Underudtryk

Underudtryk, literally “under-expression” in Danish, is a term used in mathematics and computer science to denote a subexpression — an expression that is part of a larger expression. It refers to any expression that can be identified within a bigger form, including simple terms as well as more complex constructs.

In mathematics, subexpressions are components that can be isolated for evaluation, substitution, or simplification. For example, in the expression 2x + 3y, 2x and 3y are subexpressions; in (a + b) · c, a + b is a subexpression. Subexpressions can also appear within more intricate structures such as nested parentheses or nested operations.

In computing, subexpressions appear as parts of parse trees or abstract syntax trees constructed by compilers and interpreters. They may be evaluated, constant-folded, or transformed during optimization and simplification passes. For example, in the code a + b * c, the subexpression b * c can be evaluated independently of a.

Applications of the concept include symbolic manipulation, algebraic simplification, and compiler optimizations. Recognizing subexpressions allows for rules like substituting equivalent expressions, reorganizing computation for efficiency, or isolating terms for solving equations.

See also: Subexpression, Expression, Abstract syntax tree, Constant folding, Algebraic simplification.