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