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...

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

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"...

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

is not generally the case, e.g. the simply typed lambda calculus allows only terms to depend on terms. Pure type systems were independently introduced...

systems of typed lambda calculus including the simply typed lambda calculus, Jean-Yves Girard's System F, and Thierry Coquand's calculus of constructions...

the simply typed lambda calculus, types T are either atomic type constants or function types of form T → T {\displaystyle T\rightarrow T} . Such types are...

typed lambda calculus. Church's theory of types helped the formal system avoid the Kleene–Rosser paradox that afflicted the original untyped lambda calculus...

is in defining type inference in the simply typed lambda calculus, which is the internal language of Cartesian closed categories. Typing rules specify...

the Cartesian closed categories, whose internal language is simply typed lambda calculus. In computer programming, apply applies a function to a list...

uninhabited types. For most typed calculi, the type inhabitation problem is very hard. Richard Statman proved that for simply typed lambda calculus the type inhabitation...

essentially a simply typed lambda calculus "one level up", endowed with a primitive type, denoted ∗ {\displaystyle *} and called "type", which is the...

the lambda calculus, such as the simply-typed lambda calculus, many calculi with advanced type systems, and Gordon Plotkin's beta-value calculus. Plotkin...

Is there any example of a T? This is known as type inhabitation. For the simply typed lambda calculus, all three questions are decidable. The situation...

theories with simply typed lambda calculus at the lowest corner and the calculus of constructions at the highest. Prior to 1994, many type theorists thought...

language is the simply typed lambda calculus. They are generalized by closed monoidal categories, whose internal language, linear type systems, are suitable...

closed symmetric monoidal categories, much in the same way that simply typed lambda calculus is the language of Cartesian closed categories. More precisely...

Q0 is Peter Andrews' formulation of the simply-typed lambda calculus, and provides a foundation for mathematics comparable to first-order logic plus set...

higher-kinded type). In theoretical settings and programming languages where functions are defined in curried form, such as the simply typed lambda calculus, a function...

foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem...

contrast with Turing machines. Although (untyped) lambda calculus is Turing-complete, simply typed lambda calculus is not. AI-completeness Algorithmic information...

allow the subtyping of records. Consequently, simply typed lambda calculus extended with record types is perhaps the simplest theoretical setting in...

demonstrating formal similarity between intuitionistic logic and the simply typed lambda calculus that has come to be known as the Curry–Howard correspondence...

}}X{\mbox{ and }}((mX)Z)\\\end{array}}} In simply typed lambda calculus, fixed-point combinators cannot be typed and hence are not admitted. Curry's paradox...