The lambda calculus was developed in the 1930s by AlonzoChurch. The calculus turned out to be an interesting modelof computation and became theprototype for untypedfunctional programming languages. Operational anddenotational semantics for the calculus served as examplesfor otherprogramming languages.In typed lambda calculi, lambda terms are classifiedaccording to their applicative behavior. In the 1960s it wasdiscovered that the types of typed lambda calculi are infact appearances of logical propositions. Thus there are twopossible views of typed lambda calculi:- as models of computation, where terms are viewed asprograms in a typed programming language;- as logical theories, where the types are viewed aspropositions and the terms as proofs.The practical spin-off from these studies are:- functional programming languages which aremathematically more succinct than imperative programs;- systems for automated proof checking based on lambdacaluli.This volume is the proceedings of TLCA '93, the firstinternational conference on Typed Lambda Calculi andApplications,organized by the Department of Philosophy ofUtrecht University. It includes29 papers selected from 51submissions.
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.
Series: Research Notes in Neural Computing
Number Of Pages: 443
Published: 3rd March 1993
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6
Weight (kg): 0.64