typed lambda-calculus

typed lambda-calculus

(theory)
(TLC) A variety of lambda-calculus in which every term is labelled with a type.

A function application (A B) is only synctactically valid if A has type s --> t, where the type of B is s (or an instance or s in a polymorphic language) and t is any type.

If the types allowed for terms are restricted, e.g. to Hindley-Milner types then no term may be applied to itself, thus avoiding one kind of non-terminating evaluation.

Most functional programming languages, e.g. Haskell, ML, are closely based on variants of the typed lambda-calculus.
References in periodicals archive ?
as in an ordinary typed lambda-calculus. Instead, we split the type environment in the conclusion into two parts, representing the resources consumed by v and w separately:
Dependent type theory (DTT) (an extension of the simply typed lambda-calculus) is of interest to computer scientists and mathematicians for a number of reasons: It can be seen as a more expressive-compared to the lambda-calculus-programming language and forms the basis for a number of proofs assistants, such as Coq and Lean.