[Om3] homework, describing a definition for n-ary plus

[Jan Willem Knopper]

<!--
  NOTATION: arith1.plus is <OMS cd='arith1' name='plus'/>

  This is a example description of an n-ary plus, defined based on a
binary plus (for which I use homework2.plus2).

  homework1.function_with_arguments describes an n-ary function which
can be defined by allowing access to the arguments in a single variable
(by an OMBIND). Several computer languages have a keyword or accessor to
get to an array of arguments (Javascript, GAP).

  homework1.length returns the length of an argument sequence/list

  homework1.first returns the first argument of an argument sequence/list

  homework1.rest returns a new argument sequence/list containing all but
the first argument.

  homework1.argument_sequence is implied (argument list)
-->
<--
  real question

  is the idea that I describe an n-ary function with a new cd good
enough for all applications ?

  regardless of whether we need it for this definition it might be good
to have some new kind of apply function that calls a function with the
arguments in a list (list1.list ?).

  will it be good enough to do this in a cd as well,

  homework1.apply_with_arguments:


@(homework1.apply_with_arguments,arith1.plus,@(homework1.argument_sequence,1,2,3))

  is it possible to do correct types for this, or will this run into
problems ?

  Any other comments ?
-->

<DEFMP>
  <OMS cd='arith1' name='plus'/>
  <OMBIND>
    <OMS cd='homework1' name='function_with_arguments'/>
    <OMBVAR>
      <OMV name='arguments'/>
    </OMBVAR>
    <OMA>
      <OMA>
        <OMS cd='prog1' name='if'/>
        <!-- 0 arguments: 0 -->
        <OMA>
          <OMS cd='relation1' name='eq'/>
          <OMA>
            <OMS cd='homework1' name='length'/>
            <OMV name='arguments'/>
          </OMA>
          <OMI>0</OMI>
        </OMA>
        <OMI>0</OMI>
        <OMA>
          <OMS cd='prog1' name='if'/>
          <!-- 1 arguments: value -->
          <OMA>
            <OMS cd='relation1' name='eq'/>
            <OMA>
              <OMS cd='homework1' name='length'/>
              <OMV name='arguments'/>
            </OMA>
            <OMI>1</OMI>
          </OMA>
          <OMA>
            <OMS cd='homework1' name='first'/>
            <OMV name='arguments'/>
          </OMA>
          <OMA>
            <OMS cd='prog1' name='if'/>
            <!-- 2 arguments: plus2 on first two arguments -->
            <OMA>
              <OMS cd='relation1' name='eq'/>
              <OMA>
                <OMS cd='homework1' name='length'/>
                <OMV name='arguments'/>
              </OMA>
              <OMI>1</OMI>
            </OMA>
            <OMA>
              <OMS cd='homework2' name='plus2'/>
              <OMA>
                <OMS cd='homework2' name='plus2'/>
                <OMA>
                  <OMS cd='homework1' name='first'/>
                  <OMV name='arguments'/>
                </OMA>
                <OMA>
                  <OMS cd='homework1' name='first'/>
                  <OMA>
                    <OMS cd='homework1' name='rest'/>
                    <OMV name='arguments'/>
                  </OMA>
                </OMA>
              </OMA>
            </OMA>
            <OMA>
              <OMS cd='prog1' name='if'/>
              <!-- more than 2 arguments: recursive -->
              <OMA>
                <OMS cd='arith1' name='plus'/>
                <OMA>
                  <OMS cd='homework2' name='plus2'/>
                  <OMA>
                    <OMS cd='homework1' name='first'/>
                    <OMV name='arguments'/>
                  </OMA>
                  <OMA>
                    <OMS cd='homework1' name='first'/>
                    <OMA>
                      <OMS cd='homework1' name='rest'/>
                      <OMV name='arguments'/>
                    </OMA>
                  </OMA>
                </OMA>
                <OMA>
                  <OMS cd='homework1' name='rest'/>
                  <OMA>
                    <OMS cd='homework1' name='rest'/>
                    <OMV name='arguments'/>
                  </OMA>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMA>
  </OMBIND>
</DEFMP>