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authorGravatar Samuel Mimram <smimram@debian.org>2006-04-28 14:59:16 +0000
committerGravatar Samuel Mimram <smimram@debian.org>2006-04-28 14:59:16 +0000
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+<html>
+
+<head>
+<link rel="stylesheet" href="coqdoc.css" type="text/css">
+<title>The Coq Standard Library
+</head>
+
+<body>
+
+<H1>The Coq Standard Library</H1>
+
+<p>Here is a short description of the Coq standard library, which is
+distributed with the system.
+It provides a set of modules directly available
+through the <tt>Require Import</tt> command.</p>
+
+<p>The standard library is composed of the following subdirectories:</p>
+
+<dl>
+ <dt> <b>Init</b>:
+ The core library (automatically loaded when starting Coq)
+ </dt>
+ <dd>
+ theories/Init/Notations.v
+ theories/Init/Datatypes.v
+ theories/Init/Logic.v
+ theories/Init/Logic_Type.v
+ theories/Init/Peano.v
+ theories/Init/Specif.v
+ theories/Init/Tactics.v
+ theories/Init/Wf.v
+ (theories/Init/Prelude.v)
+ </dd>
+
+ <dt> <b>Logic</b>:
+ Classical logic and dependent equality
+ </dt>
+ <dd>
+ theories/Logic/Classical_Pred_Set.v
+ theories/Logic/Classical_Pred_Type.v
+ theories/Logic/Classical_Prop.v
+ theories/Logic/Classical_Type.v
+ (theories/Logic/Classical.v)
+ theories/Logic/Decidable.v
+ theories/Logic/Eqdep_dec.v
+ theories/Logic/EqdepFacts.v
+ theories/Logic/Eqdep.v
+ theories/Logic/JMeq.v
+ theories/Logic/RelationalChoice.v
+ theories/Logic/ClassicalChoice.v
+ theories/Logic/ChoiceFacts.v
+ theories/Logic/ClassicalDescription.v
+ theories/Logic/ClassicalFacts.v
+ theories/Logic/Berardi.v
+ theories/Logic/Diaconescu.v
+ theories/Logic/Hurkens.v
+ theories/Logic/ProofIrrelevance.v
+ theories/Logic/ProofIrrelevanceFacts.v
+ </dd>
+
+ <dt> <b>Arith</b>:
+ Basic Peano arithmetic
+ </dt>
+ <dd>
+ theories/Arith/Le.v
+ theories/Arith/Lt.v
+ theories/Arith/Plus.v
+ theories/Arith/Minus.v
+ theories/Arith/Mult.v
+ theories/Arith/Gt.v
+ theories/Arith/Between.v
+ theories/Arith/Peano_dec.v
+ theories/Arith/Compare_dec.v
+ (theories/Arith/Arith.v)
+ theories/Arith/Min.v
+ theories/Arith/Max.v
+ theories/Arith/Compare.v
+ theories/Arith/Div2.v
+ theories/Arith/Div.v
+ theories/Arith/EqNat.v
+ theories/Arith/Euclid.v
+ theories/Arith/Even.v
+ theories/Arith/Bool_nat.v
+ theories/Arith/Factorial.v
+ theories/Arith/Wf_nat.v
+ </dd>
+
+ <dt> <b>NArith</b>:
+ Binary positive integers
+ </dt>
+ <dd>
+ theories/NArith/BinPos.v
+ theories/NArith/BinNat.v
+ (theories/NArith/NArith.v)
+ theories/NArith/Pnat.v
+ </dd>
+
+ <dt> <b>ZArith</b>:
+ Binary integers
+ </dt>
+ <dd>
+ theories/ZArith/BinInt.v
+ theories/ZArith/Zorder.v
+ theories/ZArith/Zcompare.v
+ theories/ZArith/Znat.v
+ theories/ZArith/Zmin.v
