Co-Induction in Relational Semantics

Abstract An application of the mathematical theory of maximum fixed points of monotonic set operators to relational semantics is presented. It is shown how an important proof method which we call co-induction , a variant of Park's (1969) principle of fixpoint induction, can be used to prove the consistency of the static and the dynamic relational semantics of a small functional programming language with recursive functions.

[1]  Robin Milner,et al.  A Theory of Type Polymorphism in Programming , 1978, J. Comput. Syst. Sci..

[2]  Gilles Kahn,et al.  Natural Semantics , 1987, STACS.

[3]  Robin Milner,et al.  Principal type-schemes for functional programs , 1982, POPL '82.

[4]  Peter Aczel,et al.  An Introduction to Inductive Definitions , 1977 .

[5]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[6]  Luís Damas.  Type assignment in programming languages , 1984 .

[7]  M. Tofte.  Operational Semantics and Polymorphic Type Inference , 1988 .

[8]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[9]  David Michael Ritchie Park,et al.  On the Semantics of Fair Parallelism , 1979, Abstract Software Specifications.