OpenMath Content Dictionary: setoid

Canonical URL:

http://www.openmath.org/cd/setoid.ocd

CD Base:

http://www.openmath.org/cd

CD File:

setoid.ocd

CD as XML Encoded OpenMath:

setoid.omcd

Defines:

Setoid, make_Setoid

Date:

2004-03-30

Version:

2 (Revision 1)

Review Date:

2017-12-31

Status:

experimental

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  Author: OpenMath Consortium
  SourceURL: https://github.com/OpenMath/CDs
            

The definition of a setoid as a set with an equivalence relations defined on its elements. Initial version: O. Caprotti

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Setoid

Role:

application

Description:

The contructor for the type of set with an equivalence relation on it.

Commented Mathematical property (CMP):

Is defined as Lambda {Carrier:> symtype; Eq: (relation Carrier)}. SigmaType{ Carrier:> symtype; Eq: (relation Carrier); (equivalence Carrier Eq) }

Example:

Signatures:

sts

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make_Setoid

Role:

application

Description:

The contructor for the tuples consisting of a set, an equivalence relation on the set, and a proof that the relation is actually an equivalence relation.

Commented Mathematical property (CMP):

Is defined as Lambda {Carrier:> symtype; Eq: (relation Carrier) proof: (equivalence Carrier Eq)}. Tuple (Carrier, Eq, proof)

Example:

Signatures:

sts

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