Abstract

The use of expansionary j-rewrite rules in various typed -calculi has become increasingly common in recent years as their advantages over contractive j-rewrite rules have become apparent. Not only does one obtain the decidability of fij-equality, but rewrite relations based on expansions give a natural interpretation of long fij-normal forms, generalise more easily to other type constructors, retain key properties when combined with other rewrite relations, and are supported by a categorical theory of reduction. This paper extends the initial results concerning the simply typed -calculus to System F, that is, we prove strong normalisation and confluence for a rewrite relation consisting of traditional fi-reductions and j-expansions satisfying certain restrictions. Further, we characterise the second order long fij-normal forms as precisely the normal forms of the restricted rewrite relation. These results are an important step towards showing that j-expansions are compatible with the m...

Citations

115	Ideas and results in proof theory - Prawitz - 1971
42	On Mints’ reduction for ccc-calculus - Akama - 1993
36	The virtues of eta-expansion - Jay, Ghani - 1995
26	equality for coproducts - Ghani
25	Adjoint Rewriting - Ghani - 1995
17	R'esolution d"equations dans des langages d'ordre 1,2 - Huet - 1976
15	Combining first order algebraic rewriting systems, recursion and extensional lambda calculi - Cosmo, Kesner - 1994
14	Teorija categorii i teoria dokazatelstv.I. Aktualnye problemy logiki i metodologii nauky - Mints - 1979
9	Expanding extensional polymorphism - Cosmo, Piperno - 1995
8	Simulating expansions without expansions - Cosmo, Kesner - 1994
7	Some -calculi with categorical sums and products - Dougherty - 1993
6	The system F of variable types - 15 years later - Girard - 1986
4	Rewriting with polymorphic extensional - calculus - Cosmo, Kesner - 1995
3	Combining algebraic rewriting, extensional -calculi and fixpoints - Cosmo, Kesner - 1995