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: OpenMath Consortium
SourceURL: https://github.com/OpenMath/CDs
This CD is intended to be `compatible' with MathML list constructs.
mapThis symbol represents a mapping function which may be used to construct lists, it takes as arguments a function from X to Y and a list over X in that order. The value that is returned is a list of values in Y. The argument list may be a set or an integer_interval.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="list1" name="map"/>
<OMBIND>
<OMS cd="fns1" name="lambda"/>
<OMBVAR>
<OMV name="x"/>
</OMBVAR>
<OMA>
<OMS cd="arith1" name="times"/>
<OMI> 2 </OMI>
<OMV name="x"/>
</OMA>
</OMBIND>
<OMA>
<OMS cd="interval1" name="integer_interval"/>
<OMI> 0 </OMI>
<OMI> 10 </OMI>
</OMA>
</OMA>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="list1">map</csymbol> <bind><csymbol cd="fns1">lambda</csymbol> <bvar><ci>x</ci></bvar> <apply><csymbol cd="arith1">times</csymbol><cn type="integer">2</cn><ci>x</ci></apply> </bind> <apply><csymbol cd="interval1">integer_interval</csymbol> <cn type="integer">0</cn> <cn type="integer">10</cn> </apply> </apply> </math>
list1.map(fns1.lambda[$x -> 2 * $x], interval1.integer_interval(0, 10))
list ( 2 x | x ∈ [ 0 , 10 ] )
This symbol represents the suchthat function which may be used to construct lists, it takes two arguments. The first argument should be the set which contains the elements of the list, the second argument should be a predicate, that is a function from the set to the booleans which describes if an element is to be in the list returned.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="list1" name="suchthat"/>
<OMS cd="setname1" name="Z"/>
<OMBIND>
<OMS cd="fns1" name="lambda"/>
<OMBVAR>
<OMV name="x"/>
</OMBVAR>
<OMA>
<OMS cd="logic1" name="and"/>
<OMA>
<OMS cd="relation1" name="geq"/>
<OMV name="x"/>
<OMS cd="alg1" name="zero"/>
</OMA>
<OMA>
<OMS cd="relation1" name="lt"/>
<OMV name="x"/>
<OMI> 100 </OMI>
</OMA>
<OMA>
<OMS cd="set1" name="in"/>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMV name="x"/>
<OMI> 2 </OMI>
</OMA>
<OMS cd="setname1" name="Z"/>
</OMA>
</OMA>
</OMBIND>
</OMA>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply><csymbol cd="list1">suchthat</csymbol>
<csymbol cd="setname1">Z</csymbol>
<bind><csymbol cd="fns1">lambda</csymbol>
<bvar><ci>x</ci></bvar>
<apply><csymbol cd="logic1">and</csymbol>
<apply><csymbol cd="relation1">geq</csymbol><ci>x</ci><csymbol cd="alg1">zero</csymbol></apply>
<apply><csymbol cd="relation1">lt</csymbol><ci>x</ci><cn type="integer">100</cn></apply>
<apply><csymbol cd="set1">in</csymbol>
<apply><csymbol cd="arith1">divide</csymbol><ci>x</ci><cn type="integer">2</cn></apply>
<csymbol cd="setname1">Z</csymbol>
</apply>
</apply>
</bind>
</apply>
</math>
list1.suchthat(setname1.Z, fns1.lambda[$x -> $x >= alg1.zero and $x < 100 and set1.in($x / 2, setname1.Z)])
list ( x ∈ Z | x ≥ 0 ∧ x < 100 ∧ x 2 ∈ Z )
This symbol denotes the list construct which is an n-ary function. The list entries must be given explicitly.
<OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="list1" name="list"/>
<OMI> 3 </OMI>
<OMI> 6 </OMI>
<OMI> 9 </OMI>
</OMA>
</OMOBJ>
<math xmlns="http://www.w3.org/1998/Math/MathML"> <apply><csymbol cd="list1">list</csymbol> <cn type="integer">3</cn> <cn type="integer">6</cn> <cn type="integer">9</cn> </apply> </math>
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