OpenMath Content Dictionary: lc

Canonical URL:

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

CD Base:

http://www.openmath.org/cd

CD File:

lc.ocd

CD as XML Encoded OpenMath:

lc.omcd

Defines:

Lambda, PiType, mapsto, type, typecoerce

Date:

2004-03-30

Version:

2 (Revision 1)

Review Date:

2017-12-31

Status:

experimental

---

     This document is distributed in the hope that it will be useful, 
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     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

     The copyright holder grants you permission to redistribute this 
     document freely as a verbatim copy. Furthermore, the copyright
     holder permits you to develop any derived work from this document
     provided that the following conditions are met.
       a) The derived work acknowledges the fact that it is derived from
          this document, and maintains a prominent reference in the 
          work to the original source.
       b) The fact that the derived work is not the original OpenMath 
          document is stated prominently in the derived work.  Moreover if
          both this document and the derived work are Content Dictionaries
          then the derived work must include a different CDName element,
          chosen so that it cannot be confused with any works adopted by
          the OpenMath Society.  In particular, if there is a Content 
          Dictionary Group whose name is, for example, `math' containing
          Content Dictionaries named `math1', `math2' etc., then you should 
          not name a derived Content Dictionary `mathN' where N is an integer.
          However you are free to name it `private_mathN' or some such.  This
          is because the names `mathN' may be used by the OpenMath Society
          for future extensions.
       c) The derived work is distributed under terms that allow the
          compilation of derived works, but keep paragraphs a) and b)
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     If you have questions about this license please contact the OpenMath
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  Author: OpenMath Consortium
  SourceURL: https://github.com/OpenMath/CDs
            

Lambda Calculus

Initial version: O. Caprotti

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type

Role:

semantic-attribution

Description:

Attribution tag to denote type-judgement

Signatures:

sts

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[Next: typecoerce] [Last: Lambda] [Top]

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typecoerce

Role:

semantic-attribution

Description:

Attribution tag to denote type-judgement with coercion

Signatures:

sts

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[Next: PiType] [Previous: type] [Top]

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PiType

Role:

application

Description:

The type constructor of dependant function space. It binds the (type-attributed) variables in the body, that is an OpenMath object.

Example:

Signatures:

sts

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[Next: mapsto] [Previous: typecoerce] [Top]

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mapsto

Role:

application

Description:

The type constructor of non-dependant function space. The first n-1 children denote the types of the arguments, the last denotes the return type. Contrary to sts:mapsto, arguments cannot be variables but have to be OpenMath objects that map to ground OpenMath terms (they contain no variables).

Signatures:

sts

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[Next: Lambda] [Previous: PiType] [Top]

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Lambda

Role:

application

Description:

The abstraction constructor. It is followed by a list of variables and an OpenMath object.

Signatures:

sts

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[First: type] [Previous: mapsto] [Top]