules for layout.
-
Use follow restrictions (
!>>) to enforce the longest match of lexical symbols.
-
-
The definition of lexical also follows a common pattern:
-
List of non-terminal is defined with their alternatives.
-
One non-terminal is designated as start symbol (
Prog). -
Each alternative has a label, this is for the benefit of converting parse trees to abstract syntaxt trees.
-
Each alternative spells out its priority and associativity.
-
3.2.3. Eval0
A Func interpreter that does not support let-expressions and pointers.
Interpreter Eval0 supports the following features of Func:
| Feature | Eval0 |
|---|---|
function declaration |
y |
integer constant |
y |
variable |
y |
arithmetic operators |
y |
comparison operators |
y |
call |
y |
if |
y |
let |
|
sequence |
|
assignment |
|
address operator |
|
dereference operator |
Here is the code for Eval0:
module demo::lang::Func::Eval0
// No let
import demo::lang::Func::AST;
import List;
alias PEnv = map[str, Func]; (1)
value eval0(str main, list[int] args, Prog prog) { (2)
penv = ( f.name: f | f <- prog.funcs );
f = penv[main];
return eval0(subst(f.body, f.formals, args), penv);
}
Exp subst(Exp exp, list[str] vars, list[int] values) { (3)
env = ( vars[i]: values[i] | i <- index(vars) );
return visit (exp) {
case var(str name) => nat(env[name])
};
}
int eval0(nat(int nat), PEnv penv) = nat; (4)
int eval0(mul(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) * eval0(rhs, penv);
int eval0(div(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) / eval0(rhs, penv);
int eval0(add(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) + eval0(rhs, penv);
int eval0(sub(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) - eval0(rhs, penv);
int eval0(gt(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) > eval0(rhs, penv) ? 1 : 0;
int eval0(lt(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) < eval0(rhs, penv) ? 1 : 0;
int eval0(geq(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) >= eval0(rhs, penv) ? 1 : 0;
int eval0(leq(Exp lhs, Exp rhs), PEnv penv) = eval0(lhs, penv) <= eval0(rhs, penv) ? 1 : 0;
int eval0(cond(Exp cond, Exp then, Exp otherwise), PEnv penv) = (5)
(eval0(cond, penv) != 0) ? eval0(then, penv) : eval0(otherwise, penv);
int eval0(call(str name, list[Exp] args), PEnv penv) = (6)
eval0(subst(penv[name].body, penv[name].formals, [ eval0(a, penv) | a <- args]), penv);Some points to note:
| 1 | PEnv is used as an alias for a map from names to functions. Such maps are used to represent the function definitions in the program. |
| 2 | Here the top level interpreter eval0 is defined. It takes the name of the main function, a list of actual parameters, and the complete Func program. Binding of variables is done by substitution. |
| 3 | The substitution function is defined. It takes an expression, a list of variables, and a list of integer values to be substituted for them. Note how a [Rascal:Visit] is used to find all the variables in the expression and to replace them. |
| 4 | The versions of eval0 for each implemented construct. They all have a PEnv argument that is needed to resolve calls. |
| 5 | The if expression is defined: the then-branch is taken when the test evaluates to a non-zero integer. |
| 6 | The call expression is interpreted. It contains the following steps:
|
Let’s try this on example F0:
fact(n) = if n <= 1 then
1
else
n * fact(n-1)
endrascal>import demo::lang::Func::Load;
ok
rascal>import demo::lang::Func::Eval0;
ok
rascal>import demo::lang::Func::programs::F0;
ok
rascal>eval0("fact", [10], load(F0));
value: 36288003.2.4. Eval1
Interpreter Eval1 supports the following features of Func:
| Feature | Eval1 |
|---|---|
function declaration |
y |
integer constant |
y |
variable |
y |
arithmetic operators |
y |
comparison operators |
y |
call |
y |
if |
y |
let |
y |
sequence |
|
assignment |
|
address operator |
|
dereference operator |
In particular, the let construct is supported and this requires the addition of an extra environment for <name, value> bindings.
module demo::lang::Func::Eval1
// using env, allowing let
import demo::lang::Func::AST;
import List;
alias Env = map[str, int]; (1)
alias PEnv = map[str, Func];
int eval1(str main, list[int] args, Prog prog) {
penv = ( f.name: f | f <- prog.funcs );
f = penv[main];
env = ( f.formals[i] : args[i] | i <- index(f.formals) );
return eval1(f.body, env, penv);
}
int eval1(nat(int nat), Env env, PEnv penv) = nat;
int eval1(var(str n), Env env, PEnv penv) = env[n]; (2)
int eval1(mul(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) * eval1(rhs, env, penv);
int eval1(div(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) / eval1(rhs, env, penv);
int eval1(add(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) + eval1(rhs, env, penv);
int eval1(sub(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) - eval1(rhs, env, penv);
int eval1(gt(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) > eval1(rhs, env, penv) ? 1 : 0;
int eval1(lt(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) < eval1(rhs, env, penv) ? 1 : 0;
int eval1(geq(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) >= eval1(rhs, env, penv) ? 1 : 0;
int eval1(leq(Exp lhs, Exp rhs), Env env, PEnv penv) =
eval1(lhs, env, penv) <= eval1(rhs, env, penv) ? 1 : 0;
int eval1(cond(Exp cond, Exp then, Exp otherwise), Env env, PEnv penv) =
(eval1(cond, env, penv) != 0) ? eval1(then, env, penv) : eval1(otherwise, env, penv);
int eval1(call(str name, list[Exp] args), Env env, PEnv penv) {
f = penv[name];
env = ( f.formals[i]: eval1(args[i], env, penv) | i <- index(f.formals) );
return eval1(f.body, env, penv);
}
int eval1(let(list[Binding] bindings, Exp exp), Env env, PEnv penv) { (3)
env += ( b.var : eval1(b.exp, env, penv) | b <- bindings );
return eval1(exp, env, penv);
}| 1 | The alias Env is introduced that maps strings to integers. All evaluation functions get an extra Env argument. |
| 2 | The environment is used to retrieve a variable’s value. |
| 3 | The environment is extended with new bindings. |
Let’s try this with F1:
fact(n) = let
x = n
in
if x <= 1 then
x
else
x * fact(x-1)
end
endThe result:
rascal>import demo::lang::Func::Load;
ok
rascal>import demo::lang::Func::Eval1;
ok
rascal>import demo::lang::Func::programs::F1;
ok
rascal>eval1("fact", [10], load(F1));
int: 36288003.2.5. Eval2
Interpreter Eval2 supports the following features of Func:
| Feature | Eval2 |
|---|---|
function declaration |
y |
integer constant |
y |
variable |
y |
arithmetic operators |
y |
comparison operators |
y |
call |
y |
if |
y |
let |
y |
sequence |
y |
assignment |
y |
address operator |
|
dereference operator |
The main additions are local side effects and the sequence operator.
module demo::lang::Func::Eval2
// local side effects, returning env
import demo::lang::Func::AST;
import List;
alias Env = map[str, int];
alias PEnv = map[str, Func];
alias Result2 = tuple[Env, int]; (1)
Result2 eval2(str main, list[int] args, Prog prog) {
penv = ( f.name: f | f <- prog.funcs );
f = penv[main];
env = ( f.formals[i] : args[i] | i <- index(f.formals) );
return eval2(f.body, env, penv);
}
Result2 eval2(nat(int nat), Env env, PEnv penv) = <env, nat>;
Result2 eval2(var(str name), Env env, PEnv penv) = <env, env[name]>;
Result2 eval2(mul(Exp lhs, Exp rhs), Env env, PEnv penv) { (2)
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, x * y>;
}
Result2 eval2(div(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, x / y>;
}
Result2 eval2(add(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, x + y>;
}
Result2 eval2(sub(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, x - y>;
}
Result2 eval2(gt(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, (x > y) ? 1 : 0>;
}
Result2 eval2(lt(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, (x < y) ? 1 : 0>;
}
Result2 eval2(geq(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, (x >= y) ? 1 : 0>;
}
Result2 eval2(leq(Exp lhs, Exp rhs), Env env, PEnv penv) {
<env, x> = eval2(lhs, env, penv);
<env, y> = eval2(rhs, env, penv);
return <env, (x <= y) ? 1 : 0>;
}
Result2 eval2(cond(Exp cond, Exp then, Exp otherwise), Env env, PEnv penv) {
<env, c> = eval2(cond, env, penv);
return (c != 0) ? eval2(then, env, penv) : eval2(otherwise, env, penv);
}
Result2 eval2(call(str name, list[Exp] args), Env env, PEnv penv) {
f = penv[name];
for (i <- index(f.formals)) {
<env, v> = eval2(args[i], env, penv);
env[f.formals[i]] = v;
}
return eval2(f.body, env, penv);
}
Result2 eval2(let(list[Binding] bindings, Exp exp), Env env, PEnv penv) {
for (b <- bindings) {
<env, x> = eval2(b.exp, env, penv);
env[b.var] = x;
}
return eval2(exp, env, penv);
}
Result2 eval2(assign(var(str name), Exp exp), Env env, PEnv penv) { (3)
<env, v> = eval2(exp, env, penv);
env[name] = v;
return <env, v>;
}
Result2 eval2(seq(Exp lhs, Exp rhs), Env env, PEnv penv) { (4)
<env, _> = eval2(lhs, env, penv);
return eval2(rhs, env, penv);
}| 1 | The alias Result is introduced: a pair of an environment and an integer value. All evaluator functions are changed from returning an integer (the result of evaluation) to
Result (the result of evaluation and the local side effects). |
| 2 | The effect of this change can be seen in all functions. For instance, when evaluating multiplication, the environment produced by the left operand ahs to be passed as argument to the right operand of the multiplication. This is needed, to propagate any side effects caused by the left operand to propagate to the right one. |
| 3 | Assignment is implemented. |
| 4 | Sequencing is implemented. Observe that that the value of the left operand is ignored and that the value of the right operand is returned. |
We apply eval2 to example F2:
fact(n) = if n <= 1 then
n := 1
else
n := n * fact(n-1)
end;
nLet’s try this.
rascal>import demo::lang::Func::Load;
ok
rascal>import demo::lang::Func::Eval2;
ok
rascal>import demo::lang::Func::programs::F2;
ok
rascal>eval2("fact", [10], load(F2));
tuple[map[str, int],int]: <("n":3628800),3628800>3.2.6. Eval3
Interpreter Eval3 supports the following features of Func:
| Feature | Eval3 |
|---|---|
function declaration |
y |
integer constant |
y |
variable |
y |
arithmetic operators |
y |
comparison operators |
y |
call |
y |
if |
y |
let |
y |
sequence |
y |
assignment |
y |
address operator |
y |
dereference operator |
y |
The main additions are the address and dereference operators.
module demo::lang::Func::Eval3
// pointers into the stack
import demo::lang::Func::AST;
import List;
alias Env = map[str, Address];
alias PEnv = map[str, Func];
alias Result3 = tuple[Mem, int];
alias Address = int;
alias Mem = list[int];
Address push(Mem mem) {
return size(mem);
}
tuple[Mem, Address] alloc(Mem mem, int v) {
mem += [v];
return <mem, size(mem) - 1>;
}
Mem pop(Mem mem, Address scope) {
return slice(mem, 0, scope);
}
Result3 eval3(str main, list[int] args, Prog prog) {
penv = ( f.name: f | f <- prog.funcs );
f = penv[main];
mem = [];
<mem, env> = bind(f.formals, args, mem);
return eval3(f.body, env, penv, mem);
}
tuple[Mem, Env] bind(list[str] fs, list[int] args, Mem mem) {
env = ();
for (i <- index(fs)) {
<mem, a> = alloc(mem, args[i]);
env[fs[i]] = a;
}
return <mem, env>;
}
Result3 eval3(nat(int nat), Env env, PEnv penv, Mem mem) = <mem, nat>;
Result3 eval3(var(str name), Env env, PEnv penv, Mem mem) = <mem, mem[env[name]]>;
Result3 eval3(mul(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, x * y>;
}
Result3 eval3(div(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, x / y>;
}
Result3 eval3(add(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, x + y>;
}
Result3 eval3(sub(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, x - y>;
}
Result3 eval3(gt(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, (x > y) ? 1 : 0>;
}
Result3 eval3(lt(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, (x < y) ? 1 : 0>;
}
Result3 eval3(geq(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, (x >= y) ? 1 : 0>;
}
Result3 eval3(leq(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, x> = eval3(lhs, env, penv, mem);
<mem, y> = eval3(rhs, env, penv, mem);
return <mem, (x <= y) ? 1 : 0>;
}
Result3 eval3(cond(Exp cond, Exp then, Exp otherwise), Env env, PEnv penv, Mem mem) {
<mem, c> = eval3(cond, env, penv, mem);
return (c != 0) ? eval3(then, env, penv, mem) : eval3(otherwise, env, penv, mem);
}
Result3 eval3(call(str name, list[Exp] args), Env env, PEnv penv, Mem mem) {
f = penv[name];
scope = push(mem);
vs = for (a <- args) {
<mem, v> = eval3(a, env, penv, mem);
append v;
}
<mem, env> = bind(f.formals, vs, mem);
<mem, v> = eval3(f.body, env, penv, mem);
return <pop(mem, scope), v>;
}
Result3 eval3(address(str var), Env env, PEnv penv, Mem mem) = <mem, env[var]>;
Result3 eval3(deref(Exp exp), Env env, PEnv penv, Mem mem) {
<mem, v> = eval3(exp, env, penv, mem);
return <mem, mem[v]>;
}
Result3 eval3(let(list[Binding] bindings, Exp exp), Env env, PEnv penv, Mem mem) {
scope = push(mem);
for (b <- bindings) {
<mem, v> = eval3(b.exp, env, penv, mem);
<mem, a> = alloc(mem, v);
env[b.var] = a;
}
<mem, v> = eval3(exp, env, penv, mem);
return <pop(mem, scope), v>;
}
Result3 eval3(seq(Exp lhs, Exp rhs), Env env, PEnv penv, Mem mem) {
<mem, _> = eval3(lhs, env, penv, mem);
return eval3(rhs, env, penv, mem);
}
Result3 eval3(assign(var(str name), Exp e), Env env, PEnv penv, Mem mem) {
<mem, v> = eval3(e, env, penv, mem);
mem[env[name]] = v;
return <mem, v>;
}
Result3 eval3(assign(deref(Exp lvalue), Exp e), Env env, PEnv penv, Mem mem) {
<mem, addr> = eval3(lvalue, env, penv, mem);
<mem, v> = eval3(e, env, penv, mem);
mem[addr] = v;
return <mem, v>;
}We apply eval3 to example F3:
swap(a, b) =
let
temp = *a
in
*a := *b;
*b := temp
end
fact(n) = let
x = 1,
y = 0
in
if n <= 1 then
x := 1
else
x := n * fact(n-1)
end;
swap(&x, &y);
y
endLet’s try this.
rascal>import demo::lang::Func::Load;
ok
rascal>import demo::lang::Func::Eval3;
ok
rascal>import demo::lang::Func::programs::F3;
ok
rascal>eval3("fact", [10], load(F3));
|TODO:///|: Ambiguity(
|unknown:///|(175,128,<13,9>,<19,10>),
"Exp",
"if n \<= 1 then \n\t x := 1\n\t else \n\t x := n * fact(n-1)\n\t end;\n\t swap(&x, &y);\n\t y")
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix!
3.2.7. Load AST
Parse Func program from string or file and convert to an abstract syntax tree.
To simplify later processing, Func programs are converted to an abstract syntax tree.
The concrete syntax for Func is described in Concrete Syntax and its abstract syntax in Abstract Syntax. Rather than manually writing conversion rules from Func parse trees to Func abstract syntax trees we use our secret weapon: implode that performs the mapping for us. As you see when you compare the concrete and abstract syntax, the ground work has already been done by appropriately labelling concrete rules with constructor names of the abstract syntax.
