helm/software/matita/contribs/procedural/Coq/Sorting/Heap.mma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "Coq.ma".
  18
  19 (*#***********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  22
  23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  24
  25 (*   \VV/  **************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the       *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1        *)
  30
  31 (*#***********************************************************************)
  32
  33 (*i $Id: Heap.v,v 1.3.2.1 2004/07/16 19:31:19 herbelin Exp $ i*)
  34
  35 (*#* A development of Treesort on Heap trees *)
  36
  37 (* G. Huet 1-9-95 uses Multiset *)
  38
  39 include "Lists/List.ma".
  40
  41 include "Sets/Multiset.ma".
  42
  43 include "Sorting/Permutation.ma".
  44
  45 include "Relations/Relations.ma".
  46
  47 include "Sorting/Sorting.ma".
  48
  49 (* UNEXPORTED
  50 Section defs
  51 *)
  52
  53 (* UNEXPORTED
  54 cic:/Coq/Sorting/Heap/defs/A.var
  55 *)
  56
  57 (* UNEXPORTED
  58 cic:/Coq/Sorting/Heap/defs/leA.var
  59 *)
  60
  61 (* UNEXPORTED
  62 cic:/Coq/Sorting/Heap/defs/eqA.var
  63 *)
  64
  65 (* UNAVAILABLE OBJECT: cic:/Coq/Sorting/Heap/defs/gtA.con *****************)
  66
  67 inline procedural "cic:/Coq/Sorting/Heap/defs/gtA.con" "defs__" as definition.
  68
  69 (* UNEXPORTED
  70 cic:/Coq/Sorting/Heap/defs/leA_dec.var
  71 *)
  72
  73 (* UNEXPORTED
  74 cic:/Coq/Sorting/Heap/defs/eqA_dec.var
  75 *)
  76
  77 (* UNEXPORTED
  78 cic:/Coq/Sorting/Heap/defs/leA_refl.var
  79 *)
  80
  81 (* UNEXPORTED
  82 cic:/Coq/Sorting/Heap/defs/leA_trans.var
  83 *)
  84
  85 (* UNEXPORTED
  86 cic:/Coq/Sorting/Heap/defs/leA_antisym.var
  87 *)
  88
  89 (* UNEXPORTED
  90 Hint Resolve leA_refl.
  91 *)
  92
  93 (* UNEXPORTED
  94 Hint Immediate eqA_dec leA_dec leA_antisym.
  95 *)
  96
  97 (* UNAVAILABLE OBJECT: cic:/Coq/Sorting/Heap/defs/emptyBag.con ************)
  98
  99 inline procedural "cic:/Coq/Sorting/Heap/defs/emptyBag.con" "defs__" as definition.
 100
 101 (* UNAVAILABLE OBJECT: cic:/Coq/Sorting/Heap/defs/singletonBag.con ********)
 102
 103 inline procedural "cic:/Coq/Sorting/Heap/defs/singletonBag.con" "defs__" as definition.
 104
 105 inline procedural "cic:/Coq/Sorting/Heap/Tree.ind".
 106
 107 (*#* [a] is lower than a Tree [T] if [T] is a Leaf
 108     or [T] is a Node holding [b>a] *)
 109
 110 inline procedural "cic:/Coq/Sorting/Heap/leA_Tree.con" as definition.
 111
 112 inline procedural "cic:/Coq/Sorting/Heap/leA_Tree_Leaf.con" as lemma.
 113
 114 inline procedural "cic:/Coq/Sorting/Heap/leA_Tree_Node.con" as lemma.
 115
 116 (* UNEXPORTED
 117 Hint Resolve leA_Tree_Leaf leA_Tree_Node.
 118 *)
 119
 120 (*#* The heap property *)
 121
 122 inline procedural "cic:/Coq/Sorting/Heap/is_heap.ind".
 123
 124 (* UNEXPORTED
 125 Hint Constructors is_heap.
 126 *)
 127
 128 inline procedural "cic:/Coq/Sorting/Heap/invert_heap.con" as lemma.
 129
 130 (* This lemma ought to be generated automatically by the Inversion tools *)
 131
 132 inline procedural "cic:/Coq/Sorting/Heap/is_heap_rec.con" as lemma.
 133
 134 inline procedural "cic:/Coq/Sorting/Heap/low_trans.con" as lemma.
 135
 136 (*#* contents of a tree as a multiset *)
 137
 138 (*#* Nota Bene : In what follows the definition of SingletonBag
 139     in not used. Actually, we could just take as postulate:
 140     [Parameter SingletonBag : A->multiset].  *)
 141
 142 inline procedural "cic:/Coq/Sorting/Heap/contents.con" as definition.
 143
 144 (*#* equivalence of two trees is equality of corresponding multisets *)
 145
 146 inline procedural "cic:/Coq/Sorting/Heap/equiv_Tree.con" as definition.
 147
 148 (*#* specification of heap insertion *)
 149
 150 inline procedural "cic:/Coq/Sorting/Heap/insert_spec.ind".
 151
 152 inline procedural "cic:/Coq/Sorting/Heap/insert.con" as lemma.
 153
 154 (*#* building a heap from a list *)
 155
 156 inline procedural "cic:/Coq/Sorting/Heap/build_heap.ind".
 157
 158 inline procedural "cic:/Coq/Sorting/Heap/list_to_heap.con" as lemma.
 159
 160 (*#* building the sorted list *)
 161
 162 inline procedural "cic:/Coq/Sorting/Heap/flat_spec.ind".
 163
 164 inline procedural "cic:/Coq/Sorting/Heap/heap_to_list.con" as lemma.
 165
 166 (*#* specification of treesort *)
 167
 168 inline procedural "cic:/Coq/Sorting/Heap/treesort.con" as theorem.
 169
 170 (* UNEXPORTED
 171 End defs
 172 *)
 173