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71 lines
1.9 KiB
Plaintext
71 lines
1.9 KiB
Plaintext
--- Towers of Hanoi is a puzzle with three rods and n disks of decresing size.
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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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---
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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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---
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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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--- Concatenates a list of strings
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--- ;concat (("a" :: nil) :: "b" :: nil); evaluates to ;"a"
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:: "b"
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:: 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 Nat;
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showList : List Nat → String;
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showList xs :=
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"[" ++str intercalate "," (map natToString xs) ++str "]";
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--- A Peg represents a peg in the towers of Hanoi game
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type Peg :=
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| left : Peg
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| middle : Peg
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| right : Peg;
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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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type Move :=
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| move : Peg → Peg → Move;
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showMove : Move → String;
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showMove (move from to) :=
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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 : Nat → Peg → Peg → Peg → List Move;
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hanoi zero _ _ _ := nil;
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hanoi (suc n) p1 p2 p3 :=
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hanoi n p1 p3 p2
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++ singleton (move p1 p2)
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++ hanoi n p3 p2 p1;
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main : IO;
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main :=
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printStringLn
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(unlines (map showMove (hanoi 5 left middle right)));
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