Expressions

An expression is a symbolic representation that can be evaluated to yield a value. The term is used in mathematics, computer science, and linguistics with related but distinct meanings. In mathematics, expressions are combinations of constants, variables, and operations that denote a value when the variables are given specific numbers. In programming languages, an expression is a syntactic unit that can be evaluated to produce a value, and it may involve literals, variables, operators, function calls, and sometimes side effects. In linguistics, an expression refers to any utterance or conventional form that conveys meaning, such as a phrase, clause, or sentence.

Key features include syntax and semantics, evaluation rules, and context dependence. Expressions may be classified by type, such as numeric, boolean, or string expressions, and by arity: unary, binary, or n-ary operators. Operator precedence and associativity determine the order of evaluation. In programming, expressions may be pure (no side effects) or may produce side effects, and many languages distinguish expressions from statements. In some languages, assignment is an expression; in others, it is a statement.

Examples illustrate differences across domains. Mathematics: 2x + 3, sqrt(a^2 + b^2). Programming: x + y * 2; "Hello" + "World" in languages that support string concatenation; boolean: a && b; relational: x > y. In compiler and interpreter design, expressions are often represented as abstract syntax trees and evaluated by an evaluation function. Expressions can often be simplified to a reduced or normal form, and it helps to distinguish them from equations, which assert equality rather than compute a value.