mirror of
https://github.com/KevinMidboe/linguist.git
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Some comments are triggering charlock binary
This commit is contained in:
Joshua Peek
@@ -1,13 +1,3 @@
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(************************************************************************)
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(* v * The Coq Proof Assistant / The Coq Development Team *)
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(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
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(* \VV/ **************************************************************)
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(* // * This file is distributed under the terms of the *)
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(* * GNU Lesser General Public License Version 2.1 *)
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(************************************************************************)
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(** This file is deprecated, for a tree on list, use [Mergesort.v]. *)
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(** A development of Treesort on Heap trees. It has an average
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complexity of O(n.log n) but of O(n²) in the worst case (e.g. if
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the list is already sorted) *)
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@@ -88,9 +78,9 @@ Section defs.
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forall P:Tree -> Type,
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P Tree_Leaf ->
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(forall (a:A) (T1 T2:Tree),
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leA_Tree a T1 ->
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leA_Tree a T2 ->
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is_heap T1 -> P T1 -> is_heap T2 -> P T2 -> P (Tree_Node a T1 T2)) ->
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leA_Tree a T1 ->
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leA_Tree a T2 ->
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is_heap T1 -> P T1 -> is_heap T2 -> P T2 -> P (Tree_Node a T1 T2)) ->
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forall T:Tree, is_heap T -> P T.
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Proof.
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simple induction T; auto with datatypes.
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@@ -105,9 +95,9 @@ Section defs.
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forall P:Tree -> Set,
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P Tree_Leaf ->
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(forall (a:A) (T1 T2:Tree),
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leA_Tree a T1 ->
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leA_Tree a T2 ->
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is_heap T1 -> P T1 -> is_heap T2 -> P T2 -> P (Tree_Node a T1 T2)) ->
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leA_Tree a T1 ->
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leA_Tree a T2 ->
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is_heap T1 -> P T1 -> is_heap T2 -> P T2 -> P (Tree_Node a T1 T2)) ->
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forall T:Tree, is_heap T -> P T.
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Proof.
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simple induction T; auto with datatypes.
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@@ -135,13 +125,13 @@ Section defs.
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(forall a, HdRel leA a l1 -> HdRel leA a l2 -> HdRel leA a l) ->
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merge_lem l1 l2.
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Require Import Morphisms.
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Instance: Equivalence (@meq A).
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Proof. constructor; auto with datatypes. red. apply meq_trans. Defined.
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Instance: Proper (@meq A ++> @meq _ ++> @meq _) (@munion A).
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Proof. intros x y H x' y' H'. now apply meq_congr. Qed.
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Lemma merge :
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forall l1:list A, Sorted leA l1 ->
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forall l2:list A, Sorted leA l2 -> merge_lem l1 l2.
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@@ -150,8 +140,8 @@ Section defs.
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apply merge_exist with l2; auto with datatypes.
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rename l1 into l.
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revert l2 H0. fix 1. intros.
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destruct l2 as [|a0 l0].
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apply merge_exist with (a :: l); simpl; auto with datatypes.
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destruct l2 as [|a0 l0].
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apply merge_exist with (a :: l); simpl; auto with datatypes.
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elim (leA_dec a a0); intros.
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(* 1 (leA a a0) *)
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@@ -159,18 +149,18 @@ Section defs.
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destruct (merge l H (a0 :: l0) H0).
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apply merge_exist with (a :: l1). clear merge merge0.
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auto using cons_sort, cons_leA with datatypes.
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simpl. rewrite m. now rewrite munion_ass.
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intros. apply cons_leA.
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simpl. rewrite m. now rewrite munion_ass.
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intros. apply cons_leA.
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apply (@HdRel_inv _ leA) with l; trivial with datatypes.
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(* 2 (leA a0 a) *)
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apply Sorted_inv in H0. destruct H0.
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destruct (merge0 l0 H0). clear merge merge0.
