Category theory and computer science : [4th Biennial Summer Conference on Category Theory and Computer Science] Paris, France, September 3-6, 1991 : proceedings

"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"--PUBLISHER'S WEBSITE.

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.

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 The problem of finding an algebraic structure for stable open subsets of a suitable domain has been recently raised by several authors.