lambdaterms
Lambdaterms, or lambda terms, are formal objects used in the lambda calculus and related areas of logic and computer science. They are expressions that denote functions and their applications. A lambdaterm is built from three constructs: variables, lambda abstractions, and applications. The standard inductive definition is: a variable x is a term; if M is a term, then λx. M is a term; if M and N are terms, then (M N) is a term. This framework allows the representation of anonymous functions and higher-order functions.
Key notions include free and bound variables and alpha-equivalence. In λx. M, x is bound by the
Examples illustrate the idea. The identity function I = λx. x, when applied to y, yields y. A
In programming language theory, lambdaterms underpin the representation of functions in functional languages and enable formal