Here is the code for the load funcion:
module demo::lang::Func::Load
import demo::lang::Func::Func;
import demo::lang::Func::AST;
import demo::lang::Func::Parse;
import ParseTree;
demo::lang::Func::AST::Prog implode(demo::lang::Func::Func::Prog p) =
implode(#demo::lang::Func::AST::Prog, p);
demo::lang::Func::AST::Prog load(loc l) = implode(parse(l));
demo::lang::Func::AST::Prog load(str s) = implode(parse(s));This looks simple but also slightly intimidating due to the many qualified names. The issue is that the names in the concrete and abstract syntax are (on purpose) overloaded. A name like Prog can be the one from the concrete syntax(i.e., demo::lang::Func::Func::Prog) or the one from the abstract syntax (i.e., demo::lang::Func::AST::Prog).
For instance, the local version of implode defined here get a concrete Prog as argument and returns an abstract one. Both load function return an abstract Prog.
Let’s try this on example F0:
fact(n) = if n <= 1 then
1
else
n * fact(n-1)
endrascal>import demo::lang::Func::Load;
ok
rascal>import demo::lang::Func::programs::F0;
ok
rascal>load(F0);
warning, ambiguity predicted: seq: Exp ";" Exp lacks left or right associativity
warning, ambiguity predicted: assign: Exp ":=" Exp lacks left or right associativity
Prog: prog(
[func(
"fact",
["n"],
cond(
leq(
var(
"n",
location=|unknown:///|(13,1,<1,13>,<1,14>),
comments=()),
nat(
1,
location=|unknown:///|(18,1,<1,18>,<1,19>),
comments=()),
location=|unknown:///|(13,6,<1,13>,<1,19>),
comments=()),
nat(
1,
location=|unknown:///|(38,1,<2,13>,<2,14>),
comments=()),
mul(
var(
"n",
location=|unknown:///|(70,1,<4,13>,<4,14>),
comments=()),
call(
"fact",
[sub(
var(
"n",
location=|unknown:///|(79,1,<4,22>,<4,23>),
comments=()),
nat(
1,
location=|unknown:///|(81,1,<4,24>,<4,25>),
comments=()),
location=|unknown:///|(79,3,<4,22>,<4,25>),
comments=())],
location=|unknown:///|(74,9,<4,17>,<4,26>),
comments=()),
location=|unknown:///|(70,13,<4,13>,<4,26>),
comments=()),
location=|unknown:///|(10,87,<1,10>,<5,13>),
comments=()),
location=|unknown:///|(0,97,<1,0>,<5,13>),
comments=())],
location=|unknown:///|(0,97,<1,0>,<5,13>),
comments=())WARNING: unexpected errors in the above SHELL example. Documentation author please fix! We get the original program and its abstract syntax tree of type Prog back. In case of doubt, compare this with the result in Parse where we did obtain a parse tree. Next, we try the same from a file:
rascal>load(|std:///demo/lang/Func/programs/F0.func|);
Prog: prog(
[func(
"fact",
["n"],
cond(
leq(
var(
"n",
location=|std:///demo/lang/Func/programs/F0.func|(13,1,<1,13>,<1,14>),
comments=()),
nat(
1,
location=|std:///demo/lang/Func/programs/F0.func|(18,1,<1,18>,<1,19>),
comments=()),
location=|std:///demo/lang/Func/programs/F0.func|(13,6,<1,13>,<1,19>),
comments=()),
nat(
1,
location=|std:///demo/lang/Func/programs/F0.func|(38,1,<2,13>,<2,14>),
comments=()),
mul(
var(
"n",
location=|std:///demo/lang/Func/programs/F0.func|(70,1,<4,13>,<4,14>),
comments=()),
call(
"fact",
[sub(
var(
"n",
location=|std:///demo/lang/Func/programs/F0.func|(79,1,<4,22>,<4,23>),
comments=()),
nat(
1,
location=|std:///demo/lang/Func/programs/F0.func|(81,1,<4,24>,<4,25>),
comments=()),
location=|std:///demo/lang/Func/programs/F0.func|(79,3,<4,22>,<4,25>),
comments=())],
location=|std:///demo/lang/Func/programs/F0.func|(74,9,<4,17>,<4,26>),
comments=()),
location=|std:///demo/lang/Func/programs/F0.func|(70,13,<4,13>,<4,26>),
comments=()),
location=|std:///demo/lang/Func/programs/F0.func|(10,87,<1,10>,<5,13>),
comments=()),
location=|std:///demo/lang/Func/programs/F0.func|(0,97,<1,0>,<5,13>),
comments=())],
location=|std:///demo/lang/Func/programs/F0.func|(0,97,<1,0>,<5,13>),
comments=())3.2.8. Parse
Parse a Func program from a string or a file.
Parsing uses the syntax rules for a given start non-terminnal to parse a string and turn it into a parse tree. The work horse is the parse function that is available in the PareTree library.
Here is how to parse Func programs from a string or file:
module demo::lang::Func::Parse
import demo::lang::Func::Func;
import ParseTree;
Prog parse(loc l) = parse(#Prog, l);
Prog parse(str s) = parse(#Prog, s);Let’s try this on example F0.func:
fact(n) = if n <= 1 then
1
else
n * fact(n-1)
endFirst, we try the version with a string argument:
rascal>import demo::lang::Func::Parse;
ok
rascal>import demo::lang::Func::programs::F0;
ok
rascal>parse(F0);
Prog: (Prog) `fact(n) = if n <= 1 then
1
else
n * fact(n-1)
end`This must be defined as success: we get the original program and its parse tree back. Next, we try the same from a file. We use the scheme std that refers to files that reside in the Rascal library. See [$Rascal:Expressions/Values/Location] for further details on other schemes.
rascal>parse(|std:///demo/lang/Func/programs/F0.func|);
Prog: (Prog) `fact(n) = if n <= 1 then
1
else
n * fact(n-1)
end`3.3. Lisra
A lisp interpreter in Rascal.
Writing a Lisp interpreter is a classical challenge. Popular word has that all large applications evolve until they include a Lisp interpreter. (A variant says the same about including an email client in every large application).
We will closely follow and reuse parts of Peter Norvig’s excellent page on Lispy, a Lisp interpreter written in Python. The Lisp variant to be implemented is the following subset of the Scheme language:
| Form | Syntax | Semantics and Example |
|---|---|---|
var |
A symbol is interpreted as a variable name; its value is the variable’s value. Example: |
|
number |
A number evaluates to itself. Example: |
|
|
Return the exp literally; do not evaluate it. Example:
|
|
|
Evaluate test; if true, evaluate and return conseq; otherwise evaluate and return
alt. <br>Example: |
|
|
Evaluate exp and assign that value to
var, which must have been previously defined (with a
|
|
|
Define a new variable in the innermost environment and give it the value of evaluating the expression exp. Examples: |
|
|
Create a procedure with parameter(s) named var… and the expression as the body. Example: |
|
|
Evaluate each of the expressions in left-to-right order, and return the final value. Example: `(begin (set! x 1) (set! x (+ x 1)) (* x 2)) ⇒ 4 |
|
|
If proc is anything other than one of the symbols |
In this table, var must be a symbol—an identifier such as x or square—and number must be an integer number, while the other italicized words can be any expression. The notation exp… means zero or more repetitions of exp.
A Lisp interpreter consists of the following parts:
-
A parser that reads a Lisp program in text form and converts it to a runtime representation that is suitable for the interpreter.
-
The interpreter itself that executes the program in runtime representation and computes its outcome.
-
A pretty printer that converts the outcome in internal representation back to text.
-
Finally, an interactive console is needed that interact with the user.
We discuss all these aspects:
3.3.1. Syntax
The textual syntax of Lisp.
The first step in defining Lisp’s textual format, we define a grammar for it:
module demo::lang::Lisra::Syntax
layout Whitespace = [\t-\n\r\ ]*;
lexical IntegerLiteral = [0-9]+ !>> [0-9];
lexical AtomExp = (![0-9()\t-\n\r\ ])+ !>> ![0-9()\t-\n\r\ ];
start syntax LispExp // TODO: remove constructor names (needed for compiler)
= int_lit: IntegerLiteral
| atom_exp: AtomExp
| par_exp: "(" LispExp* ")"
;
// end::module[]Whitespace defines the characters that can be ignored between tokens.
IntegerLiteral defines integer constants. In a first approximation [0-9] is enough. However, to ensure that the longest possible sequence of digits is used, the !>> [0-9] part ensures that an integer cannot be followed by another digit.
AtomExp defines a Lisp symbol that may contain a wide range of characters (except layout and digits).
The main syntactic concept is a LispExp that may be an IntegerLiteral, AtomExp or a list of `LispExp`s surrouned by parentheses.
This grammar is demonstrated in Parse.
3.3.2. Runtime
The runtime representation of Lisp programs and data.
There are several aspects of the runtime representation of Lisp programs and Lisp data that have to be described:
-
The representation of values (see
Lvalbelow). -
The handling of the scope of variables (see
Scope,Env,makeEnvandfindbelow). -
The way the interpreter returns its results (see
Resultbelow).
module demo::lang::Lisra::Runtime
import Prelude;
data Lval (1)
= Integer(int n)
| Atom(str name)
| List(list[Lval] elms)
| Closure(Result(list[Lval] args, Env env))
;
alias Scope = map[Lval,Lval]; (2)
alias Env = list[Scope];
public Env emptyEnv = [()];
Env makeEnv(list[Lval] vars, list[Lval] values, Env outer) = (3)
[(vars[i] : values[i] | i <- index(vars))] + outer;
int find(Lval sym, Env e){ (4)
for(n <- index(e))
if(e[n][sym]?)
return n;
return -1;
}
public Lval TRUE = Atom("#t"); (5)
public Lval FALSE = Atom("#f");
alias Result = tuple[Lval val, Env env]; (6)| 1 | The data type Lval takes care of the representation of Lisp values. It covers integers, atoms, lists and closures (the representation of a functions and the context in which it will be executed). |
| 2 | A Scope describes the binding of several related variables to their value. Since scopes may be nested, an environment (Env) consisted of a list of scope. The most inner scope is at the start of the list and the most global one at the end. |
| 3 | Creating a new scope is done by makeEnv which takes a list of variables (represented by Lval`s, in most cases this will be an atom like `Atom("X")), a list of values and creates a new scope in front of the current environment. |
| 4 | The function find tries to locate the scope in which a name was previously defined. It searches the nested scopes inside-out and returns the index in the given environment of the scope in which the name is defined, or -1 if it is not found. |
| 5 | We define useful constants for true and false (the atoms #t and #f, respectively). |
| 6 | Finally, we define Result as a tuple of an Lval and an Env. Each step during interpretation will thus return the value it computed and a possibly modified environment. |
3.3.3. Parse
Parsing a Lisp expression.
Given the Lisp Syntax, we can now apply it to parse textual Lisp expressions and convert them to the runtime representation Lval.
module demo::lang::Lisra::Parse
import Prelude;
import demo::lang::Lisra::Syntax;
import demo::lang::Lisra::Runtime;
Lval parse(str txt) = build(parse(#LispExp, txt)); (1)
// Build Abstract Synax Tree: Transform a LispExp to an Lval
Lval build((LispExp)`<IntegerLiteral il>`) = Integer(toInt("<il>")); (2)
Lval build((LispExp)`<AtomExp at>`) = Atom("<at>"); (3)
Lval build((LispExp)`( <LispExp* lst> )`) = List([build(l) | l <- lst]); (4)| 1 | First we define the actual parse function: it takes a string as argument and returns an Lval. It proceeds in two steps:
|
| 2 | Function build is defined in cases, to handle the various parse tree forms. Fortunately, we do not have to spell out the details of the parse tree, but we can use concrete patterns instead (see [Concrete Patterns], below).
The right-hand sides deserve some attention. Here the argument `il` is a _parse tree_ (!!) that represents an integer literal. We first convert it to a string using string interpolation (`"<il>"`) and then convert it to an integer. |
| 3 | The text of the atom is reconstructed in a similar fashion. |
| 4 | The concrete list elements in lst are converted one-by-one using build and are then used to create a new List value. |
rascal>import demo::lang::Lisra::Parse;
ok
rascal>import demo::lang::Lisra::Runtime;
ok
rascal>parse("1");
Lval: Integer(1)
rascal>parse("x");
Lval: Atom("x")
rascal>parse("(+ 5 7)");
Lval: List([
Atom("+"),
Integer(5),
Integer(7)
])3.3.4. Pretty
A Lisp pretty printer.
The purpose of a pretty printer is to convert an internal structure to text. We define here the simplest possible solution:
module demo::lang::Lisra::Pretty
import demo::lang::Lisra::Runtime;
// Pretty print: transform an Lval to a string
str pretty(Integer(n)) = "<n>";
str pretty(Atom(name)) = name;
str pretty(List(list[Lval] elms)) = "( <for(Lval e <- elms){><pretty(e)> <}>)";
str pretty(Closure(fn)) = "Closure(<fn>)";Compare the definition of pretty with that of parse:
Lval parse(str txt);
str pretty(Lval x);For a well-designed pair of parse/pretty functions, the latter is the inverse of the former. In other words, for every L the following should hold:
parse(pretty(L)) == Lrascal>import demo::lang::Lisra::Runtime;
ok
rascal>import demo::lang::Lisra::Pretty;
ok
rascal>pretty(Integer(42));
str: "42"
rascal>pretty(Atom("x"));
str: "x"
rascal>L = List([Atom("+"), Integer(5), Integer(7)]);
Lval: List([
Atom("+"),
Integer(5),
Integer(7)
])
rascal>pretty(L);
str: "( + 5 7 )"Now let’s explore whether pretty is indeed the inverse of parse:
rascal>import demo::lang::Lisra::Parse;
ok
rascal>parse(pretty(L)) == L;
bool: true3.3.5. Eval
A Lisp interpreter.
Here is the core of our Lisp interpreter. Its basic functionality is to take
-
An
Lvaland an Environment (both defined in Runtime). -
Distinguish the various forms an
Lvalcan have and compute the effect of evaluating it. -
Return a
Resultthat captures the value just computed and possibleside-effects on the environment.
Rascal provides pattern-directed dispatch: a function with the same name can have complete patterns as arguments. When called, a pattern match determines which variant of the function will be called. This is used extensively in the definitions below:
module demo::lang::Lisra::Eval
import Prelude;
import demo::lang::Lisra::Parse;
import demo::lang::Lisra::Runtime;
Lval eval(Lval x) = eval(x, [()]).val;
// Evaluate an Lval in a given environment and return a Result.
