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Abstract Session types support a type-theoretic formulation of structured patterns of communication, so that the communication… Expand The intuitionistic modal logic of necessity is based on the judgmental notion of categorical truth. In this article we… Expand Dependent type theories have a long history of being used for theorem proving. One aspect of type theory which makes it very… Expand Chapter Headings only. Preface. Contents. Preliminaries. Prospectus. Introduction to fibred category theory. Simple type theory… Expand Preface Introduction 1. The extended calculus of constructions 2. Basic meta-theoretic properties 3. Strong normalisation 4. The… Expand data type, 179 abstraction, 14 Abstraction rule, 143 absurdity, 43 append, 68 application, 13 Application rule, 143 apply, 48… Expand Part 1 Polymorphic sets: the semantics of the judgement forms general rules enumeration sets Cartesian product of a family of… Expand This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax… Expand The first order functional calculus was proved complete by Godel in 1930. Roughly speaking, this proof demonstrates that each… Expand The purpose of the present paper is to give a formulation of the simple theory of types which incorporates certain features of… Expand