The lambda calculus was developed in the 1930s by Alonzo
Church. The calculus turned out to be an interesting model
of computation and became theprototype for untyped
functional programming languages. Operational and
denotational semantics for the calculus served as examples
for otherprogramming languages.
In typed lambda calculi, lambda terms are classified
according to their applicative behavior. In the 1960s it was
discovered that the types of typed lambda calculi are in
fact appearances of logical propositions. Thus there are two
possible views of typed lambda calculi:
- as models of computation, where terms are viewed as
programs in a typed programming language;
- as logical theories, where the types are viewed as
propositions and the terms as proofs.
The practical spin-off from these studies are:
- functional programming languages which are
mathematically more succinct than imperative programs;
- systems for automated proof checking based on lambda
caluli.
This volume is the proceedings of TLCA '93, the first
international conference on Typed Lambda Calculi and
Applications,organized by the Department of Philosophy of
Utrecht University. It includes29 papers selected from 51
submissions.