Add Towers of Hanoi and Pascal triangle examples (#1446)

* Add new examples of Juvix programs

* Build documentation for Hanoi and Pascal examples

Makefile

@@ -15,6 +15,8 @@ EXAMPLEHTMLOUTPUT=_docs/examples/html
 EXAMPLES= 	HelloWorld/HelloWorld.juvix \
 			Collatz/Collatz.juvix \
 			Fibonacci/Fibonacci.juvix \
+            Hanoi/Hanoi.juvix \
+            PascalsTriangle/PascalsTriangle.juvix \
 			TicTacToe/CLI/TicTacToe.juvix \
 			ValidityPredicates/SimpleFungibleToken.juvix
 

README.org

@@ -43,6 +43,8 @@ The following links are clickable versions of their corresponding Juvix programs
 
 - [[https://docs.juvix.org/examples/html/HelloWorld/HelloWorld.html][HelloWorld.juvix]]
 - [[https://docs.juvix.org/examples/html/Fibonacci/Fibonacci.html][Fibonacci.juvix]]
+- [[https://docs.juvix.org/examples/html/Hanoi/Hanoi.html][Hanoi.juvix]]
+- [[https://docs.juvix.org/examples/html/PascalsTriangle/PascalsTriangle.html][PascalsTriangle.juvix]]
 - [[https://docs.juvix.org/examples/html/Collatz/Collatz.html][Collatz.juvix]]
 - [[https://docs.juvix.org/examples/html/TicTacToe/CLI/CLI.TicTacToe.html][TicTacToe.juvix]]
 - [[https://docs.juvix.org/examples/html/ValidityPredicates/SimpleFungibleToken.html][SimpleFungibleToken.juvix]]

docs/org/examples/README.org

@@ -4,6 +4,8 @@ The following links are clickable versions of their corresponding Juvix programs
 
 - [[https://docs.juvix.org/examples/html/HelloWorld/HelloWorld.html][HelloWorld.juvix]]
 - [[https://docs.juvix.org/examples/html/Fibonacci/Fibonacci.html][Fibonacci.juvix]]
+- [[https://docs.juvix.org/examples/html/Hanoi/Hanoi.html][Hanoi.juvix]]
+- [[https://docs.juvix.org/examples/html/PascalsTriangle/PascalsTriangle.html][PascalsTriangle.juvix]]
 - [[https://docs.juvix.org/examples/html/Collatz/Collatz.html][Collatz.juvix]]
 - [[https://docs.juvix.org/examples/html/TicTacToe/CLI/CLI.TicTacToe.html][TicTacToe.juvix]]
 - [[https://docs.juvix.org/examples/html/ValidityPredicates/SimpleFungibleToken.html][SimpleFungibleToken.juvix]]

examples/milestone/Hanoi/Hanoi.juvix

@@ -0,0 +1,74 @@
+--- Towers of Hanoi is a puzzle with three rods and n disks of decresing size.
+---
+--- The disks are stacked ontop of each other through the first rod.
+--- The aim of the game is to move the stack of disks to another rod while
+--- following these rules:
+---
+--- 1. Only one disk can be moved at a time
+--- 2. You may only move a disk from the top of one of the stacks to the top of another stack
+--- 3. No disk may be moved on top of a smaller disk
+---
+--- The function ;hanoi; computes the sequence of moves to solve puzzle.
+
+module Hanoi;
+
+open import Stdlib.Prelude;
+
+--- Concatenation of ;String;s
+infixr 5 ++str;
+axiom ++str : String → String → String;
+compile ++str {
+  c ↦ "concat";
+};
+
+--- Concatenates a list of strings
+---
+--- ;concat (("a" ∷ nil) ∷ ("b" ∷ nil)); evaluates to ;"a" ∷ "b" ∷ nil;
+concat : List String → String;
+concat ≔ foldl (++str) "";
+
+intercalate : String → List String → String;
+intercalate sep xs ≔ concat (intersperse sep xs);
+
+--- Joins a list of strings with the newline character
+unlines : List String → String;
+unlines ≔ intercalate "\n";
+
+--- Produce a singleton List
+singleton : {A : Type} → A → List A;
+singleton a ≔ a ∷ nil;
+
+--- Produce a ;String; representation of a ;List ℕ;
+showList : List ℕ → String;
+showList xs ≔ "[" ++str intercalate "," (map natToStr xs) ++str "]";
+
+--- A Peg represents a peg in the towers of Hanoi game
+inductive Peg {
+  left : Peg;
+  middle : Peg;
+  right : Peg;
+};
+
+showPeg : Peg → String;
+showPeg left ≔ "left";
+showPeg middle ≔ "middle";
+showPeg right ≔ "right";
+
+
+--- A Move represents a move between pegs
+inductive Move {
+  move : Peg → Peg → Move;
+};
+
+showMove : Move → String;
+showMove (move from to) ≔ showPeg from ++str " -> " ++str showPeg to;
+
+--- Produce a list of ;Move;s that solves the towers of Hanoi game
+hanoi : ℕ → Peg → Peg → Peg → List Move;
+hanoi zero _ _ _ ≔ nil;
+hanoi (suc n) p1 p2 p3 ≔ hanoi n p1 p3 p2 ++ singleton (move p1 p2) ++ hanoi n p3 p2 p1;
+
+main : IO;
+main ≔ putStrLn (unlines (map showMove (hanoi 5 left middle right)));
+
+end;

