simply typed lambda calculus - Article Index

Encyclopedia - Fixed Point Combinator: Encyclopedia Ii - Fixed Point Combinator - Existence Of Fixed Point Combinators
In certain formalizations of mathematics, such as the untyped lambda calculus and combinatorial calculus, every expression can be conside...   » Read the article

Encyclopedia - Intuitionistic Type Theory: Encyclopedia Ii - Intuitionistic Type Theory - Connectives Of Type Theory
In the context of Type Theory a connective is a way of constructing types, possibly using already given types. The basic connectives of T...   » Read the article

Encyclopedia - Type Inference: Encyclopedia Ii - Type Inference - Hindley-milner Type Inference Algorithm
The common algorithm used to perform the type inference is the one now commonly referred to as Hindley-Milner or Damas-Milner algorithm. ...   » Read the article

Encyclopedia - Calculus Of Constructions: Encyclopedia Ii - Calculus Of Constructions - The Basics Of The Calculus Of Constructions
The Calculus of Constructions can be considered an extension of the Curry-Howard isomorphism. The Curry-Howard isomorphism associates a t...   » Read the article

Encyclopedia - Type Inference: Encyclopedia Ii - Type Inference - Example
For example, let us consider the Haskell function length, which may be defined as: length [] = 0 length (first:rest) = 1 + length rest ...   » Read the article

Encyclopedia - Fixed Point Combinator: Encyclopedia Ii - Fixed Point Combinator - Other Fixed Point Combinators
A version of the Y combinator that can be used in call-by-value (applicative-order) evaluation is given by η-expansion of part of the or...   » Read the article

Encyclopedia - Intuitionistic Type Theory: Encyclopedia Ii - Intuitionistic Type Theory - Formalisation Of Type Theory
Type Theory is usually presented as a dependently typed lambda calculus, using the judgements: , Γ is a well-formed context of typing a...   » Read the article

Encyclopedia - Fixed Point Combinator: Encyclopedia Ii - Fixed Point Combinator - Example
Consider the factorial function (under Church encoding). The usual recursive mathematical equation is fact(n) = if n=0 then 1 else n * f...   » Read the article

Encyclopedia - Fixed Point Combinator: Encyclopedia Ii - Fixed Point Combinator - Other Fixed Point Combinators
A version of the Y combinator that can be used in call-by-value (applicative-order) evaluation is given by η-expansion of part of the or...   » Read the article

Encyclopedia - Intuitionistic Type Theory: Encyclopedia Ii - Intuitionistic Type Theory - Categorical Models Of Type Theory
Using the language of category theory, Seely introduced the notion of a locally cartesian closed category (LCCC) as the basic model of Ty...   » Read the article