Result eval(str exp) = eval(parse(exp), [()]);
Result eval(Integer(int x), Env e) = <Integer(x), e>; (1)
Result eval(var:Atom(str name), Env e) { (2)
n = find(var, e);
return <(n < 0) ? var : e[n][var], e>;
}
Result eval(List([Atom("quote"), *Lval exps]), Env e) = (3)
<size(exps) == 1 ? exps[0] : List(exps), e>;
Result eval(List([Atom("set!"), var, exp]), Env e) { (4)
val = eval(exp, e).val;
n = find(var, e);
if(n < 0) e[0][var] = val; else e[n][var] = val;
return <val, e>;
}
Result eval(List([Atom("if"), Lval tst, Lval conseq, Lval alt]), Env e) = (5)
eval(tst, e).val != FALSE ? eval(conseq, e) : eval(alt, e);
Result eval(List([Atom("begin"), *Lval exps]) , Env e) { (6)
val = FALSE;
for(Lval exp <- exps){
<val, e> = eval(exp, e);
}
return <val, e>;
}
Result eval(List([Atom("define"), var, exp]), Env e){ (7)
e[0][var] = eval(exp, e).val;
return <FALSE, e>;
}
Result eval(List([Atom("lambda"), List(list[Lval] vars), exp]), Env defEnv) = (8)
<Closure(Result(list[Lval] args, Env callEnv) {
return eval(exp, makeEnv(vars, args, tail(callEnv, size(defEnv))));
}),
defEnv>;
default Result eval(List([ *Lval exps ]), Env e) { (9)
if(isEmpty(exps))
return <List([]), e>;
vals = [ eval(exp, e).val | exp <- exps ];
return apply(head(vals), tail(vals), e);
}
//default Result eval(Lval exp, Env e) = <exp, e>;
// Apply an Lval to a list of arguments and return a Result
Result apply(Closure(Result(list[Lval] args, Env env) fn), list[Lval] args, Env e) { (10)
return <fn(args, e).val, e>;
}
(11)
Result apply(Atom("+"), [Integer(x), Integer(y)], Env e) = <Integer(x + y), e>;
Result apply(Atom("-"), [Integer(x), Integer(y)], Env e) = <Integer(x - y), e>;
Result apply(Atom("*"), [Integer(x), Integer(y)], Env e) = <Integer(x * y), e>;
Result apply(Atom("\<"), [Lval x, Lval y], Env e) = <x < y ? TRUE : FALSE, e>;
Result apply(Atom("\>"), [Lval x, Lval y], Env e) = <x >= y ? TRUE : FALSE, e>;
Result apply(Atom("equal?"), [Lval x, Lval y], Env e) = <x == y ? TRUE : FALSE, e>;
Result apply(Atom("null?"), [List(list[Lval] x)], Env e) = <isEmpty(x) ? TRUE : FALSE, e>;
Result apply(Atom("cons"), [Lval x, List(list[Lval] y)], Env e) = <List([x, *y]), e>;
Result apply(Atom("append"), [List(list[Lval] x), Lval y], Env e) = <List([*x, y]), e>;
Result apply(Atom("car"), [List(list[Lval] x)], Env e) = <head(x), e>;
Result apply(Atom("cdr"), [List(list[Lval] x)], Env e) = <List(tail(x)), e>;
Result apply(Atom("list"), list[Lval] x, Env e) = <List(x), e>;
default Result apply(Lval a, list[Lval] b, Env e) { (12)
println("Cannot apply <a> to <b> using <e>");
return <FALSE, e>;
}We now explain the different cases in more detail:
| 1 | An integer constant evaluates to itself. Note how Integer(int x) is used as first argument of this eval function. It is a pattern that describes that the constructor Integer
with an int argument x is to be matched. |
| 2 | An atom evaluates to the value to which it is bound or to itself. find (see [Runtime]) is used to search for the atom in question. The first argument is var:Atom(str name), a pattern that matches an Atom. The var: prefix binds the complete atom to a variable var to be used in the body of the function. |
| 3 | A quoted list evaluates to itself. The pattern List([Atom("quote"), exp*]) matches a List constructor whose first element is Atom("quote"). exp* means that the remaining list elements are assignment to exp. There are two cases: if the argument list has size 1, its first element is used, otherwise a list with all elements of exp
vare returned. This ensures that List([Atom("quote"), Integer(17)]) evaluates to Integer(17) and not to List([ Integer(17)]. |
| 4 | Evaluates a set! expression that assigns the value of exp to variable var. |
| 5 | Evaluates the if expression. The test tst is evaluated and is not false, the value of conseq is returned and otherwise that of alt. |
| 6 | Evaluates a block expression. The list of expressions exps is evaluated one by one. Observe that in the for loop
<val, e> = eval(exp, e); captures both the value and the environment that results from executing one expression. That new environment is is used to evaluate the next expression(s) in the list. The value of the last expression and a possible modied environment are returned. |
| 7 | Evaluate a define expression that binds the value of exp to variable var. The value of the expression is bound var in the local scope. |
| 8 | Evaluate a lambda expression. Essentially we return a Closure value that contains the expression in the lambda expression properly wrapped to do variable binding and environment management. A Closure contains a function that return type Results and has two arguments:
list[lval] args the actual parameter values when the closure is applied, and
Env e the environment at the site of the call. In the body of the closure we construct a new environment makeEnv(vars, args, tail(callEnv, size(defEnv))) that binds the variables in the lambda expression to the actual parameter values. What is special here is that we shorten the calling environment to the same length as the defining environment. This implements lexical scoping and avoids that names are visible in the called function that were not visible when the function was defined. Remember that Rascal values are immutable, meaning that after a value was created it cannot be changed. Using the above trick, we ensure that the called function has access to the most recent version of its environment. |
| 9 | Evaluates an arbitrary list. As a special case, the empty list is returned as false. Otherwise, all elements are evaluated and the auxiliary function ` apply` is used to apply the value of the first element to the values of the remaining elements. |
| 10 | Apply an Lval to a list of arguments and return a Result. The first case handles a Closure; it amounts to calling the function in the closure (environment handling and parameter binding are done in the closure as discussed above. |
| 11 | Definition of all built-in functions. |
| 12 | A default function that prints an error message when an undefined function is called. |
rascal>import demo::lang::Lisra::Runtime;
ok
rascal>import demo::lang::Lisra::Eval;
ok
rascal>eval(Integer(5));
Lval: Integer(5)
rascal>eval(Atom("x"));
Lval: Atom("x")
rascal>eval(List([Atom("+"), Integer(5), Integer(7)]));
Lval: Integer(12)-
A very modular, rule-based, type safe Lisp interpreter.
-
It is no pleasure to type in `Lval`s directly, that is why a parser is needed, see Parse.
3.3.6. Test
Tests for the Lisp interpreter.
It is good practice to write tests for your software.
Here are our tests for Lisra:
module demo::lang::Lisra::Test
import demo::lang::Lisra::Runtime;
import demo::lang::Lisra::Eval;
test bool eval01() = eval("42").val == Integer(42);
test bool eval02() = eval("x").val == Atom("x");
test bool eval03() = eval("(quote 1)").val == Integer(1);
test bool eval04() = eval("(quote 1 2)").val == List([Integer(1), Integer(2)]);
test bool eval05() = eval("(+ 1 2)").val == Integer(3);
test bool eval06() = eval("(- 5 3)").val == Integer(2);
test bool eval07() = eval("(* 5 3)").val == Integer(15);
test bool eval08() = eval("(\< 3 4)").val != FALSE;
test bool eval09() = eval("(\< 3 2)").val == FALSE;
test bool eval10() = eval("(\> 3 2)").val != FALSE;
test bool eval11() = eval("(\>3 4)").val == FALSE;
test bool eval12() = eval("(equal? 3 3)").val != FALSE;
test bool eval13() = eval("(equal? 3 2)").val == FALSE;
test bool eval14() = eval("(null? ())").val != FALSE;
test bool eval15() = eval("(null? (quote 1 2))").val == FALSE;
test bool eval16() = eval("(begin (define swap (lambda (a b) (list b a))) (swap 1 2))").val ==
List([Integer(2), Integer(1)]);
test bool eval17() = eval("(begin (define * (lambda (a b) (+ a b))) (* 1 2))"). val == Integer(3);
test bool eval18() = eval("(begin (set! x 1) x)").val == Integer(1);
test bool eval19() = eval("(if (\> 5 2) 10 20)").val == Integer(10);
test bool eval20() = eval("(if (\> 2 5) 10 20)").val == Integer(20);
test bool eval21() = eval("(begin (define fac (lambda (n) (if (\> n 1) (* n (fac (- n 1))) 1))) (fac 3))").val == Integer(6);
test bool eval22() = eval("(begin (define length (lambda (x) (if(null? x) 0 (+ 1 (length (cdr x)))))) (length (quote (1 2 3))))").val == Integer(3);
test bool eval23() = eval("(begin (define rev (lambda (x) (if (null? x) () (append (rev (cdr x)) (car x))))) (rev (quote 1 2 3)))").val == List([Integer(3), Integer(2), Integer(1)]);
test bool eval24() = eval("(begin (define F (lambda (x) y)) (set! y 10) (F 1))").val == Integer(10);3.4. Pico
The classical toy language, including a specialized IDE.
Pico is a toy language that has been used as example over the years in many projects and disguishes, Pico has a single purpose in life: being so simple that specifications of every possible language aspect are so simple that they fit on a few pages. It can be summarized as follows:
-
There are two types: natural numbers and strings.
-
Variables have to be declared.
-
Statements are assignment, if-then-else and while-do.
-
Expressions may contain naturals, strings, variables, addition (
+), subtraction (-) and concatenation (||). -
The operators
+and-have operands of type natural and their result is natural. -
The operator
||has operands of type string and its results is also of type string. -
Tests in if-then-else statement and while-statement should be of type natural.
The following aspects of the Pico language will be discussed:
-
Abstract: Abstract syntax for Pico.
-
Assembly: Assembly language for Pico.
-
Compile: Compile a Pico program to assembly language.
-
ControlFlow: Compute the control flow graph for a Pico program.
-
Evaluate: Evaluate a Pico program.
-
IDE: An Integrated Development Environment for Pico.
-
Load: Convert a Pico parse tree into a Pico abstract syntax tree.
-
Syntax: Concrete syntax for Pico.
-
Typecheck: Typechecker a Pico program.
-
Uninit: Find unitialized variables in a Pico program.
-
UseDef: Compute use-def information for the variables in a Pico program.
-
Visualize: Visualize Pico Control Flow Graphs.
Here is a — not so simple — Pico program that computes the factorial function:
begin declare input : natural, (1)
output : natural,
repnr : natural,
rep : natural;
input := 14;
output := 1;
while input - 1 do (2)
rep := output;
repnr := input;
while repnr - 1 do
output := output + rep;
repnr := repnr - 1
od;
input := input - 1
od
endNotes:
| 1 | Pico programs do not have input/output statements, so we use variables for that purpose. |
| 2 | Pico has no multiplication operator so we have to simulate it with repeated addition (yes, simplicity comes at a price!). |
3.4.1. Abstract
Abstract syntax for Pico.
Here is the complete abstract syntax for Pico:
module demo::lang::Pico::Abstract
public data TYPE = natural() | string(); (1)
public alias PicoId = str; (2)
public data PROGRAM = (3)
program(list[DECL] decls, list[STATEMENT] stats);
public data DECL =
decl(PicoId name, TYPE tp);
public data EXP =
id(PicoId name)
| natCon(int iVal)
| strCon(str sVal)
| add(EXP left, EXP right)
| sub(EXP left, EXP right)
| conc(EXP left, EXP right)
;
public data STATEMENT =
asgStat(PicoId name, EXP exp)
| ifElseStat(EXP exp, list[STATEMENT] thenpart, list[STATEMENT] elsepart)
| whileStat(EXP exp, list[STATEMENT] body)
;
anno loc TYPE@location; (4)
anno loc PROGRAM@location;
anno loc DECL@location;
anno loc EXP@location;
anno loc STATEMENT@location;
public alias Occurrence = tuple[loc location, PicoId name, STATEMENT stat]; (5)Notes:
| 1 | The types that may occur in a Pico program are either natural or string. |
| 2 | Introduce PicoId as an alias for Rascal’s str datatype. |
| 3 | Define the various data types that constitute an AST for Pico. Observe that the constructor names match the names used in the concrete syntax, e.g., strCon, add, ifElseStat. |
| 4 | Define an annotation with name location and of type loc (source code location) for all AST types. This will be used when imploding a parse tree into an abstract syntax tree. |
| 5 | Introduce Occurrence as a genereic way of describing the location of various items in the AST. |
3.4.2. Assembly
Assembly language for Pico.
The Compiler will translate Pico programs into the following assembly language.
module demo::lang::Pico::Assembly
import demo::lang::Pico::Abstract;
public data Instr =
dclNat(PicoId Id) // Reserve a memory location for a natural variable
| dclStr(PicoId Id) // Reserve a memory location for a string variable
| pushNat(int intCon) // Push integer constant on the stack
| pushStr(str strCon) // Push string constant on the stack
| rvalue(PicoId Id) // Push the value of a variable on the stack
| lvalue(PicoId Id) // Push the address of a variable on the stack
| assign() // Assign value on top, to variable at address top-1
| add2() // Replace top two stack values by their sum
| sub2() // Replace top two stack values by their difference
| conc2() // Replace top two stack values by their concatenation
| label(str label) // Associate a label with the next instruction
| go(str label) // Go to instruction with given label
| gotrue(str label) // Go to instruction with given label, if top equals 0
| gofalse(str label) // Go to instruction with given label, if top not equal to 0
;
// tag::module[]3.4.3. Compile
Compile a Pico program to assembly language.
The Pico compiler translates Pico programs to Assembly language programs.
module demo::lang::Pico::Compile
import Prelude;
import demo::lang::Pico::Abstract;
import demo::lang::Pico::Assembly;
import demo::lang::Pico::Load;
alias Instrs = list[Instr]; (1)
// compile Expressions.
Instrs compileExp(natCon(int N)) = [pushNat(N)]; (2)
Instrs compileExp(strCon(str S)) = [pushStr(substring(S,1,size(S)-1))];
Instrs compileExp(id(PicoId Id)) = [rvalue(Id)];
public Instrs compileExp(add(EXP E1, EXP E2)) = (3)
[*compileExp(E1), *compileExp(E2), add2()];
Instrs compileExp(sub(EXP E1, EXP E2)) =
[*compileExp(E1), *compileExp(E2), sub2()];
Instrs compileExp(conc(EXP E1, EXP E2)) =
[*compileExp(E1), *compileExp(E2), conc2()];
// Unique label generation
private int nLabel = 0; (4)
private str nextLabel() {
nLabel += 1;
return "L<nLabel>";
}
// Compile a statement
Instrs compileStat(asgStat(PicoId Id, EXP Exp)) =
[lvalue(Id), *compileExp(Exp), assign()];
Instrs compileStat(ifElseStat(EXP Exp, (5)
list[STATEMENT] Stats1,
list[STATEMENT] Stats2)){
elseLab = nextLabel();
endLab = nextLabel();
return [*compileExp(Exp),
gofalse(elseLab),
*compileStats(Stats1),
go(endLab),
label(elseLab),
*compileStats(Stats2),
label(endLab)];
}
Instrs compileStat(whileStat(EXP Exp,
list[STATEMENT] Stats1)) {
entryLab = nextLabel();
endLab = nextLabel();
return [label(entryLab),
*compileExp(Exp),
gofalse(endLab),
*compileStats(Stats1),
go(entryLab),
label(endLab)];
}
// Compile a list of statements
Instrs compileStats(list[STATEMENT] Stats1) = (6)
[ *compileStat(S) | S <- Stats1 ];
// Compile declarations
Instrs compileDecls(list[DECL] Decls) =
[ ((tp == natural()) ? dclNat(Id) : dclStr(Id)) | (7)
decl(PicoId Id, TYPE tp) <- Decls
];
// Compile a Pico program
public Instrs compileProgram(PROGRAM P){ (8)
nLabel = 0;
if(program(list[DECL] Decls, list[STATEMENT] Series) := P){
return [*compileDecls(Decls), *compileStats(Series)];
} else
throw "Cannot happen";
}
public Instrs compileProgram(str txt) = compileProgram(load(txt));Notes:
| 1 | We introduce Instrs as an alias for a list of assembly language instructions. |
| 2 | The compiler consists of the functions compileExp, compileStat, compileStats, compileDecls and compileProgram. They all have a program fragment as argument and return the corresponding list of instructions. |
| 3 | When compiling expressions, note how list splicing (see [Rascal:Values/List]) is used to insert the instructions that are generated for the operands of an operator into the list of instructions for the whole expression. |
| 4 | In order to conveniently write code generators for statements, we introduce a unique label generator. The global variable nLabel contains the index of the last generated label and nextLabel uses this to generate a new, unique label. |
| 5 | Consider code generation for an if-the-else statement:
|
| 6 | Compiling a list of statements conveniently uses a list comprehension and list splicing. |
| 7 | Compiling declarations allocates memory locations of the appropriate type for each declared variable. |
| 8 | compileProgram compiles a gives Pico program to assembly language. |
Here is an example:
rascal>import demo::lang::Pico::Compile;
ok
rascal>compileProgram("begin declare x : natural; x := 47 end");
list[Instr]: [
dclStr("x"),
lvalue("x"),
pushNat(47),
assign()
]Here is the compilation of the factorial program:
rascal>compileProgram("begin declare input : natural,
>>>>>>> ' output : natural,
>>>>>>> ' repnr : natural,
>>>>>>> ' rep : natural;
>>>>>>> ' input := 14;
>>>>>>> ' output := 1;
>>>>>>> ' while input - 1 do
>>>>>>> ' rep := output;
>>>>>>> ' repnr := input;
>>>>>>> ' while repnr - 1 do
>>>>>>> ' output := output + rep;
>>>>>>> ' repnr := repnr - 1
>>>>>>> ' od;
>>>>>>> ' input := input - 1
>>>>>>> ' od
>>>>>>> 'end");
list[Instr]: [
dclStr("input"),
dclStr("output"),
dclStr("repnr"),
dclStr("rep"),
lvalue("input"),
pushNat(14),
assign(),
lvalue("output"),
pushNat(1),
assign(),
label("L1"),
rvalue("input"),
pushNat(1),
sub2(),
gofalse("L2"),
lvalue("rep"),
rvalue("output"),
assign(),
lvalue("repnr"),
rvalue("input"),
assign(),
label("L3"),
rvalue("repnr"),
pushNat(1),
sub2(),
gofalse("L4"),
lvalue("output"),
rvalue("output"),
rvalue("rep"),
add2(),
assign(),
lvalue("repnr"),
rvalue("repnr"),
pushNat(1),
sub2(),
assign(),
go("L3"),
label("L4"),
lvalue("input"),
rvalue("input"),
pushNat(1),
sub2(),
assign(),
go("L1"),
label("L2")
]3.4.4. ControlFlow
Compute the control flow graph for a Pico program.