examples/milestone/PascalsTriangle/PascalsTriangle.juvix

@@ -0,0 +1,60 @@
+--- Pascal's triangle is the arrangement of binomial coefficients in a triangular array.
+---
+--- The rows of the triangle are staggered so that each number can be computed as the
+--- sum of the numbers to the left and right in the previous row.
+---
+--- The function ;pascal; produces the triangle to a given depth.
+
+module PascalsTriangle;
+
+open import Stdlib.Prelude;
+
+zipWith : {A : Type} → {B : Type} → {C : Type} → (A → B → C) -> List A → List B → List C;
+zipWith f nil _ ≔ nil;
+zipWith f _ nil ≔ nil;
+zipWith f (x ∷ xs) (y ∷ ys) ≔ f x y ∷ zipWith f xs ys;
+
+--- Return a list of repeated applications of a given function
+iterate : {A : Type} → ℕ → (A → A) → A → List A;
+iterate zero _ _ ≔ nil;
+iterate (suc n) f a ≔ a ∷ iterate n f (f a);
+
+--- Produce a singleton List
+singleton : {A : Type} → A → List A;
+singleton a ≔ a ∷ nil;
+
+--- Concatenation of ;String;s
+infixr 5 ++str;
+axiom ++str : String → String → String;
+compile ++str {
+  c ↦ "concat";
+};
+
+--- Concatenates a list of strings
+---
+--- ;concat (("a" ∷ nil) ∷ ("b" ∷ nil)); evaluates to ;"a" ∷ "b" ∷ nil;
+concat : List String → String;
+concat ≔ foldl (++str) "";
+
+intercalate : String → List String → String;
+intercalate sep xs ≔ concat (intersperse sep xs);
+
+--- Joins a list of strings with the newline character
+unlines : List String → String;
+unlines ≔ intercalate "\n";
+
+showList : List ℕ → String;
+showList xs ≔ "[" ++str intercalate "," (map natToStr xs) ++str "]";
+
+--- Compute the next row of Pascal's triangle
+pascalNextRow : List ℕ → List ℕ;
+pascalNextRow row ≔ zipWith (+) (singleton zero ++ row) (row ++ singleton zero);
+
+--- Produce Pascal's triangle to a given depth
+pascal : ℕ → List (List ℕ);
+pascal rows ≔ iterate rows pascalNextRow (singleton one);
+
+main : IO;
+main ≔ putStrLn (unlines (map showList (pascal 10)));
+
+end;

test/BackendC/Examples.hs

@@ -41,5 +41,7 @@ tests =
   [ ExampleTest "Validity Predicate example" "ValidityPredicates" "Tests.juvix" "ValidityPredicates" "" (WASI StdlibInclude),
     ExampleTest "TicTacToe CLI example" "TicTacToe" "CLI/TicTacToe.juvix" "TicTacToe" "aaa\n0\n10\n1\n2\n3\n3\n4\n5\n6\n7\n8\n9\n" (WASI StdlibInclude),
     ExampleTest "Fibonacci example" "Fibonacci" "Fibonacci.juvix" "Fibonacci" "" (WASI StdlibInclude),
-    ExampleTest "Collatz sequence generator" "Collatz" "Collatz.juvix" "Collatz" "123\n" (WASI StdlibInclude)
+    ExampleTest "Collatz sequence generator" "Collatz" "Collatz.juvix" "Collatz" "123\n" (WASI StdlibInclude),
+    ExampleTest "Towers of Hanoi" "Hanoi" "Hanoi.juvix" "Hanoi" "" (WASI StdlibInclude),
+    ExampleTest "Pascal's triangle" "PascalsTriangle" "PascalsTriangle.juvix" "PascalsTriangle" "" (WASI StdlibInclude)
   ]

tests/examplesExpected/Hanoi/expected.golden

@@ -0,0 +1,31 @@
+left -> middle
+left -> right
+middle -> right
+left -> middle
+right -> left
+right -> middle
+left -> middle
+left -> right
+middle -> right
+middle -> left
+right -> left
+middle -> right
+left -> middle
+left -> right
+middle -> right
+left -> middle
+right -> left
+right -> middle
+left -> middle
+right -> left
+middle -> right
+middle -> left
+right -> left
+right -> middle
+left -> middle
+left -> right
+middle -> right
+left -> middle
+right -> left
+right -> middle
+left -> middle

tests/examplesExpected/PascalsTriangle/expected.golden

@@ -0,0 +1,10 @@
+[1]
+[1,1]
+[1,2,1]
+[1,3,3,1]
+[1,4,6,4,1]
+[1,5,10,10,5,1]
+[1,6,15,20,15,6,1]
+[1,7,21,35,35,21,7,1]
+[1,8,28,56,70,56,28,8,1]
+[1,9,36,84,126,126,84,36,9,1]