Category Theory and Computer Science: Paris, France, September 3–6, 1991 Proceedings

Thomas Ehrhard, Pasquale Malacaria (auth.), David H. Pitt, Pierre-Louis Curien, Samson Abramsky, Andrew M. Pitts, Axel Poigné, David E. Rydeheard (eds.)354054495X, 9783540544951

The papers in this volume were presented at the fourth biennial Summer Conference on Category Theory and Computer Science, held in Paris, September3-6, 1991. Category theory continues to be an important tool in foundationalstudies in computer science. It has been widely applied by logicians to get concise interpretations of many logical concepts. Links between logic and computer science have been developed now for over twenty years, notably via the Curry-Howard isomorphism which identifies programs with proofs and types with propositions. The triangle category theory – logic – programming presents a rich world of interconnections. Topics covered in this volume include the following. Type theory: stratification of types and propositions can be discussed in a categorical setting. Domain theory: synthetic domain theory develops domain theory internally in the constructive universe of the effective topos. Linear logic: the reconstruction of logic based on propositions as resources leads to alternatives to traditional syntaxes. The proceedings of the previous three category theory conferences appear as Lecture Notes in Computer Science Volumes 240, 283 and 389.

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Table of contents :
Stone duality for stable functions….Pages 1-15
Bifinite domains: Stable case….Pages 16-33
Local variables and non-interference in algol-like languages….Pages 34-36
Categories of information systems….Pages 37-52
Collapsing graph models by preorders….Pages 53-73
Linear logic and interference control….Pages 74-93
Higher dimensional word problem….Pages 94-105
BCK-formulas having unique proofs….Pages 106-120
Proof nets and coherence theorems….Pages 121-137
A modular approach to denotational semantics….Pages 138-139
Programs in partial algebras — A categorical approach….Pages 140-150
Tail recursion from universal invariants….Pages 151-163
A direct proof of the intuitionistic Ramsey Theorem….Pages 164-172
Constructions and predicates….Pages 173-196
Relating models of impredicative type theories….Pages 197-218
Two results on set-theoretic polymorphism….Pages 219-235
An algebra of graphs and graph rewriting….Pages 236-260
Dataflow networks are fibrations….Pages 261-281
Applications of the calculus of trees to process description languages….Pages 282-301