OpenMath Content Dictionary: aggregate_cats

Canonical URL:

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

CD File:

aggregate_cats.ocd

CD as XML Encoded OpenMath:

aggregate_cats.omcd

Defines:

aggregateType, continuousSetType, discreteSetType, finiteSetType, infiniteSetType, multisetType, non_continuousSetType, piecewiseContinuousSetType, setType

Date:

2002-08-25

Version:

0 (Revision 1)

Review Date:

2017-12-31

Status:

experimental

---

     This document is distributed in the hope that it will be useful, 
     but WITHOUT ANY WARRANTY; without even the implied warranty of 
     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)
          intact.  The simplest way to do this is to distribute the derived
          work under the OpenMath license, but this is not a requirement.
     If you have questions about this license please contact the OpenMath
     society at http://www.openmath.org.

  Author: Bill Naylor

A CD of basic aggregate category constructors. This CD holds constructors of individual instances of the categories, with defining properties of the categories.

---

aggregateType

Description:

This symbol represents a generic type for aggregates (or collections of objects.

Signatures:

sts

---

[Next: multisetType] [Last: discreteSetType] [Top]

---

multisetType

Description:

This symbol represents the type of multisets.

Commented Mathematical property (CMP):

multisetType is an aggregate type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="multisetType"/>
        <OMS cd="aggregate_cats" name="aggregateType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">multisetType</csymbol>
  <csymbol cd="aggregate_cats">aggregateType</csymbol>
 </apply>
</math>

Prefix

has (multisetType, aggregateType)

Popcorn

meta_cats.has(aggregate_cats.multisetType, aggregate_cats.aggregateType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{multisetType},\mathrm{aggregateType})$$

Signatures:

sts

---

[Next: setType] [Previous: aggregateType] [Top]

---

setType

Description:

This symbol represents the type of sets.

Commented Mathematical property (CMP):

setType is an aggregate type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="setType"/>
        <OMS cd="aggregate_cats" name="aggregateType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
  <csymbol cd="aggregate_cats">aggregateType</csymbol>
 </apply>
</math>

Prefix

has (setType, aggregateType)

Popcorn

meta_cats.has(aggregate_cats.setType, aggregate_cats.aggregateType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{setType},\mathrm{aggregateType})$$

Signatures:

sts

---

[Next: finiteSetType] [Previous: multisetType] [Top]

---

finiteSetType

Description:

This symbol represents the type of finite sets.

Commented Mathematical property (CMP):

finite set type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="finiteSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">finiteSetType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (finiteSetType, setType)

Popcorn

meta_cats.has(aggregate_cats.finiteSetType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{finiteSetType},\mathrm{setType})$$

Signatures:

sts

---

[Next: infiniteSetType] [Previous: setType] [Top]

---

infiniteSetType

Description:

This symbol represents the type of infinite sets.

Commented Mathematical property (CMP):

infinite set type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="infiniteSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">infiniteSetType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (infiniteSetType, setType)

Popcorn

meta_cats.has(aggregate_cats.infiniteSetType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{infiniteSetType},\mathrm{setType})$$

Commented Mathematical property (CMP):

infinite set type does not have finite set type

Signatures:

sts

---

[Next: continuousSetType] [Previous: finiteSetType] [Top]

---

continuousSetType

Description:

This symbol represents the type of continuous sets.

Commented Mathematical property (CMP):

continuous set type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="continuousSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">continuousSetType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (continuousSetType, setType)

Popcorn

meta_cats.has(aggregate_cats.continuousSetType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{continuousSetType},\mathrm{setType})$$

Signatures:

sts

---

[Next: piecewiseContinuousSetType] [Previous: infiniteSetType] [Top]

---

piecewiseContinuousSetType

Description:

This symbol represents the type of piecewise continuous sets.

Commented Mathematical property (CMP):

piecewise continuous set type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="piecewiseContinuousSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">piecewiseContinuousSetType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (piecewiseContinuousSetType, setType)

Popcorn

meta_cats.has(aggregate_cats.piecewiseContinuousSetType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{piecewiseContinuousSetType},\mathrm{setType})$$

Signatures:

sts

---

[Next: non_continuousSetType] [Previous: continuousSetType] [Top]

---

non_continuousSetType

Description:

This symbol represents the type of non-continuous sets.

Commented Mathematical property (CMP):

non-continuous set type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="non_continuousSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">non_continuousSetType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (non_continuousSetType, setType)

Popcorn

meta_cats.has(aggregate_cats.non_continuousSetType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{non\_continuousSetType},\mathrm{setType})$$

Commented Mathematical property (CMP):

non-continuous set type does not have continuous set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="logic1" name="not"/>
        <OMA>
          <OMS cd="meta_cats" name="has"/>
          <OMS cd="aggregate_cats" name="non_continuousSetType"/>
          <OMS cd="aggregate_cats" name="continuousSetType"/>
        </OMA>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="logic1">not</csymbol>
  <apply><csymbol cd="meta_cats">has</csymbol>
   <csymbol cd="aggregate_cats">non_continuousSetType</csymbol>
   <csymbol cd="aggregate_cats">continuousSetType</csymbol>
  </apply>
 </apply>
</math>

Prefix

not (has (non_continuousSetType, continuousSetType) )

Popcorn

not(meta_cats.has(aggregate_cats.non_continuousSetType, aggregate_cats.continuousSetType))

Rendered Presentation MathML

$$\neg \mathrm{has}(\mathrm{non\_continuousSetType},\mathrm{continuousSetType})$$

Signatures:

sts

---

[Next: discreteSetType] [Previous: piecewiseContinuousSetType] [Top]

---

discreteSetType

Description:

This symbol represents the type of discrete sets.

Commented Mathematical property (CMP):

discrete set type has set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="meta_cats" name="has"/>
        <OMS cd="aggregate_cats" name="discreteSetType"/>
        <OMS cd="aggregate_cats" name="setType"/>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="meta_cats">has</csymbol>
  <csymbol cd="aggregate_cats">discreteSetType</csymbol>
  <csymbol cd="aggregate_cats">setType</csymbol>
 </apply>
</math>

Prefix

has (discreteSetType, setType)

Popcorn

meta_cats.has(aggregate_cats.discreteSetType, aggregate_cats.setType)

Rendered Presentation MathML

$$\mathrm{has}(\mathrm{discreteSetType},\mathrm{setType})$$

Commented Mathematical property (CMP):

discrete set type does not have continuous set type or piecewise continuous set type

Formal Mathematical property (FMP):

OpenMath XML (source)

    <OMOBJ xmlns="http://www.openmath.org/OpenMath">
      <OMA>
        <OMS cd="logic1" name="not"/>
        <OMA>
          <OMS cd="meta_cats" name="has"/>
          <OMS cd="aggregate_cats" name="discreteSetType"/>
          <OMS cd="aggregate_cats" name="continuousSetType"/>
        </OMA>
      </OMA>
    </OMOBJ>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="logic1">not</csymbol>
  <apply><csymbol cd="meta_cats">has</csymbol>
   <csymbol cd="aggregate_cats">discreteSetType</csymbol>
   <csymbol cd="aggregate_cats">continuousSetType</csymbol>
  </apply>
 </apply>
</math>

Prefix

not (has (discreteSetType, continuousSetType) )

Popcorn

not(meta_cats.has(aggregate_cats.discreteSetType, aggregate_cats.continuousSetType))

Rendered Presentation MathML

$$\neg \mathrm{has}(\mathrm{discreteSetType},\mathrm{continuousSetType})$$

Signatures:

sts

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[First: aggregateType] [Previous: non_continuousSetType] [Top]