A control flow graph shows how the entry and exit points of a program are connected with each other via all decision points and statements in the program. Typically, an assignment statement is a single node in the graph and an if-then-else statement creates a decision point (its test) that connects the then branch and the else branch. The exits of each branch are connected to the exit of the if-then-else statement as a whole.
A control flow graph for Pico programs can be created as follows:
module demo::lang::Pico::ControlFlow
import analysis::graphs::Graph;
import demo::lang::Pico::Abstract;
import demo::lang::Pico::Load;
import List;
public data CFNode (1)
= entry(loc location)
| exit()
| choice(loc location, EXP exp)
| statement(loc location, STATEMENT stat);
alias CFGraph = tuple[set[CFNode] entry, Graph[CFNode] graph, set[CFNode] exit]; (2)
CFGraph cflowStat(s:asgStat(PicoId Id, EXP Exp)) { (3)
S = statement(s@location, s);
return <{S}, {}, {S}>;
}
CFGraph cflowStat(ifElseStat(EXP Exp, (4)
list[STATEMENT] Stats1,
list[STATEMENT] Stats2)){
CF1 = cflowStats(Stats1);
CF2 = cflowStats(Stats2);
E = {choice(Exp@location, Exp)};
return < E, (E * CF1.entry) + (E * CF2.entry) + CF1.graph + CF2.graph, CF1.exit + CF2.exit >;
}
CFGraph cflowStat(whileStat(EXP Exp, list[STATEMENT] Stats)) { (5)
CF = cflowStats(Stats);
E = {choice(Exp@location, Exp)};
return < E, (E * CF.entry) + CF.graph + (CF.exit * E), E >;
}
CFGraph cflowStats(list[STATEMENT] Stats){ (6)
if(size(Stats) == 1) {
return cflowStat(Stats[0]);
}
CF1 = cflowStat(Stats[0]);
CF2 = cflowStats(tail(Stats));
return < CF1.entry, CF1.graph + CF2.graph + (CF1.exit * CF2.entry), CF2.exit >;
}
CFGraph cflowProgram(PROGRAM P:program(list[DECL] _, list[STATEMENT] Series)){ (7)
CF = cflowStats(Series);
Entry = entry(P@location);
Exit = exit();
return <{Entry}, ({Entry} * CF.entry) + CF.graph + (CF.exit * {Exit}), {Exit}>;
}
public CFGraph cflowProgram(str txt) = cflowProgram(load(txt)); (8)Notes:
| 1 | First we define a data type CFNODE that represents the various elements of a control flow graph:
|
| 2 | Next we define CFGRAPH , an alias for a tuple consisting of the following three elements:
|
| 3 | The control flow of an assignment statement is computed by wrapping the assignment statement as a CFNODE and return a CFGRAPH with the assignment statement as entry and exit node, and no internal connections. |
| 4 | The control flow of an if-then-else statement is computed as follows:
|
| 5 | The control flow of while-statement is computed in a similar fashion, except that the exit of the loop body has to be connected with the entry of the while loop. |
| 6 | The control flow graph for a series of statements is obtained by connecting the exits and entries of consecutive statements. |
| 7 | The control flow graph of a complete program is obtained by creating an entry and an exit node and connecting them to the graph of the statements of the program. |
| 8 | Shows the steps from text to control flow graph. |
We can now create a CFG for a small Pico program:
rascal>import demo::lang::Pico::ControlFlow;
ok
rascal>cflowProgram("begin declare n : natural, s : string; n := 10; s := \"a\"; while n do s := s + \"a\"; n := n - 1 od end");
tuple[set[CFNode] entry,Graph[CFNode] graph,set[CFNode] exit]: <{entry(|unknown:///|(0,100,<1,0>,<1,100>))},{
<statement(
|unknown:///|(48,8,<1,48>,<1,56>),
asgStat(
"s",
strCon(
"\"a\"",
location=|unknown:///|(53,3,<1,53>,<1,56>),
comments=()),
location=|unknown:///|(48,8,<1,48>,<1,56>),
comments=())),choice(
|unknown:///|(64,1,<1,64>,<1,65>),
id(
"n",
location=|unknown:///|(64,1,<1,64>,<1,65>),
comments=()))>,
<statement(
|unknown:///|(69,12,<1,69>,<1,81>),
asgStat(
"s",
add(
id(
"s",
location=|unknown:///|(74,1,<1,74>,<1,75>),
comments=()),
strCon(
"\"a\"",
location=|unknown:///|(78,3,<1,78>,<1,81>),
comments=()),
location=|unknown:///|(74,7,<1,74>,<1,81>),
comments=()),
location=|unknown:///|(69,12,<1,69>,<1,81>),
comments=())),statement(
|unknown:///|(83,10,<1,83>,<1,93>),
asgStat(
"n",
sub(
id(
"n",
location=|unknown:///|(88,1,<1,88>,<1,89>),
comments=()),
natCon(
1,
location=|unknown:///|(92,1,<1,92>,<1,93>),
comments=()),
location=|unknown:///|(88,5,<1,88>,<1,93>),
comments=()),
location=|unknown:///|(83,10,<1,83>,<1,93>),
comments=()))>,
<statement(
|unknown:///|(39,7,<1,39>,<1,46>),
asgStat(
"n",
natCon(
10,
location=|unknown:///|(44,2,<1,44>,<1,46>),
comments=()),
location=|unknown:///|(39,7,<1,39>,<1,46>),
comments=())),statement(
|unknown:///|(48,8,<1,48>,<1,56>),
asgStat(
"s",
strCon(
"\"a\"",
location=|unknown:///|(53,3,<1,53>,<1,56>),
comments=()),
location=|unknown:///|(48,8,<1,48>,<1,56>),
comments=()))>,
<statement(
|unknown:///|(83,10,<1,83>,<1,93>),
asgStat(
"n",
sub(
id(
"n",
location=|unknown:///|(88,1,<1,88>,<1,89>),
comments=()),
natCon(
1,
location=|unknown:///|(92,1,<1,92>,<1,93>),
comments=()),
location=|unknown:///|(88,5,<1,88>,<1,93>),
comments=()),
location=|unknown:///|(83,10,<1,83>,<1,93>),
comments=())),choice(
|unknown:///|(64,1,<1,64>,<1,65>),
id(
"n",
location=|unknown:///|(64,1,<1,64>,<1,65>),
comments=()))>,
<entry(|unknown:///|(0,100,<1,0>,<1,100>)),statement(
|unknown:///|(39,7,<1,39>,<1,46>),
asgStat(
"n",
natCon(
10,
location=|unknown:///|(44,2,<1,44>,<1,46>),
comments=()),
location=|unknown:///|(39,7,<1,39>,<1,46>),
comments=()))>,
<choice(
|unknown:///|(64,1,<1,64>,<1,65>),
id(
"n",
location=|unknown:///|(64,1,<1,64>,<1,65>),
comments=())),exit()>,
<choice(
|unknown:///|(64,1,<1,64>,<1,65>),
id(
"n",
location=|unknown:///|(64,1,<1,64>,<1,65>),
comments=())),statement(
|unknown:///|(69,12,<1,69>,<1,81>),
asgStat(
"s",
add(
id(
"s",
location=|unknown:///|(74,1,<1,74>,<1,75>),
comments=()),
strCon(
"\"a\"",
location=|unknown:///|(78,3,<1,78>,<1,81>),
comments=()),
location=|unknown:///|(74,7,<1,74>,<1,81>),
comments=()),
location=|unknown:///|(69,12,<1,69>,<1,81>),
comments=()))>
},{exit()}>Is the above not very motivating to move on to Visualize?
3.4.5. Evaluate
Evaluate a Pico program.
A complete evaluator (interpreter) for Pico is defined below.
module demo::lang::Pico::Eval
import demo::lang::Pico::Abstract;
import demo::lang::Pico::Load;
data PicoValue = natval(int n) | strval(str s) | errorval(loc l, str msg); (1)
alias VENV = map[PicoId, PicoValue]; (2)
// Evaluate Expressions.
PicoValue evalExp(exp:natCon(int N), VENV env) = natval(N);
PicoValue evalExp(exp:strCon(str S), VENV env) = strval(S);
PicoValue evalExp(exp:id(PicoId Id), VENV env) =
env[Id]? ? env[Id] : errorval(exp@location, "Uninitialized variable <Id>");
PicoValue evalExp(exp:add(EXP E1, EXP E2), VENV env) =
(natval(n1) := evalExp(E1, env) &&
natval(n2) := evalExp(E2, env)) ? natval(n1 + n2)
: errorval(exp@location, "+ requires natural arguments");
PicoValue evalExp(exp:sub(EXP E1, EXP E2), VENV env) =
(natval(n1) := evalExp(E1, env) &&
natval(n2) := evalExp(E2, env)) ? natval(n1 - n2)
: errorval(exp@location, "- requires natural arguments");
PicoValue evalExp(exp:conc(EXP E1, EXP E2), VENV env) =
(strval(s1) := evalExp(E1, env) &&
strval(s2) := evalExp(E2, env)) ? strval(s1 + s2)
: errorval(exp@location, "|| requires string arguments");
// Evaluate a statement
VENV evalStat(stat:asgStat(PicoId Id, EXP Exp), VENV env) {
env[Id] = evalExp(Exp, env);
return env;
}
VENV evalStat(stat:ifElseStat(EXP Exp,
list[STATEMENT] Stats1,
list[STATEMENT] Stats2),
VENV env) =
evalStats(evalExp(Exp, env) != natval(0) ? Stats1 : Stats2, env);
VENV evalStat(stat:whileStat(EXP Exp,
list[STATEMENT] Stats1),
VENV env) {
while(evalExp(Exp, env) != natval(0)){
env = evalStats(Stats1, env);
}
return env;
}
// Evaluate a list of statements
VENV evalStats(list[STATEMENT] Stats1, VENV env) {
for(S <- Stats1){
env = evalStat(S, env);
}
return env;
}
// Eval declarations
VENV evalDecls(list[DECL] Decls) =
( Id : (tp == demo::lang::Pico::Abstract::natural() ? natval(0) : strval(""))
| decl(PicoId Id, TYPE tp) <- Decls
);
// Evaluate a Pico program
public VENV evalProgram(PROGRAM P){
if(program(list[DECL] Decls, list[STATEMENT] Series) := P){
VENV env = evalDecls(Decls);
return evalStats(Series, env);
} else
throw "Cannot happen";
}
public VENV evalProgram(str txt) = evalProgram(load(txt));Notes:
| 1 | First we introduce a data type PicoValue that wraps all possible values that can occur at run-time. |
| 2 | Compared to [Pico/Typecheck], we use VENV, a value environment (a map from Pico identifiers to Pico values).
|
Here is how to evaluate a Pico program:
rascal>import demo::lang::Pico::Eval;
ok
rascal>evalProgram("begin declare x : natural, y : natural; x := 1; y := x + 5 end");
map[str, PicoValue]: (
"x":natval(1),
"y":natval(6)
)3.4.6. IDE
An Integrated Development Environment for Pico.
Unresolved directive in Languages/Pico/IDE/IDE.adoc - include::/export/scratch1/jenkins/home/workspace/usethesource_rascal_master-S5ZKBVP7G6AAXOCX5AHV2IJ2QL35PDF5FJHTCPD6ZB5NPZDM4Q3Q/src/org/rascalmpl/library/demo/lang/Pico/Plugin.rsc[tags=module]-
First the name of the language and its file name extension are defined (image:../images//1.png).
-
Next the connection with the parser (image:../images//2.png), checkers (image:../images//3.png), evaluator (image:../images//4.png), compiler (image:../images//5.png), and visualizer (image:../images//6.png) are defined.
-
(image:../images//7.png) combines the above into a set of contributions to the Pico IDE.
-
The actual creation of the Pico IDE is done by
registerPico(image:../images//8.png) that:-
Registers the Pico language with name, file name extension and Parser. Whenever a user clicks on a
.picofile an editor will opened and the parsed file will be displayed in it. -
Registers annotators for Pico programs. Annotators run whenever a change is made to a Pico program in an open editor.
-
Registers contributions to the context menu in the editor. When the user right-clicks, the context menu pops up and it will show a Pico entry with actions defined in the contributions.
-
Let’s write a Pico program that produces a string of "a"s:
As can be seen in the editor above, we get an error since we made a typo (missing comma) in the declarations. We correct it:
Now it turns out that we had erroneously used the + operator on strings (it should be ||). We correct it:
Now we get a warning that variable n is not initialized. We correct it and get an error-free and warning-free program:
3.4.7. Load
Convert a Pico parse tree into a Pico abstract syntax tree.
The mapping between parse tree and abstract sybtax tree is achieved as follows:
module demo::lang::Pico::Load
import Prelude;
import demo::lang::Pico::Syntax;
import demo::lang::Pico::Abstract;
public PROGRAM load(str txt) = implode(#PROGRAM, parse(#Program, txt));Notes:
-
The function
loadtakes a string as argument (supposedly the source code of a Pico program) and returns a value of typePROGRAM, the abstract syntax tree of the input program. In case the input program is syntactically incorrect, aParseErrorexception will be thrown, see RuntimeException. -
parse(#Program, txt): parsetxtaccording to the non-terminalProgram. Note that#Programis a reified type, i.e., the typeProgramis represented as an ordinary Rascal value and passed as argument to theparsefunction, see reified types. Theparsefunction returns a parse tree of the input program. -
implode(#PROGRAM, parse(#Program, txt)): transform the parse returned byparseinto an abstract syntax tree of typePROGRAM. The [$Rascal:implode] function performs the automatic mapping between elements in the parse tree and their counterpart in the abstract syntax.
The function load can be used as follows:
rascal>import demo::lang::Pico::Load;
ok
rascal>load("begin declare x : natural; x := 3 end");
warning, ambiguity predicted: conc: Expression lhs "||" Expression rhs lacks left or right associativity
PROGRAM: program(
[decl(
"x",
natural(
location=|unknown:///|(18,7,<1,18>,<1,25>),
comments=()),
location=|unknown:///|(14,11,<1,14>,<1,25>),
comments=())],
[asgStat(
"x",
natCon(
3,
location=|unknown:///|(32,1,<1,32>,<1,33>),
comments=()),
location=|unknown:///|(27,6,<1,27>,<1,33>),
comments=())],
location=|unknown:///|(0,37,<1,0>,<1,37>),
comments=())WARNING: unexpected errors in the above SHELL example. Documentation author please fix! Observe how the various parts of the abstract syntax tree are annotated with location attributes.
