Expr×
Expr× is a notation and software concept introduced to formalize a cross-expression operator in symbolic computation. The term combines 'Expr', shorthand for expression, with the multiplication sign to indicate a structured product of two expression trees. It originated in the symbolic algebra community in the late 2010s as a means to express pairwise composition of subexpressions while retaining their identities for rewriting and simplification. In implementations, Expr× is typically an infix binary operator with left-to-right associativity and user-definable semantics via a context-specific algebra.
Notation and semantics: In a given algebra, E×F denotes the cross product of the expressions E and
Implementation: Reference libraries and languages have experimented with Expr× as an extension to existing CAS or
Use and reception: Expr× is used in research on symbolic programming, automated theorem proving, and advanced
See also: Symbolic computation, Expression templates, Algebra, Cross product, Formal language.