Simply typed lambda calculus

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Simply typed lambda calculus - Types: Encyclopedia II - Simply typed lambda calculus - Types

The types of the simply typed lambda calculus are constructed from base types (or type variables) and given types σ,τ we can construct . Church used only two base types o for the type of propositions and ι for the type of individuals. Frequently the calculus with only one base type, usually o, is considered. associates to the right: we read as . To each type σ we assign a ...

To define the set of well typed lambda terms of a given type, we introduce typing contexts which are sequences of typing assumptions of the form x:σ where x is a variable. We introduce the judgment which means that t is a term of type σ in context Γ which is given by the following typing rules: Examples of closed terms are: (I), (K), and (S). These are the typed lambda calculus represen ...

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