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apply merge_exist with (a0 :: l1);
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destruct (merge0 l0 H0). clear merge merge0.
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apply merge_exist with (a0 :: l1);
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auto using cons_sort, cons_leA with datatypes.
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simpl; rewrite m. simpl. setoid_rewrite munion_ass at 1. rewrite munion_comm.
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repeat rewrite munion_ass. setoid_rewrite munion_comm at 3. reflexivity.
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intros. apply cons_leA.
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intros. apply cons_leA.
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apply (@HdRel_inv _ leA) with l0; trivial with datatypes.
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Qed.
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@@ -186,7 +176,7 @@ Section defs.
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match t with
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| Tree_Leaf => emptyBag
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| Tree_Node a t1 t2 =>
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munion (contents t1) (munion (contents t2) (singletonBag a))
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munion (contents t1) (munion (contents t2) (singletonBag a))
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end.
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@@ -272,11 +262,11 @@ Section defs.
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apply flat_exist with (a :: l); simpl; auto with datatypes.
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apply meq_trans with
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(munion (list_contents _ eqA_dec l1)
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(munion (list_contents _ eqA_dec l2) (singletonBag a))).
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(munion (list_contents _ eqA_dec l2) (singletonBag a))).
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apply meq_congr; auto with datatypes.
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apply meq_trans with
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(munion (singletonBag a)
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(munion (list_contents _ eqA_dec l1) (list_contents _ eqA_dec l2))).
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(munion (list_contents _ eqA_dec l1) (list_contents _ eqA_dec l2))).
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apply munion_rotate.
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apply meq_right; apply meq_sym; trivial with datatypes.
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Qed.
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@@ -1,11 +1,3 @@
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(************************************************************************)
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(* v * The Coq Proof Assistant / The Coq Development Team *)
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(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
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(* \VV/ **************************************************************)
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(* // * This file is distributed under the terms of the *)
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(* * GNU Lesser General Public License Version 2.1 *)
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(************************************************************************)
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Require Import Omega Relations Multiset SetoidList.
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(** This file is deprecated, use [Permutation.v] instead.
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@@ -154,7 +146,7 @@ Lemma permut_add_cons_inside :
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Proof.
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intros;
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replace (a :: l) with ([] ++ a :: l); trivial;
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apply permut_add_inside; trivial.
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apply permut_add_inside; trivial.
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Qed.
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Lemma permut_middle :
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@@ -168,8 +160,8 @@ Lemma permut_sym_app :
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Proof.
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intros l1 l2;
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unfold permutation, meq;
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intro a; do 2 rewrite list_contents_app; simpl;
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auto with arith.
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intro a; do 2 rewrite list_contents_app; simpl;
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auto with arith.
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Qed.
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Lemma permut_rev :
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@@ -1,17 +1,5 @@
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(************************************************************************)
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(* v * The Coq Proof Assistant / The Coq Development Team *)
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(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
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(* \VV/ **************************************************************)
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(* // * This file is distributed under the terms of the *)
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(* * GNU Lesser General Public License Version 2.1 *)
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(************************************************************************)
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(*********************************************************************)
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(** * List permutations as a composition of adjacent transpositions *)
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(*********************************************************************)
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(* Adapted in May 2006 by Jean-Marc Notin from initial contents by
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Laurent Théry (Huffmann contribution, October 2003) *)
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Laurent Thery (Huffmann contribution, October 2003) *)
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Require Import List Setoid Compare_dec Morphisms.
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Import ListNotations. (* For notations [] and [a;b;c] *)
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@@ -1,10 +1,2 @@
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(************************************************************************)
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(* v * The Coq Proof Assistant / The Coq Development Team *)
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(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *)
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(* \VV/ **************************************************************)
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(* // * This file is distributed under the terms of the *)
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(* * GNU Lesser General Public License Version 2.1 *)
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(************************************************************************)
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Require Export Sorted.
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Require Export Mergesort.
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