Program equivalence in a linear functional language

Abstract

Researchers have recently proposed that for certain applications it is advantageous to use functional languages whose type systems are based upon linear logic: so-called linear functional languages. In this paper we develop reasoning techniques for programs in a linear functional language, linPCF , based on their operational behaviour. The principal theorem of this paper is to show that contextual equivalence of linPCF programs can be characterised coinductively. This characterisation provides a tractable method for reasoning about contextual equivalence, and is used in three ways: [bull ] A number of useful contextual equivalences between linPCF programs is given. [bull ] A notion of type isomorphism with respect to contextual equivalence, called operational isomorphism, is given. In particular the types !ϕ[otimes ]!ψ and !(ϕ&ψ) are proved to be operationally isomorphic. [bull ] A translation of non-strict PCF into linPCF is shown to be adequate, but not fully abstract, with respect to contextual equivalence.