Full Description
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.
Contents
On Mints' reduction for ccc-calculus.- A formalization of the strong normalization proof for System F in LEGO.- Partial intersection type assignment in applicative term rewriting systems.- Extracting constructive content from classical logic via control-like reductions.- Combining first and higher order rewrite systems with type assignment systems.- A term calculus for Intuitionistic Linear Logic.- Program extraction from normalization proofs.- A semantics for ? &-early: a calculus with overloading and early binding.- An abstract notion of application.- The undecidability of typability in the Lambda-Pi-calculus.- Recursive types are not conservative over F?.- The conservation theorem revisited.- Modified realizability toposes and strong normalization proofs.- Semantics of lambda-I and of other substructure lambda calculi.- Translating dependent type theory into higher order logic.- Studying the fully abstract model of PCF within its continuous function model.- A new characterization of lambda definability.- Combining recursive and dynamic types.- Lambda calculus characterizations of poly-time.- Pure type systems formalized.- Orthogonal higher-order rewrite systems are confluent.- Monotonic versus antimonotonic exponentiation.- Inductive definitions in the system Coq rules and properties.- Intersection types and bounded polymorphism.- A logic for parametric polymorphism.- Call-by-value and nondeterminism.- Lower and upper bounds for reductions of types in ? and ?P (extended abstract).- ?-Calculi with conditional rules.- Type reconstruction in F? is undecidable.