3.4.8. Syntax
Concrete syntax for Pico.
module demo::lang::Pico::Syntax
import ParseTree;
lexical Id = [a-z][a-z0-9]* !>> [a-z0-9];
lexical Natural = [0-9]+ ;
lexical String = "\"" ![\"]* "\"";
layout Layout = WhitespaceAndComment* !>> [\ \t\n\r%];
lexical WhitespaceAndComment
= [\ \t\n\r]
| @category="Comment" ws2: "%" ![%]+ "%"
| @category="Comment" ws3: "%%" ![\n]* $
;
start syntax Program
= program: "begin" Declarations decls {Statement ";"}* body "end" ;
syntax Declarations
= "declare" {Declaration ","}* decls ";" ;
syntax Declaration = decl: Id id ":" Type tp;
syntax Type
= natural:"natural"
| string :"string"
;
syntax Statement
= asgStat: Id var ":=" Expression val
| ifElseStat: "if" Expression cond "then" {Statement ";"}* thenPart "else" {Statement ";"}* elsePart "fi"
| whileStat: "while" Expression cond "do" {Statement ";"}* body "od"
;
syntax Expression
= id: Id name
| strCon: String string
| natCon: Natural natcon
| bracket "(" Expression e ")"
> left conc: Expression lhs "||" Expression rhs
> left ( add: Expression lhs "+" Expression rhs
| sub: Expression lhs "-" Expression rhs
)
;
public start[Program] program(str s) {
return parse(#start[Program], s);
}
public start[Program] program(str s, loc l) {
return parse(#start[Program], s, l);
}Notes:
-
Id,NaturalandStringare the basic lexical tokens of the Pico language. -
Layoutdefines the white space and comments that may occur in a Pico program. -
Some lexical rules are labeled with
@category="Comment". This is for the benefit of syntax highlighting. -
The start symbol of the Pico grammar is called
Program. -
The rules for
Expressiondescribe the priority and associativity of the operators: all operators are left-associative and||has a higher priority then+and-. -
Two auxiliary functions
programare defined that parse a given string or a given location as Pico program.
3.4.9. Typecheck
Typechecker a Pico program.
Recall the following properties of Pico that are relevant for type checking:
-
There are two types: natural numbers and strings.
-
Variables have to be declared.
-
Expressions may contain naturals, strings, variables, addition (
+), subtraction (-) and concatenation (||). -
The operators
+and-have operands of type natural and their result is natural. -
The operator
||has operands of type string and its results is also of type string. -
Tests in if-then-else statement and while-statement should be of type natural.
The type checker is going to check these rules and will produce an error message when they are violated.
module demo::lang::Pico::Typecheck
import Prelude;
import demo::lang::Pico::Abstract;
import demo::lang::Pico::Load;
alias TENV = tuple[ map[PicoId, TYPE] symbols, list[tuple[loc l, str msg]] errors]; (1)
TENV addError(TENV env, loc l, str msg) = env[errors = env.errors + <l, msg>]; (2)
str required(TYPE t, str got) = "Required <getName(t)>, got <got>"; (3)
str required(TYPE t1, TYPE t2) = required(t1, getName(t2));
// compile Expressions.
TENV checkExp(exp:natCon(int N), TYPE req, TENV env) = (4)
req == natural() ? env : addError(env, exp@location, required(req, "natural"));
TENV checkExp(exp:strCon(str S), TYPE req, TENV env) =
req == string() ? env : addError(env, exp@location, required(req, "string"));
TENV checkExp(exp:id(PicoId Id), TYPE req, TENV env) { (5)
if(!env.symbols[Id]?)
return addError(env, exp@location, "Undeclared variable <Id>");
tpid = env.symbols[Id];
return req == tpid ? env : addError(env, exp@location, required(req, tpid));
}
TENV checkExp(exp:add(EXP E1, EXP E2), TYPE req, TENV env) = (6)
req == natural() ? checkExp(E1, natural(), checkExp(E2, natural(), env))
: addError(env, exp@location, required(req, "natural"));
TENV checkExp(exp:sub(EXP E1, EXP E2), TYPE req, TENV env) = (7)
req == natural() ? checkExp(E1, natural(), checkExp(E2, natural(), env))
: addError(env, exp@location, required(req, "natural"));
TENV checkExp(exp:conc(EXP E1, EXP E2), TYPE req, TENV env) = (8)
req == string() ? checkExp(E1, string(), checkExp(E2, string(), env))
: addError(env, exp@location, required(req, "string"));
// check a statement
TENV checkStat(stat:asgStat(PicoId Id, EXP Exp), TENV env) { (9)
if(!env.symbols[Id]?)
return addError(env, stat@location, "Undeclared variable <Id>");
tpid = env.symbols[Id];
return checkExp(Exp, tpid, env);
}
TENV checkStat(stat:ifElseStat(EXP Exp, (10)
list[STATEMENT] Stats1,
list[STATEMENT] Stats2),
TENV env){
env0 = checkExp(Exp, natural(), env);
env1 = checkStats(Stats1, env0);
env2 = checkStats(Stats2, env1);
return env2;
}
TENV checkStat(stat:whileStat(EXP Exp,
list[STATEMENT] Stats1),
TENV env) {
env0 = checkExp(Exp, natural(), env);
env1 = checkStats(Stats1, env0);
return env1;
}
// check a list of statements
TENV checkStats(list[STATEMENT] Stats1, TENV env) { (11)
for(S <- Stats1){
env = checkStat(S, env);
}
return env;
}
// check declarations
TENV checkDecls(list[DECL] Decls) = (12)
<( Id : tp | decl(PicoId Id, TYPE tp) <- Decls), []>;
// check a Pico program
public TENV checkProgram(PROGRAM P){ (13)
if(program(list[DECL] Decls, list[STATEMENT] Series) := P){
TENV env = checkDecls(Decls);
return checkStats(Series, env);
} else
throw "Cannot happen";
}
(14)
public list[tuple[loc l, str msg]] checkProgram(str txt) = checkProgram(load(txt)).errors;Notes:
| 1 | We will use TENV (short for type environment, as an alias for a tuple that contains all relevant type information:
|
| 2 | addError is an auxiliary function to add in a given type environment an error message to the list of errors. It returns a new type environment. |
| 3 | required`is an auxiliarty function to produce readable messages, e.g., `"Required natural, got string". |
| 4 | The actual type checking is done by the functions checkExp, checkStat, checkStats, checkDecls and checkProgram. They all have three arguments:
|
| 5 | An important case is to check whether an identifier has been defined and, if so, whether it is defined with the expected type. |
| 6 | Check add. |
| 7 | Check sub. |
| 8 | Check conc. |
| 9 | An assignment statement is checked: the identifier on the left-hand side should have been declared and should be type compatible with the expression on the right-hand side. |
| 10 | Checking if- and while-statements amounts to checking the embedded statements and ensuring that the type of the test is natural. |
| 11 | Checking a list of statements amounts to checking each statement in the list. |
| 12 | Checking declarations amounts to extracting each (id, type) pair form the declarations and using a map comprehension to build a type environment. |
| 13 | Checking a complete Pico program is achieved by first checking the declarations of the program and using the resulting type environment to check its body. |
| 14 | checkProgram defines how to check the source code of a given Pico program. |
Checking an erroneous program goes like this:
rascal>import demo::lang::Pico::Typecheck;
ok
rascal>checkProgram("begin declare x : natural; x := \"abc\" end");
warning, ambiguity predicted: conc: Expression lhs "||" Expression rhs lacks left or right associativity
lrel[loc l,str msg]: [<|unknown:///|(33,5,<1,33>,<1,38>),"Required natural, got string">]WARNING: unexpected errors in the above SHELL example. Documentation author please fix! The error location will be use later to give specific messages in the IDE.
3.4.10. Uninit
Find unitialized variables in a Pico program.
Uninitialized variables are variables that are used without being initialized. This means that there is a path in the control flow graph from the entry point of the program to a specific use of a variable, where that path does not contain a definition of that variable.
This can be computed as follows:
module demo::lang::Pico::Uninit
import demo::lang::Pico::Abstract;
import demo::lang::Pico::Load;
import demo::lang::Pico::UseDef;
import demo::lang::Pico::ControlFlow;
import analysis::graphs::Graph;
public set[CFNode] defNodes(PicoId Id, set[Occurrence] Defs) =
{statement(occ.stat@location, occ.stat) | Occurrence occ <- Defs, occ.name == Id};
public set[Occurrence] uninitProgram(PROGRAM P) {
D = defs(P); (1)
CFG = cflowProgram(P); (2)
return { occ | occ <- uses(P), (3)
any(CFNode N <- reachX(CFG.graph, CFG.entry, defNodes(occ.name, D)),
N has location && occ.location <= N.location)
}; (4)
}
public set[Occurrence] uninitProgram(str txt) = uninitProgram(load(txt)); (5)| 1 | First, we determine the variable definitions of the program, |
| 2 | and its control flow graph. |
| 3 | Next we ask for every use of a variable the question: can it be reached from the entries of the program without encountering a definition? This determined as follows:
|
| 4 | The complete comprehension returns the set of occurrences of uninitialized variables. |
The function uninitProgram performs this analysis on the source text of a Pico program.
Here is a simple example, where variable p is used without intialization:
rascal>import demo::lang::Pico::Uninit;
ok
rascal>uninitProgram("begin declare n : natural, m : natural, p : natural; n := 10; m := n + p end");
rel[loc location,str name,STATEMENT stat]: {<|unknown:///|(71,1,<1,71>,<1,72>),"p",asgStat(
"m",
add(
id(
"n",
location=|unknown:///|(67,1,<1,67>,<1,68>),
comments=()),
id(
"p",
location=|unknown:///|(71,1,<1,71>,<1,72>),
comments=()),
location=|unknown:///|(67,5,<1,67>,<1,72>),
comments=()),
location=|unknown:///|(62,10,<1,62>,<1,72>),
comments=())>}3.4.11. UseDef
Compute use-def information for the variables in a Pico program.
The definitions of a variable are the source code locations where a variable gets a value. The uses of a variable are the location where the value of that variable is used. Both concepts are relevant for program analysis and are defined here.
module demo::lang::Pico::UseDef
import demo::lang::Pico::Abstract;
set[Occurrence] usesExp(EXP e, STATEMENT s) = (1)
u:id(PicoId Id1) := e ? {< u@location, Id1, s>}
: {< u@location, Id2, s> | /u:id(PicoId Id2) <- e };
set[Occurrence] usesStat(s:asgStat(PicoId Id, EXP e)) = usesExp(e, s); (2)
set[Occurrence] usesStat(s: ifElseStat(EXP e,
list[STATEMENT] s1,
list[STATEMENT] s2)) =
usesExp(e, s) + usesStats(s1) + usesStats(s2);
set[Occurrence] usesStat(s: whileStat(EXP e,
list[STATEMENT] s1)) =
usesExp(e, s) + usesStats(s1);
set[Occurrence] usesStats(list[STATEMENT] stats) =
{*usesStat(s) | s <- stats};
public set[Occurrence] uses(PROGRAM p) = usesStats(p.stats); (3)
public set[Occurrence] defs(PROGRAM p) = (4)
{ < stat@location, v, stat > | /stat:asgStat(PicoId v, EXP _) <- p.stats};
// end::module[]Recall that Occurrence was introduced in Abstract; it is a parameterized container to associate program entities with their location.
| 1 | The function usesExp computes a set of occurrences (uses) of Pico identifiers in a given statement:
|
| 2 | useStat extracts uses from all statement variants. |
| 3 | The function uses simply applies usesStats to the statement part of its program argument. |
| 4 | The function defs has a Pico program as argument and returns a set of occurrences (definitions) of Pico identifiers. The definition consists of a single set comprehension that consists of the following parts:
|
3.4.12. Visualize
Visualize Pico Control Flow Graphs.
|
Description
The visualization library is being reimplemented and reorganized; the information provided here maybe inaccurate or even incorrect.
|
Unresolved directive in Languages/Pico/Visualize/Visualize.adoc - include::/export/scratch1/jenkins/home/workspace/usethesource_rascal_master-S5ZKBVP7G6AAXOCX5AHV2IJ2QL35PDF5FJHTCPD6ZB5NPZDM4Q3Q/src/org/rascalmpl/library/demo/lang/Pico/Visualize.rsc[tags=module]| 1 | We want to include the text of expressions in the relevant Figure nodes, this is achieved by make. |
| 2 | An editor property is attached to each Figure node: clicking on the node opens an editor for the corresponding file. |
| 3 | visNode implements the visualization per CFG node. |
| 4 | Since Figure nodes in a visual graph need an id property, we define here a scheme to associate unique identifiers to each Figure node. |
| 5 | The complete visualization of a CFG is implemented by visCFG: it gets the CFG hraph as arguments and then
|
Let’s now apply this:
import demo::lang::Pico::ControlFlow;
import demo::lang::Pico::Visualize;
CFG = cflowProgram("begin declare n : natural, s : string; n := 10; s := \"a\"; while n do s := s + \"a\"; n := n - 1 od end");
render(visCFG(CFG.graph));The resulting visualization looks like this:
4. Metrics
Computing
4.1. Measuring Java
A few steps using the M3 model to compute basic metrics for a Java project in Eclipse
This is a recipe for computing basic or more advanced metrics from a Java project in Eclipse. We assume:
-
You have Rascal installed in an Eclipse instance.
-
You have a Java project in your Eclipse workspace that compiles without errors. Let’s call it
HelloWorld.
Now we will follow the EASY paradigm:
-
a library will be used to parse the Java code generating [Rascalopedia:AbstractSyntaxTree]
-
the same library will generate a [Rascal:Values/Relation]al model to represent interesting facts between Java source code artifacts
-
then we can write queries over the generated trees and relations using [Rascal:Expressions].
These are a number of recipes for measuring different things about Java:
-
[MeasuringClasses]
-
[MeasuringMethods]
First we import the basic data types for representing Java. The model is called M3, and its definition is split acros a generic language independent module called [Rascal:analysis/m3/Core] and a Java specific part called [Rascal:lang/java/m3/Core]. Have a look at the documentation of these modules later. For now we will go through using them in a few examples.
rascal>import lang::java::m3::Core;
okThen we import the API for extracting an M3 model from an Eclipse project.
rascal>import lang::java::jdt::m3::Core;
|prompt:///|(0,33,<1,0>,<1,33>): Could not import module lang::java::jdt::m3::Core: can not find in search path
Advice: |http://tutor.rascal-mpl.org/Errors/Static/ModuleImport/ModuleImport.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! Calling the following function generates an enormous value representing everything the Eclipse Java compiler knows about this project:
rascal>myModel = createM3FromEclipseProject(|project://example-project|);
|prompt:///|(10,26,<1,10>,<1,36>): Undeclared variable: createM3FromEclipseProject
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! .Benefits
-
Notice that all these [$Rascal:Values/Location] literals are hyperlinks and you can click on them to go the source code that they point to. Try it!
