The simply typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with...

A typed lambda calculus is a typed formalism that uses the lambda-symbol ( λ {\displaystyle \lambda } ) to denote anonymous function abstraction. In this...

can. On the other hand, typed lambda calculi allow more things to be proven. For example, in the simply typed lambda calculus it is a theorem that every...

polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism...

language. One of Curry's examples was the correspondence between simply typed lambda calculus and intuitionistic logic. Predicate logic is an extension of...

these categories is the linear type system (corresponding to linear logic), which generalizes simply-typed lambda calculus as the internal language of cartesian...

applications of unary type operators. Therefore, we can view the type operators as a simply typed lambda calculus, which has only one basic type, usually denoted...

the predicative calculus of inductive constructions (which removes some impredicativity). The CoC is a higher-order typed lambda calculus, initially developed...

the different dimensions in which the calculus of constructions is a generalization of the simply typed λ-calculus. Each dimension of the cube corresponds...

value of type a. In the simply typed lambda calculus extended with recursive data types, fixed-point operators can be written, but the type of a "useful"...