The Coq Standard Library
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 Require command.
The standard library is composed of the following subdirectories:
- Init:
The core library
-
Datatypes,
DatatypesSyntax,
Logic,
LogicSyntax,
Logic_Type,
Logic_TypeSyntax,
Peano,
Prelude,
SpecifSyntax,
Specif,
Wf
- Logic:
Classical logic and dependent equality
-
Berardi,
Classical_Pred_Set,
Classical_Pred_Type,
Classical_Prop,
Classical_Type,
Classical,
Decidable,
Elimdep,
Eqdep_dec,
Eqdep,
JMeq
- Arith:
Basic Peano arithmetic
-
Arith,
Between,
Compare_dec,
Compare,
Div2,
Div,
EqNat,
Euclid,
Even,
Gt,
Le,
Lt,
Max,
Minus,
Min,
Mult,
Peano_dec,
Plus,
Wf_nat
- ZArith:
Binary integers (those used by the Omega decision
tactic)
-
auxiliary,
fast_integer,
Wf_Z,
zarith_aux,
ZArith_dec,
ZArith,
Zcomplements,
Zhints,
Zlogarithm,
Zmisc,
Zpower,
Zdiv,
Zsyntax
- Reals:
Formalization of real numbers
-
DiscrR,
Ranalysis,
Raxioms,
Rbase,
Rbasic_fun,
Rdefinitions,
Rderiv,
Reals,
Rfunctions,
Rgeom,
R_Ifp,
Rlimit,
Rseries,
Rsigma,
R_sqr,
Rsyntax,
Rtrigo_fun,
Rtrigo,
SplitAbsolu,
SplitRmult,
TypeSyntax
- Bool:
Booleans (basic functions and results)
-
BoolEq,
Bool,
DecBool,
IfProp,
Sumbool,
Zerob
- Lists :
Monomorphic and polymorphic lists,
Streams (infinite sequences)
-
ListSet,
List,
PolyListSyntax,
PolyList,
Streams,
TheoryList
- Sets:
Sets (classical, constructive, finite, infinite, powerset,
etc.)
-
Classical_sets,
Constructive_sets,
Cpo,
Ensembles,
Finite_sets_facts,
Finite_sets,
Image,
Infinite_sets,
Integers,
Multiset,
Partial_Order,
Permut,
Powerset_Classical_facts,
Powerset_facts,
Powerset,
Relations_1_facts,
Relations_1,
Relations_2_facts,
Relations_2,
Relations_3_facts,
Relations_3,
Uniset
- Relations:
Relations (definitions and basic results)
-
Newman,
Operators_Properties,
Relation_Definitions,
Relation_Operators,
Relations,
Rstar
- Wellfounded:
Well founded Relations
-
Disjoint_Union,
Inclusion,
Inverse_Image,
Lexicographic_Exponentiation,
Lexicographic_Product,
Transitive_Closure,
Union,
Wellfounded,
Well_Ordering
- Sorting:
Axiomatizations of sorts
-
Heap,
Permutation,
Sorting
- Setoids:
-
Setoid
- IntMap:
Finite sets/maps as trees indexed by adresses
-
Adalloc,
Addec,
Addr,
Adist,
Allmaps,
Fset,
Lsort,
Mapaxioms,
Mapcanon,
Mapcard,
Mapc,
Mapfold,
Mapiter,
Maplists,
Mapsubset,
Map
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