package coq

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Formal proof management system

Install 

dune-project
 Dependency

coq.inria.fr Edit opam file Versions (40)

Authors

  1. T
    The Coq development team, INRIA, CNRS, and contributors.

Maintainers

  1. C
    coqdev@inria.fr

Sources

coq-8.14.1.tar.gz
sha256=3cbfc1e1a72b16d4744f5b64ede59586071e31d9c11c811a0372060727bfd9c3

doc/coq-core.kernel/Names/Id/Pred/index.html

Module Id.PredSource

Predicates over identifiers.

type elt = t

The type of the elements in the set.

type t

The type of sets.

val empty : t

The empty set.

val full : t

The set of all elements (of type elm).

val is_empty : t -> bool

Test whether a set is empty or not.

val is_full : t -> bool

Test whether a set contains the whole type or not.

val mem : elt -> t -> bool

mem x s tests whether x belongs to the set s.

val singleton : elt -> t

singleton x returns the one-element set containing only x.

val add : elt -> t -> t

add x s returns a set containing all elements of s, plus x. If x was already in s, then s is returned unchanged.

val remove : elt -> t -> t

remove x s returns a set containing all elements of s, except x. If x was not in s, then s is returned unchanged.

val union : t -> t -> t

Set union.

val inter : t -> t -> t

Set intersection.

val diff : t -> t -> t

Set difference.

val complement : t -> t

Set complement.

val equal : t -> t -> bool

equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

val subset : t -> t -> bool

subset s1 s2 tests whether the set s1 is a subset of the set s2.

val elements : t -> bool * elt list

Gives a finite representation of the predicate: if the boolean is false, then the predicate is given in extension. if it is true, then the complement is given