Category Theory and Computer Science

The papers in this volume were presented at the fourthbiennial Summer Conference on Category Theory and ComputerScience, held in Paris, September3-6, 1991. Category theorycontinues to be an important tool in foundationalstudies incomputer science. It has been widely applied by logicians toget concise interpretations of many logical concepts. Linksbetween logic and computer science have been developed nowfor over twenty years, notably via the Curry-Howardisomorphism which identifies programs with proofs and typeswith propositions. The triangle category theory - logic -programming presents a rich world of interconnections.Topics covered in this volume include the following. Typetheory: stratification of types and propositions can bediscussed in a categorical setting. Domain theory: syntheticdomain theory develops domain theory internally in theconstructive universe of the effective topos. Linear logic:the reconstruction of logic based on propositions asresources leads to alternatives to traditional syntaxes. Theproceedings of the previous three category theoryconferences appear as Lecture Notes in Computer ScienceVolumes 240, 283 and 389.

The papers in this volume were presented at the fourth biennial Summer Conference on Category and Computer Science. Category theory continues to be an important tool in foundational studies in computer science.

Stone duality for stable functions.- Bifinite domains: Stable case.- Local variables and non-interference in algol-like languages.- Categories of information systems.- Collapsing graph models by preorders.- Linear logic and interference control.- Higher dimensional word problem.- BCK-formulas having unique proofs.- Proof nets and coherence theorems.- A modular approach to denotational semantics.- Programs in partial algebras - A categorical approach.- Tail recursion from universal invariants.- A direct proof of the intuitionistic Ramsey Theorem.- Constructions and predicates.- Relating models of impredicative type theories.- Two results on set-theoretic polymorphism.- An algebra of graphs and graph rewriting.- Dataflow networks are fibrations.- Applications of the calculus of trees to process description languages.