4.1.1. Measuring Classes
First we import the basic data types for representing Java. The model is called M3, and its definition is split acros a generic language independent module called [Rascal:analysis/m3/Core] and a Java specific part called [Rascal:lang/java/m3/Core]. Have a look at the documentation of these modules later. For now we will go through using them in a few examples.
rascal>import lang::java::m3::Core;
okThen we import the API for extracting an M3 model from an Eclipse project.
rascal>import lang::java::jdt::m3::Core;
|prompt:///|(0,33,<1,0>,<1,33>): Could not import module lang::java::jdt::m3::Core: can not find in search path
Advice: |http://tutor.rascal-mpl.org/Errors/Static/ModuleImport/ModuleImport.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! Calling the following function generates an enormous value representing everything the Eclipse Java compiler knows about this project:
rascal>myModel = createM3FromEclipseProject(|project://example-project|);
|prompt:///|(10,26,<1,10>,<1,36>): Undeclared variable: createM3FromEclipseProject
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! Next, let’s focus on the containment relation. This defines what parts of the source code are parts of which other parts:
rascal>myModel.containment
|prompt:///|(0,7,<1,0>,<1,7>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! As you can read, classes contain methods, methods contain variables, etc. Classes could also contain other classes (nested classes), and methods can even contain classes (anonymous classes). Let’s focus on a specific class, and project what it contains from the relation:
rascal>myModel.containment[|java+class:///HelloWorld|]
|prompt:///|(0,7,<1,0>,<1,7>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! Let’s filter the methods:
rascal>helloWorldMethods = [ e | e <- myModel.containment[|java+class:///HelloWorld|], e.scheme == "java+method"];
|prompt:///|(31,7,<1,31>,<1,38>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! And we are ready to compute our first metric. How many methods does this class contain?
rascal>import List;
ok
rascal>size(helloWorldMethods)
|prompt:///|(5,17,<1,5>,<1,22>): Undeclared variable: helloWorldMethods
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! No magic applied! It is just a little query on a model that knows everything about the code. Let’s generalize and compute the number of methods for all classes in one big expression. First a function to compute the number for a given class:
rascal>int numberOfMethods(loc cl, M3 model) = size([ m | m <- model.containment[cl], isMethod(m)]);
int (loc, M3): function(|prompt:///|(0,93,<1,0>,<1,93>))then we apply this new function to give us a map from classes to integers:
rascal>map[loc class, int methodCount] numberOfMethodsPerClass = (cl:numberOfMethods(cl, myModel) | <cl,_> <- myModel.containment, isClass(cl));
|prompt:///|(103,7,<1,103>,<1,110>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! how about the number of fields?
rascal>int numberOfFields(loc cl, M3 model) = size([ m | m <- model.containment[cl], isField(m)]);
int (loc, M3): function(|prompt:///|(0,91,<1,0>,<1,91>))
rascal>map[loc class, int fieldCount] numberOfFieldsPerClass = (cl:numberOfFields(cl, myModel) | <cl,_> <- myModel.containment, isClass(cl));
|prompt:///|(100,7,<1,100>,<1,107>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! what is the ratio between fields and methods for each class?
rascal>(cl : (numberOfFieldsPerClass[cl] * 1.0) / (numberOfMethodsPerClass[cl] * 1.0) | cl <- classes(myModel))
|prompt:///|(95,7,<1,95>,<1,102>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! .Benefits
4.1.2. Measuring Methods
rascal>import lang::java::m3::Core;
ok
rascal>import lang::java::jdt::m3::Core;
|prompt:///|(0,33,<1,0>,<1,33>): Could not import module lang::java::jdt::m3::Core: can not find in search path
Advice: |http://tutor.rascal-mpl.org/Errors/Static/ModuleImport/ModuleImport.html|
ok
rascal>import lang::java::jdt::m3::AST;
|prompt:///|(0,32,<1,0>,<1,32>): Could not import module lang::java::jdt::m3::AST: can not find in search path
Advice: |http://tutor.rascal-mpl.org/Errors/Static/ModuleImport/ModuleImport.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! First extract our overview model
rascal>myModel = createM3FromEclipseProject(|project://example-project|);
|prompt:///|(10,26,<1,10>,<1,36>): Undeclared variable: createM3FromEclipseProject
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! Now let’s focus on the methods
rascal>myMethods = methods(myModel);
|prompt:///|(20,7,<1,20>,<1,27>): Undeclared variable: myModel
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! What is the source code for a method?
rascal>import IO;
ok
rascal>methodSrc = readFile(|java+method:///HelloWorld/main(java.lang.String%5B%5D)|);
|std:///IO.rsc|(12308,1718,<531,0>,<567,24>): IO("Unsupported scheme java+method")
at *** somewhere ***(|std:///IO.rsc|(12308,1718,<531,0>,<567,24>))
at readFile(|prompt:///|(21,56,<1,21>,<1,77>))
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! let’s print it:
rascal>println(methodSrc)
|prompt:///|(8,9,<1,8>,<1,17>): Undeclared variable: methodSrc
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! how many words in this method?
rascal>(0 | it + 1 | /\W+/ := methodSrc)
|prompt:///|(23,9,<1,23>,<1,32>): Undeclared variable: methodSrc
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! let’s get its AST
rascal>methodAST = getMethodASTEclipse(|java+method:///HelloWorld/main(java.lang.String%5B%5D)|, model=myModel);
|prompt:///|(12,19,<1,12>,<1,31>): Undeclared variable: getMethodASTEclipse
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! Now we count the number of expressions:
rascal>(0 | it + 1 | /Expression _ := methodAST)
|prompt:///|(31,9,<1,31>,<1,40>): Undeclared variable: methodAST
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! or give us the locations of all expressions:
rascal>[m@src | /Expression m := methodAST]
|prompt:///|(26,9,<1,26>,<1,35>): Undeclared variable: methodAST
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! the size should be the same, right?
rascal>import List;
ok
rascal>size([m@src | /Expression m := methodAST]) == (0 | it + 1 | /Expression _ := methodAST)
|prompt:///|(31,9,<1,31>,<1,40>): Undeclared variable: methodAST
Advice: |http://tutor.rascal-mpl.org/Errors/Static/UndeclaredVariable/UndeclaredVariable.html|
okWARNING: unexpected errors in the above SHELL example. Documentation author please fix! .Benefits
5. Visualization
Recipes for creating visualizations.
|
Description
The visualization library is being reimplemented and reorganized; the information provided here maybe inaccurate or even incorrect
|
We cover the following topics:
-
ADT: Visualize an Algebraic Datatype as a tree.
-
Draw a Logo: Draw the Rascal logo.
-
Interactive Box Height: Control the height of a box with user input.
-
My First Box: Drawing a box in many variations.
-
ParseTree: Visualize a parse tree.
-
Playing With Properties: Illustrate the effect of various figure properties.
5.1. ADT
Visualize an Algebraic Datatype as a tree.
In [ColoredTrees] we have discussed the Algebraic Data Type ColoredTree. Here we show how to create a visualization for them. The global approach is:
-
Define a function
visColoredTreethat has a ColoredTree as argument and creates aFigurefor it. -
Display the resulting figure using [$Rascal:Render/render].
Here is our solution:
module demo::vis::VisADT
//import vis::Figure;
//import vis::Render;
//
//data ColoredTree = leaf(int N)
// | red(ColoredTree left, ColoredTree right)
// | black(ColoredTree left, ColoredTree right)
// | green(ColoredTree left, ColoredTree right)
// ;
//
//Figure visColoredTree(leaf(int N)) =
// box(text("<N>"), gap(2), fillColor("lightyellow")); (1)
//
//Figure visColoredTree(red(ColoredTree left, ColoredTree right)) =
// visNode("red", left, right); (2)
//
//Figure visColoredTree(black(ColoredTree left, ColoredTree right)) =
// visNode("black", left, right);
//
//Figure visColoredTree(green(ColoredTree left, ColoredTree right)) =
// visNode("green", left, right);
//
//Figure visNode(str color, ColoredTree left, ColoredTree right) = (3)
// tree(ellipse(fillColor(color)), [visColoredTree(left), visColoredTree(right)]);
//
//ColoredTree rb = red(black(leaf(1), red(leaf(2),leaf(3))), green(leaf(3), leaf(4)));| 1 | A leaf is represented as its number converted to text, surrounded by a lightyellow box. |
| 2 | The figure for non-leaf nodes of a ColoredTree is generated by the auxiliary function visNode. |
| 3 | visNode represents the node itself as a [$Rascal:Figures/tree] that has a colored ellipse as root and the visualization of two ColoredTrees as children. |
For the example ColoredTree rb we can set a standard (see /Libraries#std) size and standard gap:
import demo::vis::VisADT;
render(space(visColoredTree(rb), std(size(30)), std(gap(30))));and the result is:
Note that:
-
We place the Figure that is produced by
viscoloredTreein aspacefor the sole purpose that add extra properties to it. -
We use
std(size(30))and ` std(gap(30))` to achieve that these properties are set for all subfigures.
Some further custumizations are possible. By default, the tree visualization uses manhattan style. If we turn it off
import demo::vis::VisADT;
render(space(visColoredTree(rb), std(size(30)), std(gap(30)), std(manhattan(false))));the result is:
It is also possible to change the orientation of the tree and draw it, for example, from left to right:
import demo::vis::VisADT;
render(space(visColoredTree(rb), std(size(30)), std(gap(30)), std(orientation(leftRight()))));the result is:
5.2. Draw a Logo
Draw the Rascal logo.
Given a 50x50 matrix containing the colors of the Rascal logo, we can reproduce it as visualization.
Here is the solution:
module demo::vis::Logo
//import vis::Figure;
//import vis::Render;
//
//public list[int] LogoData = [
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xfff9f9f9, 0xff9d9c9e, 0xff616063, 0xffa3a2a4, 0xfffcfcfc, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xfff7f7f7, 0xff595759, 0xff121014, 0xff616063, 0xfffcfcfc, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xfffbfbfb, 0xff7f7e80, 0xff646163, 0xffc2c1c3, 0xfff7f7f7,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffdddddd, 0xff747375, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffc1c0c1, 0xff8e8782, 0xffc6bdb2, 0xff908984, 0xff5b595a,
//0xffcccccd, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xff565357, 0xffd7d7d7, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xfff3f3f3, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff504e4f, 0xffd3c9be, 0xffe2d7cb, 0xffe1d7cb, 0xffdfd4c9,
//0xff4c4848, 0xffb5b5b7, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffdcdbdc, 0xff242226, 0xffdfdfdf, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff7f7e80, 0xff131115, 0xff636264, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffc8c8c9, 0xff696360, 0xffeadfd2, 0xffbcb3aa, 0xffbbb2a9, 0xffdfd5c8,
//0xffe5d9cd, 0xff645e5c, 0xffa09ea1, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xff7c7b7d, 0xff161418, 0xff9d9c9e, 0xfff9f9f9, 0xffffffff, 0xfffefefe, 0xffffffff,
//0xfffefefe, 0xffffffff, 0xffe4e4e4, 0xffe5e5e5, 0xffffffff, 0xffffffff, 0xfff7f7f7, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff747274, 0xff0e0c10, 0xff09070c, 0xfffafafa, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff58575a, 0xffd5cbc0, 0xffe0d5c9, 0xffdfd4c8, 0xffb5ada4, 0xff948d87,
//0xffede1d5, 0xffded4c8, 0xff7c7672, 0xff8c8b8d, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xfffefefe, 0xffffffff, 0xffffffff, 0xfff7f7f8, 0xff4a484b, 0xff151217, 0xff454447, 0xffe6e7e6, 0xffffffff, 0xffffffff,
//0xffd8d7d8, 0xffd7d7d7, 0xffffffff, 0xffa3a2a4, 0xfff4f4f4, 0xffffffff, 0xffd5d4d5, 0xffffffff, 0xffffffff, 0xffffffff,
//0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xfff7f7f7, 0xff939193, 0xff717072, 0xfffefefe, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xfff5f5f6, 0xff504d4f, 0xffede2d4, 0xffdfd5c9, 0xffe1d6ca, 0xffe8ddd1, 0xffa8a099,
//0xff817b76, 0xffdfd5ca, 0xffe4dace, 0xff6a6562, 0xffc2c2c2, 0xffffffff, 0xfffefefe, 0xffffffff, 0xfffdfdfd, 0xffffffff,
//0xffffffff, 0xffe3e3e4, 0xfff2f2f3, 0xffffffff, 0xffffffff, 0xff403d41, 0xff141217, 0xff131116, 0xff9a999b, 0xffd3d3d4,