+ theories/ZArith/Zmax.v
+ theories/ZArith/Zminmax.v
+ theories/ZArith/Zabs.v
+ theories/ZArith/Zeven.v
+ theories/ZArith/auxiliary.v
+ theories/ZArith/ZArith_dec.v
+ theories/ZArith/Zbool.v
+ theories/ZArith/Zmisc.v
+ theories/ZArith/Wf_Z.v
+ theories/ZArith/Zhints.v
+ (theories/ZArith/ZArith_base.v)
+ theories/ZArith/Zcomplements.v
+ theories/ZArith/Zsqrt.v
+ theories/ZArith/Zpower.v
+ theories/ZArith/Zdiv.v
+ theories/ZArith/Zlogarithm.v
+ (theories/ZArith/ZArith.v)
+ theories/ZArith/Zwf.v
+ theories/ZArith/Zbinary.v
+ theories/ZArith/Znumtheory.v
+ </dd>
+
+ <dt> <b>Reals</b>:
+ Formalization of real numbers
+ </dt>
+ <dd>
+ theories/Reals/Rdefinitions.v
+ theories/Reals/Raxioms.v
+ theories/Reals/RIneq.v
+ theories/Reals/DiscrR.v
+ (theories/Reals/Rbase.v)
+ theories/Reals/RList.v
+ theories/Reals/Ranalysis.v
+ theories/Reals/Rbasic_fun.v
+ theories/Reals/Rderiv.v
+ theories/Reals/Rfunctions.v
+ theories/Reals/Rgeom.v
+ theories/Reals/R_Ifp.v
+ theories/Reals/Rlimit.v
+ theories/Reals/Rseries.v
+ theories/Reals/Rsigma.v
+ theories/Reals/R_sqr.v
+ theories/Reals/Rtrigo_fun.v
+ theories/Reals/Rtrigo.v
+ theories/Reals/SplitAbsolu.v
+ theories/Reals/SplitRmult.v
+ theories/Reals/Alembert.v
+ theories/Reals/AltSeries.v
+ theories/Reals/ArithProp.v
+ theories/Reals/Binomial.v
+ theories/Reals/Cauchy_prod.v
+ theories/Reals/Cos_plus.v
+ theories/Reals/Cos_rel.v
+ theories/Reals/Exp_prop.v
+ theories/Reals/Integration.v
+ theories/Reals/MVT.v
+ theories/Reals/NewtonInt.v
+ theories/Reals/PSeries_reg.v
+ theories/Reals/PartSum.v
+ theories/Reals/R_sqrt.v
+ theories/Reals/Ranalysis1.v
+ theories/Reals/Ranalysis2.v
+ theories/Reals/Ranalysis3.v
+ theories/Reals/Ranalysis4.v
+ theories/Reals/Rcomplete.v
+ theories/Reals/RiemannInt.v
+ theories/Reals/RiemannInt_SF.v
+ theories/Reals/Rpower.v
+ theories/Reals/Rprod.v
+ theories/Reals/Rsqrt_def.v
+ theories/Reals/Rtopology.v
+ theories/Reals/Rtrigo_alt.v
+ theories/Reals/Rtrigo_calc.v
+ theories/Reals/Rtrigo_def.v
+ theories/Reals/Rtrigo_reg.v
+ theories/Reals/SeqProp.v
+ theories/Reals/SeqSeries.v
+ theories/Reals/Sqrt_reg.v
+ (theories/Reals/Reals.v)
+ </dd>
+
+ <dt> <b>Bool</b>:
+ Booleans (basic functions and results)
+ </dt>
+ <dd>
+ theories/Bool/Bool.v
+ theories/Bool/BoolEq.v
+ theories/Bool/DecBool.v
+ theories/Bool/IfProp.v
+ theories/Bool/Sumbool.v
+ theories/Bool/Zerob.v
+ theories/Bool/Bvector.v
+ </dd>
+
+ <dt> <b>Lists</b>:
+ Polymorphic lists, Streams (infinite sequences)
+ </dt>
+ <dd>
+ theories/Lists/List.v
+ theories/Lists/ListSet.v
+ theories/Lists/MonoList.v
+ theories/Lists/MoreList.v
+ theories/Lists/SetoidList.v
+ theories/Lists/Streams.v
+ theories/Lists/TheoryList.v
+ </dd>
+
+ <dt> <b>Sets</b>:
+ Sets (classical, constructive, finite, infinite, powerset, etc.)
