package coq-core

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The Coq Proof Assistant -- Core Binaries and Tools

Install

Dune Dependency

coq.inria.fr Readme Edit opam file Versions (9)

Authors

T

The Coq development team, INRIA, CNRS, and contributors

Maintainers

T

The Coq development team <coqdev@inria.fr>

Sources

coq-8.19.2.tar.gz

md5=5d1187d5e44ed0163f76fb12dabf012e

sha512=91bc81530fa4f6498961583ad51eac5001f139881788b88e360a866ad8e2a6e2c5bce86d1a580ab4cd4782bf49d48318767df82471ce33ba3ac143e5569ad33c

doc/coq-core.clib/Predicate/Make/index.html

Module `Predicate.Make`Source

The Make functor constructs an implementation for any OrderedType.

Parameters

module Ord : OrderedType

Signature

Sourcetype elt = Ord.t

The type of the elements in the set.

Sourcetype t

The type of sets.

Sourceval empty : t

The empty set.

Sourceval full : t

The set of all elements (of type elm).

Sourceval is_empty : t -> bool

Test whether a set is empty or not.

Sourceval is_full : t -> bool

Test whether a set contains the whole type or not.

Sourceval mem : elt -> t -> bool

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

Sourceval singleton : elt -> t

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

Sourceval 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.

Sourceval 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.

Sourceval union : t -> t -> t

Set union.

Sourceval inter : t -> t -> t

Set intersection.

Sourceval diff : t -> t -> t

Set difference.

Sourceval complement : t -> t

Set complement.

Sourceval equal : t -> t -> bool

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

Sourceval subset : t -> t -> bool

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

Sourceval 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

Sourceval is_finite : t -> bool

true if the predicate can be given as a finite set (if elt is a finite type, we can have is_finite x = false yet x is finite, but we don't know how to list its elements)

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Parameters
Signature