//0xffdfdfdf, 0xff59575a, 0xffc6c6c7, 0xff3a373b, 0xffecebec, 0xffdfdfdf, 0xffbcbcbd, 0xffeaeaea, 0xffdddcdd, 0xffeeedee,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffe2e1e2, 0xffa3a2a4, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffd0d0d1, 0xff8a8480, 0xffe8ded1, 0xffcbc1b7, 0xffaca49c, 0xffebe1d3, 0xffe7ddd0,
//0xffbab1a8, 0xff827b76, 0xffe9ded1, 0xffdacfc4, 0xff4f4b4b, 0xffcccccd, 0xffffffff, 0xffffffff, 0xfffcfcfc, 0xffc1c0c1,
//0xffffffff, 0xfffefefe, 0xffb4b3b5, 0xffcccccc, 0xfff9f8f8, 0xff211f24, 0xff2c2924, 0xff373323, 0xff0a0a13, 0xff0f0c11,
//0xff18161a, 0xff1d1b1f, 0xff18161a, 0xff323034, 0xff666568, 0xff4b494c, 0xff838183, 0xff878688, 0xfff6f6f6, 0xffffffff,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffabaaac, 0xffbcbbbc, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffb5b5b6, 0xffaba39d, 0xffe2d8cc, 0xffdfd4c8, 0xffcec4ba, 0xff6b6563, 0xffc1b9af,
//0xffe3d8cc, 0xffb1a8a0, 0xff6d6764, 0xffe8dcd0, 0xffd9cfc3, 0xff3f3c3e, 0xffebebeb, 0xffffffff, 0xffffffff, 0xffedeced,
//0xff5d5c5f, 0xfff0f0f0, 0xffffffff, 0xff5d5b5e, 0xff312f32, 0xff2e2b24, 0xffe3d54c, 0xffe7d42d, 0xff625122, 0xff211e24,
//0xff403e42, 0xff1a181c, 0xff1a181c, 0xff1a181c, 0xff1a181c, 0xff19161b, 0xff151317, 0xffa6a4a6, 0xff838284, 0xffa3a2a4,
//0xffcfced0, 0xffffffff, 0xffffffff, 0xffffffff, 0xffefeeef, 0xff312f33, 0xfff1f1f1, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffa3a2a4, 0xffc3b9b0, 0xffe4d9cd, 0xffe2d7cb, 0xffe4dacd, 0xffe4d9ce, 0xff89827e,
//0xff817a75, 0xffa9a199, 0xffa39a93, 0xff938b86, 0xffe1d6ca, 0xffb9b0a7, 0xff777577, 0xffffffff, 0xfffefefe, 0xffffffff,
//0xffcfcecf, 0xff323134, 0xff858385, 0xff8e8d8f, 0xff1a181c, 0xffcdc262, 0xfff4df32, 0xff786320, 0xff8b898e, 0xffffffff,
//0xffffffff, 0xffb0b0b1, 0xff171519, 0xff383417, 0xffcdc45f, 0xffa9a8a8, 0xff6a653a, 0xff161413, 0xff6c6a6f, 0xffcfcfcf,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xffe8e8e8, 0xff302e32, 0xff919092, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xff9b9a9b, 0xffc4bbb1, 0xffe3d8cb, 0xffbab1a8, 0xff918a84, 0xffb3aba2, 0xffe9ded1,
//0xffdbcfc4, 0xffbab1a8, 0xff736e6b, 0xff403b3c, 0xffa29992, 0xffe6dbcf, 0xff77706c, 0xffa9a8aa, 0xffffffff, 0xfff9f9f9,
//0xfff2f2f2, 0xffdddcdd, 0xff262327, 0xff13111a, 0xff989260, 0xfffcea49, 0xff8f7b1f, 0xff747374, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xff454346, 0xff131116, 0xffb2a947, 0xfffffb8f, 0xfffdee50, 0xffd7c826, 0xff26221a, 0xff211f24,
//0xff5d5b5e, 0xfff6f6f7, 0xffdfdfe0, 0xff2e2c30, 0xff525154, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xff959394, 0xffc7bdb4, 0xffe0d6ca, 0xffe1d6ca, 0xffe1d6ca, 0xffa8a199, 0xff66615e,
//0xffbab0a7, 0xffddd3c7, 0xffe4d9cd, 0xffc8bfb5, 0xff494545, 0xffbdb4ab, 0xffe6dbcf, 0xff363234, 0xffe1e0e1, 0xffffffff,
//0xffa7a6a8, 0xff5f5d61, 0xff5e5d5f, 0xff2e2b20, 0xffe7dc7a, 0xffdfcb27, 0xff3b321c, 0xfff8f8f8, 0xffffffff, 0xffefefef,
//0xfff9f9f9, 0xffffffff, 0xff9e9d9e, 0xff100e12, 0xff12111a, 0xffada123, 0xffcbbc25, 0xffaca125, 0xff474221, 0xff18161b,
//0xff161419, 0xff2a282c, 0xff120f14, 0xff484649, 0xfff4f4f5, 0xfffefefe, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xff959495, 0xffc8beb4, 0xffe4d9cd, 0xffe1d7cb, 0xffdfd4c8, 0xffe7dccf, 0xffe1d6ca,
//0xffa69e97, 0xff76706c, 0xffdfd5c8, 0xffe6dbcf, 0xffe4dace, 0xff7c7572, 0xffcac1b7, 0xffcbc1b7, 0xff636264, 0xfff9f9f9,
//0xffffffff, 0xffc6c6c7, 0xff838284, 0xff635e38, 0xfffbee60, 0xffae9925, 0xff5a585a, 0xffffffff, 0xffffffff, 0xff545356,
//0xff69686a, 0xfffcfcfc, 0xff939194, 0xff3f3418, 0xff19171b, 0xff14121b, 0xff161314, 0xff1c191d, 0xff151319, 0xff17151a,
//0xff13111c, 0xff1c1819, 0xff2f2d30, 0xffc7c6c7, 0xffaeacae, 0xffe3e3e4, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xff9b9a9b, 0xffc4bab0, 0xffe3d8cc, 0xffded3c7, 0xffe3d9cc, 0xffe0d5ca, 0xffddd3c7,
//0xffe2d7cb, 0xffccc3b9, 0xff3b3839, 0xffd5cbc0, 0xffdfd5c9, 0xffcfc4ba, 0xff847d79, 0xffe4d9cc, 0xff817a76, 0xffc3c2c3,
//0xffffffff, 0xffffffff, 0xffabaaab, 0xff999351, 0xfffcec4a, 0xff7f6b23, 0xff85848b, 0xffffffff, 0xffffffff, 0xff383639,
//0xff1b191d, 0xffc1c1c1, 0xff575558, 0xff947d21, 0xff23201c, 0xff1a181c, 0xff817f82, 0xffffffff, 0xffdfdee0, 0xff3d3a30,
//0xffa59120, 0xff4c3a20, 0xff29262b, 0xff8b898b, 0xffededee, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffa5a5a7, 0xffc0b7ad, 0xffe3d8cb, 0xffe0d5c9, 0xffdacfc4, 0xffbfb5ad, 0xffb5ada4,
//0xffd3c8bd, 0xffebdfd2, 0xffd0c6bb, 0xff55504f, 0xffc3bab0, 0xffe7dccf, 0xff97908a, 0xff918a84, 0xffdad0c4, 0xff484446,
//0xfffafafa, 0xffffffff, 0xff676468, 0xffcbc375, 0xfff8e645, 0xff625122, 0xffa5a5aa, 0xffdad9d9, 0xfff5f5f5, 0xff323034,
//0xff161418, 0xff939295, 0xff2f2920, 0xffd4bc2d, 0xff29261a, 0xff6c6a6d, 0xffffffff, 0xffffffff, 0xffffffff, 0xff575444,
//0xffe9d223, 0xff33271c, 0xff413f43, 0xff89888a, 0xffa1a0a2, 0xffbfbfbf, 0xfff3f3f4, 0xffffffff, 0xfffefefe, 0xfffefefe,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffbcbcbe, 0xffa29b94, 0xffe4dacd, 0xffdfd5c9, 0xffe3d8cb, 0xffdcd2c6, 0xffd5cbc0,
//0xff968f8a, 0xff645f5d, 0xff827b76, 0xff958e87, 0xff403d3d, 0xffc5bbb2, 0xffeadfd2, 0xff726b69, 0xffb2aaa1, 0xffa8a098,
//0xff636266, 0xffffffff, 0xff2b292d, 0xffe4dd96, 0xfff9e744, 0xff655423, 0xffb3b3b8, 0xff727174, 0xff525054, 0xff1e1c20,
//0xff18161a, 0xff4a4a52, 0xff665722, 0xffefdc30, 0xff2e2b1d, 0xfffdfdfd, 0xffeaeaea, 0xff515052, 0xfff0f0f2, 0xff535146,
//0xffd5be24, 0xff140f13, 0xff858486, 0xffc7c7c8, 0xffdddcdd, 0xfff4f4f4, 0xffd7d7d8, 0xff838184, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffe0e0e0, 0xff6c6866, 0xffebe0d3, 0xffe1d6ca, 0xffd9d0c4, 0xffdad0c4, 0xffd9cfc4,
//0xffeadfd2, 0xffeee2d6, 0xffc6beb5, 0xff96908a, 0xff87817d, 0xff605a58, 0xffc1b8ae, 0xffe5d9ce, 0xff5f5a58, 0xffdfd4c9,
//0xff64605e, 0xffd2d1d3, 0xff19171b, 0xffece7ac, 0xfffded54, 0xff856f23, 0xffa0a0a6, 0xff9d9c9e, 0xff0d0b0f, 0xff19171b,
//0xff1b191e, 0xff1d1a1f, 0xffd3bb1f, 0xffecdd40, 0xff656256, 0xffffffff, 0xffd7d6d7, 0xff18161a, 0xff6a696e, 0xff6c683c,
//0xff9b8822, 0xff3b3b44, 0xff464347, 0xffa5a5a6, 0xfffbfbfb, 0xffe9e9e9, 0xff656262, 0xff1b191d, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff4d4b4f, 0xffd8cec2, 0xffe0d5ca, 0xffd2c8bd, 0xffc8bfb5, 0xffa8a199,
//0xffa29a94, 0xff9d958e, 0xff928985, 0xffded3c8, 0xffe3d8cb, 0xffded3c8, 0xff6d6764, 0xffcbc1b6, 0xff9e968f, 0xff847d78,
//0xffcdc3b8, 0xff6a686a, 0xff19171c, 0xffe4dfaf, 0xfffef587, 0xffc0a920, 0xff504d4e, 0xffe8e7e8, 0xff4d4c4f, 0xff16151b,
//0xff16131a, 0xffa49311, 0xfffbe923, 0xffe4d764, 0xff444241, 0xff5a585b, 0xff7d7b7e, 0xff1a181c, 0xff23212b, 0xff9d9129,
//0xff3a321f, 0xffababad, 0xffffffff, 0xffffffff, 0xffffffff, 0xff666466, 0xffa79f97, 0xff403e42, 0xffffffff, 0xfffefefe,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffc1c2c3, 0xff655e5c, 0xffe6dccf, 0xffe4d9cd, 0xffe2d7cb, 0xffe8ded2,
//0xff726c67, 0xff524f49, 0xff97936f, 0xff3a3632, 0xffc5bcb2, 0xffdfd4c8, 0xffe3d8cd, 0xff3d3a3a, 0xffdacfc3, 0xff3c383a,
//0xffbdb4aa, 0xff686261, 0xff19171b, 0xffcdc789, 0xfffffde9, 0xfff1e36f, 0xff504822, 0xff1a171b, 0xff17141b, 0xff37331a,
//0xffd3c627, 0xfffff252, 0xfffbeb49, 0xffd6cd7f, 0xff29272b, 0xff1a181c, 0xff1a181c, 0xff19171b, 0xff1f1d1c, 0xffa09020,
//0xff23232e, 0xffe2e1e2, 0xffffffff, 0xffffffff, 0xff6d6d6f, 0xff99938e, 0xffa09890, 0xff838284, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xff636163, 0xffbab1a7, 0xffded4c8, 0xffddd3c7, 0xff534e53,
//0xff7d7725, 0xffffffd1, 0xfffef47d, 0xffe6db55, 0xff565134, 0xff9e9694, 0xffe5dacd, 0xffd2c8bd, 0xff5b5655, 0xffbcb3aa,
//0xff363234, 0xffb5aca4, 0xff1a181c, 0xffa59f62, 0xfff8f3c5, 0xff8d864b, 0xffd7ca62, 0xffbcb036, 0xff9e941d, 0xff6f6717,
//0xff6a663f, 0xffaeab97, 0xfffffacc, 0xffbfbb9e, 0xff5c595c, 0xff1c1a1e, 0xff19171b, 0xff312f35, 0xff615a1d, 0xff403a19,
//0xff69676b, 0xffffffff, 0xfffbfafb, 0xff7e7d7f, 0xff9a938e, 0xffb7afa6, 0xff6c6561, 0xffcdcdce, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffe2e2e2, 0xff5a5556, 0xffe6dbce, 0xff7f797a, 0xff6d6413,
//0xfffff02c, 0xffedd933, 0xffb59d25, 0xffbfb228, 0xffe7d730, 0xff605b2d, 0xff605a5c, 0xffe8ddd0, 0xff98908a, 0xff756f6b,
//0xff87807b, 0xff847c78, 0xff18161b, 0xff736f47, 0xfff2e891, 0xff242117, 0xff776f24, 0xffd4c626, 0xffecdb28, 0xffbfb224,
//0xff544d19, 0xff13121b, 0xff646265, 0xffadaba4, 0xff777678, 0xffeeedee, 0xff92919c, 0xff4d4928, 0xffa19521, 0xff181517,
//0xfff7f6f7, 0xfff3f3f3, 0xff444246, 0xffbab1a9, 0xff857e79, 0xffd2c9be, 0xff595453, 0xfffcfcfc, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffabaaac, 0xff585453, 0xff302c21, 0xffe6db55,
//0xfffef8c6, 0xffe3d04b, 0xff3e3a2a, 0xff2f2c23, 0xff7d7628, 0xffcbbc19, 0xff58534f, 0xff575251, 0xffd4cabf, 0xff413e3e,
//0xff8c8480, 0xff423d3e, 0xff292629, 0xff47442b, 0xfff3ea90, 0xff80761d, 0xfff8e60c, 0xffe2d548, 0xfffbeb3d, 0xfff9e92e,
//0xffefdf25, 0xff847b24, 0xff1e1b1a, 0xff2a272a, 0xff252218, 0xff393418, 0xff958b26, 0xffecdc28, 0xff2c2919, 0xffa3a2a5,
//0xffdededf, 0xff514f50, 0xffd7cdc4, 0xffada59c, 0xffaba39c, 0xffcbc1b7, 0xff737171, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xff7d7d7e, 0xff564f0c, 0xfffaf291,
//0xfffdf59e, 0xfffbed44, 0xfff2e43c, 0xffc1b74d, 0xff4a472e, 0xff433e1e, 0xff534f3f, 0xff423d41, 0xff312d32, 0xff585354,
//0xff111016, 0xff221f24, 0xff1c1a1d, 0xff1a181a, 0xffdcd15f, 0xffe4d52a, 0xffcdc026, 0xff26242d, 0xffc2ba77, 0xfffff250,
//0xfffae82d, 0xffe1d121, 0xff898127, 0xff211e1c, 0xffa1951d, 0xfffcf5a0, 0xfff4e763, 0xff4b461f, 0xff535259, 0xff908f92,
//0xff696564, 0xffd8cec3, 0xffaca49b, 0xff7e7875, 0xffcac1b7, 0xffaca39b, 0xff9c9b9d, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff5e5c5f, 0xff938813, 0xffffed17,
//0xffe5d518, 0xffc0ae24, 0xffc9bb22, 0xffdccc1d, 0xfffeeb17, 0xff544f19, 0xffc9bf5f, 0xfff6efa1, 0xffbdb888, 0xff989371,
//0xff8f8b66, 0xff676450, 0xff36332c, 0xff1b171b, 0xff776e20, 0xfffef05f, 0xfffff344, 0xff504a1f, 0xff19171e, 0xff8a866a,
//0xfff6ee8c, 0xfffaee63, 0xffe2d338, 0xffa1951b, 0xffdace4b, 0xffefe79b, 0xff5d561e, 0xff232024, 0xff6b6a6d, 0xff8f8a86,
//0xffe5d9ce, 0xff978f88, 0xff686462, 0xffa59d96, 0xffdcd1c6, 0xff65605e, 0xffd0d0d1, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff3f3d40, 0xffc0b546, 0xfffffab0,
//0xffd7c138, 0xff352f22, 0xff2f2b21, 0xff534d24, 0xff807720, 0xff4a441d, 0xffe6d625, 0xfff2e223, 0xffe7d726, 0xff978c20,
//0xff39341e, 0xff6b641f, 0xffbda71e, 0xffd9bd1f, 0xff6a5c1c, 0xffdfd264, 0xfffdef67, 0xffe8d935, 0xff2b281b, 0xff100e16,
//0xff100e14, 0xff3b392f, 0xff6d6629, 0xfffbe812, 0xffd5c736, 0xff5e5719, 0xff241d1b, 0xff383538, 0xffa59e97, 0xffcec4b9,
//0xff75706c, 0xff4b4848, 0xff8f8983, 0xffb7afa7, 0xffd5cbc0, 0xff3e3c40, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff504e51, 0xffcab420, 0xfffef153,
//0xfff9eb55, 0xffe1d64c, 0xffd3c41e, 0xff8a801e, 0xff191719, 0xff4e4820, 0xffa59b2e, 0xff7c7527, 0xff2d291c, 0xff18161b,
//0xff2a271b, 0xffd4c728, 0xfffaef62, 0xfffdf594, 0xfff1e558, 0xff726c3b, 0xfffffcb6, 0xffeedd37, 0xffbeb232, 0xff151317,
//0xff85826d, 0xffebe16e, 0xffecdb1e, 0xffa39824, 0xff2e2c1d, 0xff211d1c, 0xff8f7120, 0xff3c383b, 0xff76706b, 0xff565151,
//0xffc1b8b0, 0xffcbc0b7, 0xff706a68, 0xffddd3c7, 0xff5e5956, 0xffaeadaf, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffa3a2a4, 0xff6c5d1d, 0xffa19120,
//0xff9f931f, 0xff988d1f, 0xff807727, 0xff484429, 0xff5d5c5e, 0xff737177, 0xff241f1d, 0xff755c23, 0xff3e381b, 0xff19171b,
//0xff302c1b, 0xffeade66, 0xfffdfdfd, 0xfffdfdff, 0xfffff9a8, 0xffbaae33, 0xffccc9af, 0xfff7efb0, 0xffe0d033, 0xffddd048,
//0xffe0d677, 0xffbfb124, 0xff5f5924, 0xff26211d, 0xff6c5821, 0xff342c1d, 0xffcba721, 0xff372c1e, 0xff746f6f, 0xffe5dace,
//0xffaea69d, 0xff605c5a, 0xffded5ca, 0xffcbc1b6, 0xff403c3f, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffb6b6bb, 0xff969497,
//0xff918f8f, 0xff9a999d, 0xffacacb3, 0xffcbcbce, 0xffffffff, 0xff807b71, 0xffa58d24, 0xffe3ce31, 0xfff1e13a, 0xff8f841b,
//0xff564e1e, 0xfff9ec5c, 0xfffdf8c3, 0xfffbf6c9, 0xfffbf5c0, 0xfff2e240, 0xff938c4a, 0xffffffda, 0xffe5db78, 0xff8f8521,
//0xff49421c, 0xff4c461f, 0xff80761e, 0xffad9524, 0xff43381f, 0xff3c351b, 0xfff4da17, 0xff977925, 0xff5d5a5f, 0xff807a76,
//0xffa69f98, 0xffaaa29a, 0xffd4cac0, 0xff827b76, 0xffbcbbbd, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xfffcfcfc, 0xff494852, 0xffab8f2a, 0xffead942, 0xfffefad1, 0xfffdfdf8, 0xfffaed69,
//0xffcdb722, 0xffe8d62e, 0xfffbed61, 0xfffbee6d, 0xfffbee7d, 0xfffbeb46, 0xffc2b428, 0xff4c4629, 0xff524b22, 0xff938824,
//0xffddcd28, 0xffd3c522, 0xffc3b523, 0xff443e1e, 0xff13121c, 0xff82771b, 0xffffef20, 0xffd4be20, 0xff4a4240, 0xffc3bab0,