+ </dt>
+ <dd>
+ theories/Sets/Classical_sets.v
+ theories/Sets/Constructive_sets.v
+ theories/Sets/Cpo.v
+ theories/Sets/Ensembles.v
+ theories/Sets/Finite_sets_facts.v
+ theories/Sets/Finite_sets.v
+ theories/Sets/Image.v
+ theories/Sets/Infinite_sets.v
+ theories/Sets/Integers.v
+ theories/Sets/Multiset.v
+ theories/Sets/Partial_Order.v
+ theories/Sets/Permut.v
+ theories/Sets/Powerset_Classical_facts.v
+ theories/Sets/Powerset_facts.v
+ theories/Sets/Powerset.v
+ theories/Sets/Relations_1_facts.v
+ theories/Sets/Relations_1.v
+ theories/Sets/Relations_2_facts.v
+ theories/Sets/Relations_2.v
+ theories/Sets/Relations_3_facts.v
+ theories/Sets/Relations_3.v
+ theories/Sets/Uniset.v
+ </dd>
+
+ <dt> <b>Relations</b>:
+ Relations (definitions and basic results)
+ </dt>
+ <dd>
+ theories/Relations/Relation_Definitions.v
+ theories/Relations/Relation_Operators.v
+ theories/Relations/Relations.v
+ theories/Relations/Operators_Properties.v
+ theories/Relations/Rstar.v
+ theories/Relations/Newman.v
+ </dd>
+
+ <dt> <b>Wellfounded</b>:
+ Well-founded Relations
+ </dt>
+ <dd>
+ theories/Wellfounded/Disjoint_Union.v
+ theories/Wellfounded/Inclusion.v
+ theories/Wellfounded/Inverse_Image.v
+ theories/Wellfounded/Lexicographic_Exponentiation.v
+ theories/Wellfounded/Lexicographic_Product.v
+ theories/Wellfounded/Transitive_Closure.v
+ theories/Wellfounded/Union.v
+ theories/Wellfounded/Wellfounded.v
+ theories/Wellfounded/Well_Ordering.v
+ </dd>
+
+ <dt> <b>Sorting</b>:
+ Axiomatizations of sorts
+ </dt>
+ <dd>
+ theories/Sorting/Heap.v
+ theories/Sorting/Permutation.v
+ theories/Sorting/Sorting.v
+ </dd>
+
+ <dt> <b>Setoids</b>:
+ <dd>
+ theories/Setoids/Setoid.v
+ </dd>
+
+ <dt> <b>IntMap</b>:
+ Finite sets/maps as trees indexed by addresses
+ </dt>
+ <dd>
+ theories/IntMap/Addr.v
+ theories/IntMap/Adist.v
+ theories/IntMap/Addec.v
+ theories/IntMap/Adalloc.v
+ theories/IntMap/Map.v
+ theories/IntMap/Fset.v
+ theories/IntMap/Mapaxioms.v
+ theories/IntMap/Mapiter.v
+ theories/IntMap/Mapcanon.v
+ theories/IntMap/Mapsubset.v
+ theories/IntMap/Lsort.v
+ theories/IntMap/Mapfold.v
+ theories/IntMap/Mapcard.v
+ theories/IntMap/Mapc.v
+ theories/IntMap/Maplists.v
+ theories/IntMap/Allmaps.v
+ </dd>
+
+ <dt> <b>FSets</b>:
+ Modular implementation of finite sets/maps using lists
+ </dt>
+ <dd>
+ theories/FSets/DecidableType.v
+ theories/FSets/OrderedType.v
+ theories/FSets/FSetInterface.v
+ theories/FSets/FSetBridge.v
+ theories/FSets/FSetProperties.v
+ theories/FSets/FSetEqProperties.v
+ theories/FSets/FSetFacts.v
+ theories/FSets/FSetList.v
+ theories/FSets/FSet.v
+ theories/FSets/FMapInterface.v
+ theories/FSets/FMapList.v
+ theories/FSets/FMap.v
+ theories/FSets/FSetWeakInterface.v
+ theories/FSets/FSetWeakFacts.v
+ theories/FSets/FSetWeakList.v
+ theories/FSets/FSetWeak.v
+ theories/FSets/FMapWeakInterface.v
+ theories/FSets/FMapWeakList.v
+ theories/FSets/FMapWeak.v
+ </dd>
+
+ <dt> <b>Strings</b>
+ Implementation of string as list of ascii characters
+ </dt>
+ <dd>
+ theories/Strings/Ascii.v
+ theories/Strings/String.v
+ </dd>
+
+ </dd>
+</dl>
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