Representing expressions in the semantic memory
Peter Schodl, Arnold Neumaier · 2011
This paper assumes [1]. We aim to represent in a transparent fashion all possible mathematical expression in the semantic memory. An operation is anything that can be applied to mathematical expressions E1, E2, . . . such that the result E is an expression again. We call E1, E2, . . . the subexpressions of E. In particular, all standard functions, binary operations, and relations are operations, and so are quantification, merging expressions to form a set, a vector, etc. The operations are those categories that match the category Expression in the sense of [1]. We store the information in a fashion inspired by automatic differentiation, meaning we proceed from the most elementary subexpressions (its variables and constants) to the more complicated subexpressions by applying operations until the expression is fully covered.