Created
March 21, 2017 13:32
Revisions
-
erutuf created this gist
Mar 21, 2017 .There are no files selected for viewing
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,72 @@ Require Import List. Import ListNotations. Definition Board := list (list nat). Definition size (board : Board) := length board. Definition val (n m : nat)(board : Board) := nth m (nth n board []) 1. Fixpoint fill' m (l : list nat) : list nat := match l with | [] => [] | x::xs => match m with | O => 1::xs | S m' => x :: fill' m' xs end end. Fixpoint fill (n m : nat)(board : Board) : Board := match board with | [] => [] | r::rs => match n with | O => fill' m r :: rs | S n' => r :: fill n' m rs end end. Inductive Dirc := Left | Right | Up | Down. Inductive move : nat -> nat -> nat -> nat -> Board -> Board -> Dirc -> Prop := | moveLeft : forall n m board, val n (pred m) board = 0 -> move n m n (pred m) board (fill n (pred m) board) Left | moveRight : forall n m board, val n (S m) board = 0 -> move n m n (S m) board (fill n (S m) board) Right | moveUp : forall n m board, val (pred n) m board = 0 -> move n m (pred n) m board (fill (pred n) m board) Up | moveDown : forall n m board, val (S n) m board = 0 -> move n m (S n) m board (fill (S n) m board) Down. Inductive accept : nat -> nat -> nat -> nat -> Board -> list Dirc -> Prop := | accept_goal : forall n m board, accept n m n m board [] | accept_next : forall n m n' m' goaln goalm board board' d ds, move n m n' m' board board' d -> accept n' m' goaln goalm board' ds -> accept n m goaln goalm board (d :: ds). Hint Constructors move accept. Definition example := [[1;0;1;0]; [0;0;0;1]; [1;0;1;0]; [0;0;0;0]]. Example ex : { ds | accept 0 0 2 3 example ds }. eexists. eauto 20. Defined. Eval simpl in proj1_sig ex. (* = [Down; Right; Down; Down; Right; Right; Up] : list Dirc *)