The Coq Standard Library
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 Import command.
The standard library is composed of the following subdirectories:
Init :
The core library
Datatypes
Logic_Type
Logic
Notations
Peano
Prelude
Specif
Wf
Logic :
Classical logic and dependent equality
Berardi
ChoiceFacts
ClassicalChoice
ClassicalDescription
ClassicalFacts
Classical_Pred_Set
Classical_Pred_Type
Classical_Prop
Classical_Type
Classical
Decidable
Diaconescu
Eqdep_dec
Eqdep
Hurkens
JMeq
ProofIrrelevance
RelationalChoice
Arith :
Basic Peano arithmetic
Arith
Between
Bool_nat
Compare_dec
Compare
Div2
Div
EqNat
Euclid
Even
Factorial
Gt
Le
Lt
Max
Minus
Min
Mult
Peano_dec
Plus
Wf_nat
NArith :
Binary positive integers
BinNat
BinPos
NArith
Pnat
ZArith :
Binary integers
auxiliary
BinInt
Wf_Z
Zabs
ZArith_base
ZArith_dec
ZArith
Zbinary
Zbool
Zcompare
Zcomplements
Zdiv
Zeven
Zhints
Zlogarithm
Zmin
Zmisc
Znat
Znumtheory
Zorder
Zpower
Zsqrt
Zwf
Reals :
Formalization of real numbers
Alembert
AltSeries
ArithProp
Binomial
Cauchy_prod
Cos_plus
Cos_rel
DiscrR
Exp_prop
Integration
MVT
NewtonInt
PartSum
PSeries_reg
Ranalysis1
Ranalysis2
Ranalysis3
Ranalysis4
Ranalysis
Raxioms
Rbase
Rbasic_fun
Rcomplete
Rdefinitions
Rderiv
Reals
Rfunctions
Rgeom
RiemannInt_SF
RiemannInt
R_Ifp
RIneq
Rlimit
RList
Rpower
Rprod
Rseries
Rsigma
Rsqrt_def
R_sqrt
R_sqr
Rtopology
Rtrigo_alt
Rtrigo_calc
Rtrigo_def
Rtrigo_fun
Rtrigo_reg
Rtrigo
SeqProp
SeqSeries
SplitAbsolu
SplitRmult
Sqrt_reg
Bool :
Booleans (basic functions and results)
BoolEq
Bool
Bvector
DecBool
IfProp
Sumbool
Zerob
Lists :
Monomorphic and polymorphic lists,
Streams (infinite sequences)
ListSet
List
MonoList
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 addresses
Adalloc
Addec
Addr
Adist
Allmaps
Fset
Lsort
Mapaxioms
Mapcanon
Mapcard
Mapc
Mapfold
Mapiter
Maplists
Mapsubset
Map
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