We will specify several translation functions. The detailed definitions will be presented through a series of schema in the following subsections. First we give some general definitions.
A function, , on expression terms returns the result of translating an expression , assuming that the expression is not a multiarray.
Translation functions for multiarray-expressions are more complicated. In section A.3.1 we defined a subset of composite multiarray-valued expressions. The remaining non-composite multiarray-valued expressions are:
The composite expressions only appear in restricted contexts and do not have translation functions in their own right (instead they are effectively handled as part of the translation of a top-level assignment statements). For non-composite multiarray-valued expressions there are separate parts of the evaluation: , and , ..., , where is the rank of the array. The interpretation of these separate terms will be given in the following sections.
Finally the translation function for statements,
translates the statement or block in the context of as active
process group. In the schemas given below for translation of statements
we will just use the name apg to refer to the effective active
process group. Hence a schema of the form