//0xff56514f, 0xff9f9792, 0xffdbd1c5, 0xff525052, 0xfff5f5f5, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xff777577, 0xff0d0c18, 0xffc4ac32, 0xffffffc7, 0xffa0a6a4, 0xffa0b39d, 0xfff6ea97,
//0xffead926, 0xffd8c924, 0xfff9e937, 0xfffbea35, 0xfffae932, 0xfffcec33, 0xfff0df25, 0xffb0a41f, 0xff9f973a, 0xff847c30,
//0xff776e1d, 0xffc8ba22, 0xffa19723, 0xff2a261e, 0xff12111b, 0xffccbe1e, 0xfffcea2e, 0xffe8d918, 0xff4c401e, 0xff484447,
//0xffbfb7ae, 0xffe9ded1, 0xff454040, 0xffc4c3c4, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xfffefefe, 0xffffffff, 0xff8a898b, 0xff151317, 0xff12101b, 0xffa89b29, 0xfffffb91, 0xffceca7e, 0xff157688, 0xff44756b,
//0xffe1cb24, 0xffd7c826, 0xfff0df28, 0xfffbe92a, 0xfffbea1f, 0xffe2d214, 0xff7e793c, 0xffded894, 0xffecece0, 0xfff4f3e7,
//0xffb5aa39, 0xff5d571c, 0xffada22a, 0xff7a6627, 0xff554820, 0xffdacb23, 0xfffbeb4f, 0xfff4e222, 0xff70621b, 0xff908986,
//0xffe3d8cc, 0xff5f5956, 0xffa7a6a7, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe,
//0xffffffff, 0xffbcbcbe, 0xff241e18, 0xff1c1a1c, 0xff11101c, 0xff95891b, 0xfffff854, 0xffb9b155, 0xff24899c, 0xff07a9ba,
//0xff25574d, 0xffdecb25, 0xffd4c525, 0xfffae828, 0xfff3e216, 0xff686335, 0xffeee587, 0xffddc62f, 0xfffcee55, 0xfffbf06b,
//0xfffdf28a, 0xff998f2b, 0xff514723, 0xff655325, 0xffa68b25, 0xffd4c424, 0xfffbec5a, 0xfff7e841, 0xff86781c, 0xff696361,
//0xff8a827d, 0xff807e81, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe,
//0xfff1f1f2, 0xff4c433c, 0xffb49723, 0xffac9f12, 0xff544d16, 0xff57501d, 0xffdcc81c, 0xff617c76, 0xff17aebd, 0xff00616e,
//0xff56562a, 0xffb9ac2f, 0xffb4a019, 0xfff3e023, 0xff79701f, 0xffddcf2d, 0xff655e23, 0xff352d15, 0xffe7dd68, 0xfffefce7,
//0xfffaf2a0, 0xffffee2f, 0xffbaad2a, 0xff463f20, 0xffaa8e25, 0xffdccd25, 0xfffbee62, 0xfff8ea4d, 0xff94861e, 0xff2c2828,
//0xff979798, 0xfffdfdfd, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xff797779, 0xff7b651d, 0xffecdd4d, 0xfffffbd3, 0xfffcf057, 0xffd4c418, 0xff6d7b60, 0xff28adbb, 0xff008694, 0xff13656f,
//0xff317c84, 0xff319ca7, 0xff369da8, 0xff70772c, 0xff645c1b, 0xff8b8124, 0xff2d2a24, 0xffe1d873, 0xfffbed5e, 0xfffbec35,
//0xfff7e948, 0xfff8ea50, 0xfffae81a, 0xffeddc24, 0xff6c641f, 0xff8f8521, 0xfff6eb75, 0xfffaed5b, 0xff9a8919, 0xff5d5b5a,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffc3c2c3,
//0xff171210, 0xffb09d25, 0xfffbf8da, 0xfff7f1c9, 0xffebe18f, 0xff7e8a5e, 0xff2ca7b9, 0xff007a89, 0xff414b28, 0xffc1ae21,
//0xffdfc913, 0xff556e39, 0xff007485, 0xff626a2a, 0xff413c1e, 0xff3e3a24, 0xffdcd268, 0xffa89d35, 0xff87750f, 0xfff9ec68,
//0xfffdf8bb, 0xfffaee64, 0xfffae924, 0xfffbe91f, 0xfffff55b, 0xfff5e647, 0xfff9f193, 0xfffbf286, 0xff9b8915, 0xff6f6b6b,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfff2f2f2, 0xff3a383b,
//0xff17151b, 0xff8e8222, 0xff808568, 0xff6d9a93, 0xff7ea19b, 0xff28a8b7, 0xff007f8f, 0xff273427, 0xffcfbf24, 0xfffae92e,
//0xfff3e12a, 0xff4f7753, 0xff4d5523, 0xffe6d519, 0xff3e3920, 0xffab9f20, 0xff887f2b, 0xff1e1c1d, 0xff837f52, 0xfff7f0a3,
//0xfff7ea60, 0xfff1e037, 0xfff7e726, 0xfffbe90e, 0xfffbed52, 0xfffcf9e1, 0xfffdfdff, 0xfffaf17f, 0xff927e15, 0xff8b8888,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffa2a1a3, 0xff27221d,
//0xff1a181a, 0xff29261d, 0xffc7b913, 0xff0a6c7b, 0xff01a0b1, 0xff008e9e, 0xff234137, 0xffeede29, 0xffe3d326, 0xffe1d029,
//0xfff8e72d, 0xffb9a923, 0xfff1df1d, 0xffcabb16, 0xff25221b, 0xff625b23, 0xff4d471a, 0xfff9eb4c, 0xfffffa7d, 0xfff2e12f,
//0xffbfaa1e, 0xff7c6522, 0xffbba51f, 0xffe2ce19, 0xfff2df0f, 0xfff7e62b, 0xfff8eb56, 0xffecd91c, 0xff856b1c, 0xffafadad,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xff3f3932, 0xffa89321,
//0xffada447, 0xff655d19, 0xff8a7e1e, 0xff838225, 0xff016b7a, 0xff037c88, 0xffab9f23, 0xfffbea2d, 0xfff9e82a, 0xffd0ba23,
//0xffcaba28, 0xfff0df1f, 0xffe5d41a, 0xffdacb1b, 0xff645b23, 0xff13111b, 0xff4f491d, 0xffaea220, 0xffbcad20, 0xff928021,
//0xff3f351c, 0xff606068, 0xff352e26, 0xff4b3e15, 0xff7a691c, 0xff93811d, 0xff95821a, 0xff79661a, 0xff4c3d26, 0xffdfdedf,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xff848385, 0xff504216, 0xffe5d87a,
//0xfffefef9, 0xfffbf3a2, 0xfff4e32d, 0xffd7c025, 0xff7b6f1d, 0xff054a57, 0xff24645a, 0xfff9e82c, 0xfffae92a, 0xffe5d51e,
//0xff211e1e, 0xff887e23, 0xffc5b322, 0xffc6b724, 0xffaa8b29, 0xff11111b, 0xff1a181c, 0xff19171b, 0xff18161a, 0xff2f2d30,
//0xffb2b1b3, 0xffffffff, 0xfffcfcfc, 0xffb1b1b1, 0xff6b696c, 0xff4f4d50, 0xff5b5a5c, 0xff9d9c9d, 0xfff3f3f3, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffe3e3e4, 0xff18161a, 0xff887324, 0xfff6eec2,
//0xfffcf6c6, 0xfffbf4b7, 0xfffaec66, 0xfff7e628, 0xffe1cb24, 0xffb09c1c, 0xff79731b, 0xfff5e423, 0xffeada21, 0xffb4a427,
//0xff0f0e1b, 0xff11101b, 0xff14121c, 0xff342c1f, 0xff513c1f, 0xff111117, 0xff525053, 0xffc9c8c9, 0xffffffff, 0xffffffff,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xff727073, 0xff19171b, 0xff675721, 0xfff4e15a,
//0xfffaeb42, 0xfffae93e, 0xfffae933, 0xfffae931, 0xfff2e124, 0xffb9a720, 0xff322d1c, 0xff625b1f, 0xffaa9827, 0xff776325,
//0xff15141b, 0xff1a181c, 0xff171519, 0xff0d0a0f, 0xff474649, 0xffc7c6c8, 0xfff8f8f8, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffdcdcdc, 0xff252326, 0xff1a181c, 0xff312a1d, 0xffd3c122,
//0xfff7e72d, 0xfff5e42d, 0xfff3e22d, 0xffecdb2d, 0xffd3c423, 0xffaf9f25, 0xff261f1d, 0xff15131a, 0xff141119, 0xff1a171a,
//0xff232125, 0xff302e32, 0xff626063, 0xffd0d0d1, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xfffdfdfd, 0xffe0e0e1, 0xffb1b0b2, 0xff39373a, 0xff0a070c, 0xff0e0b10, 0xff0b0910, 0xff332e12,
//0xff797019, 0xff96891d, 0xff93831d, 0xff817219, 0xff716217, 0xff62511f, 0xff373233, 0xff525053, 0xff777679, 0xffa6a5a7,
//0xffc9c9ca, 0xfff1f1f1, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffe2e2e2, 0xffc0bfc0, 0xffbcbbbc, 0xffbcbcbd, 0xffbab9ba, 0xffb6b5b6, 0xffb4b3b4,
//0xffb4b3b5, 0xffb7b6b7, 0xffbfbfc0, 0xffd4d4d5, 0xffeeeeee, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xfffefefe, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff,
//0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff];
//
//int width = 50;
//int height = 50;
//
//Figure logo(){
// list[list[Figure]] boxes;
// boxes = for(i <- [0..height]){
// append for(j <- [0..width]){
// append box(fillColor(LogoData[i*50+j]),lineWidth(0));
// }
// }
// return grid(boxes,aspectRatio(1.0));
//}
//
//void renderLogo() {
// render(logo());
//}We can use it as follows:
import demo::vis::Logo;
render(logo());will produce:
or as a screenshot:
5.3. Interactive Box Height
Control the height of a box with user input.
-
A text entry field to enter numbers.
-
A box, whose height is controlled by the numer entered in the text field.
Here is a solution:
module demo::vis::Higher
//import vis::Figure;
//import vis::Render;
//import String;
//
//bool intInput(str s){
// return /^[0-9]+$/ := s;
//}
//
//Figure higher(){
// int H = 100;
// return vcat( [ textfield("<H>", void(str s){H = toInt(s);}, intInput),
// box(width(100), vresizable(false), vsize(num(){return H;}), fillColor("red"))
// ], shrink(0.5), resizable(false));
//}The auxiliary function intInput checks that a strings consists solely of digits. Function higher can be understood as follows:
-
A local variable
His used to maintain the current height. -
It returns a vertical concatenation of two elements: a [Rascal:textfield] and a [Rascal:box].
-
The textfield has three arguments:
-
A string that is the initial value of the text field.
-
A call back function
void(str s){H = toInt(s);}that is called when text entry is complete: argumentsis the text entered and the effect is to convert that text to a number and assign it toH. -
Function
intInputthat checks that only numbers are entered. -
The box has
-
a fixed width
-
it is not vertically resizable.
-
It has a vertical size that that depends on an anonymous function
vsize(num(){return H;})that returns the value ofH. -
Its color is red.
-
Rendering this figure:
import demo::vis::Higher;
render(higher());gives
Unfortunately we cannot show the interaction here, so run this example from the demo directory and watch how the height of the box changes when you enter a new number in the text field.
5.4. My First Box
Drawing a box in many variations.
Drawing a red box is as simple as this:
import vis::Figure;
import vis::Render;
b = box(fillColor("red"));
render(b);and it will look like this:
or rather, it will look like this:
Wow, the box fills the whole window! So lets give our box a size:
import vis::Figure;
import vis::Render;
b = box(fillColor("red"), size(200,100));
render(b);and it will look like this:
On screen however, it still fills the whole window as shown above. The lesson here is that size is to be taken as minimum size (and probably we should rename size to minSize to emphasize this).
So how can we produce a box that does not fill the whole window? The answer is to define the size of the box relative to its surroundings by using shrink:
import vis::Figure;
import vis::Render;
b = box(fillColor("red"), shrink(0.5));
render(b);which says: I am a red box and I want to occupy 50% of the available space. The result is:
import vis::Figure;
import vis::Render;
b = box(fillColor("red"), hshrink(0.5));
render(b);which says:_ I am a red box and I want to occupy 50% of the available space in the horizontal direction and 100% of the available space in the vertical direction._ The result is:
Relative sizes can also be used when figures are nested.
import vis::Figure;
import vis::Render;
b1 = box(fillColor("red"), hshrink(0.5));
b2 = box(b1, fillColor("yellow"), size(200,100));
render(b2);
In the above examples we have consistently added the two imports:
import vis::Figure;
import vis::Render;In other recipes and the Rascal documentation we omit these two imports to avoid cluttering our examples with irrelevant details. Be aware that you will always need them when creating a visualisation.
5.5. ParseTree
Visualize a parse tree.
A parse tree is a (usually large) internal representation of a parsed text. In the rare situation that it is necessary to read or inspect a parse tree, a visualization can be useful.
We embark on visualizing parse trees for the language Exp:
rascal>import demo::lang::Exp::Concrete::WithLayout::Syntax;
ok
rascal>import ParseTree;
ok
rascal>parse(#Exp, "1+2*3");
warning, ambiguity predicted: Exp "+" Exp lacks left or right associativity
warning, ambiguity predicted: Exp "*" Exp lacks left or right associativity
Exp: (Exp) `1+2*3`WARNING: unexpected errors in the above SHELL example. Documentation author please fix! As can be seen, even for such a trivial example, the details in the parse tree representation become sizeable.
We can visualize it as follows:
import demo::lang::Exp::Concrete::WithLayout::Syntax;
import ParseTree;
import vis::Figure;
import vis::ParseTree;
import vis::Render;
render(visParsetree(parse(#Exp, "1+2*3")));With as result:
The figure is interactive (not available here):
-
Rectangles with blue text are terminal symbols.
-
Little circles represent non-terminals: hovering over them shows the corresponding grammar rule.
-
Little grey rectangles represent layout: hovering over them also shows the corresponding lexical rule.
-
A dense, structured, representation of a parse tree that provides extra information via interaction.
-
This visualization does not scale to huge trees.
5.6. Playing With Properties
Illustrate the effect of various figure properties.
Here is an ellipse with minimum size 200x300 that occupies 80% of the available space:
e = ellipse(size(200,100), shrink(0.8));
render(e);
(we add the shrink to leave some space for thick lines and shadows below).
Change the style of its border using lineStyle:
e = ellipse(size(200,100), shrink(0.8), lineStyle("dot"));
render(e);
Change the thickness of its border using lineWidth:
e = ellipse(size(200,100), shrink(0.8), lineWidth(5));
render(e);
Change the color of its border using lineColor:
e = ellipse(size(200,100), shrink(0.8), lineColor("blue"));
render(e);
Change the color of its area using fillColor:
e = ellipse(size(200,100), shrink(0.8), fillColor("yellow"));
render(e);
Add a shadow using shadow:
e = ellipse(size(200,100), shrink(0.8), shadow(true));
render(e);
Add the color of the shadow using shadowColor:
e = ellipse(size(200,100), shrink(0.8), shadow(true), shadowColor("grey"));
render(e);
Finally, enjoy the grande finale:
e = ellipse(size(200,100), shrink(0.8), lineStyle("dot"), lineWidth(5), lineColor("blue"), fillColor("yellow"), shadow(true), shadowColor("grey"));
render(e);