This paper shows how a fully abstract model for a rich metalanguage like FPC can be used to prove theorems about other languages. In particular, we use results obtained from a game semantics of FPC to show that the natural translation of the lazy -calculus into the metalanguage is fully abstract, thus obtaining a new full abstraction result from an old one. The proofs involved are very easy---all the hard work was done in giving the original games model. So far we have been unable to prove the completeness of our translation without recourse to the denotational model; we therefore have an indication of the worth of such fully abstract models. 1 Introduction Plotkin, in his CSLI notes [18], showed how denotational semantics can be viewed as a two-stage process. First one defines a metalanguage which describes elements of the intended semantic model, usually some category of domains. Then to give semantics to a language L it suffices to translate it into the metalanguage. While this is ...

This paper considers some theoretical and practical issues concerning the use of linear logic as a logical foundation of functional programming languages such as Haskell and SML. First I give an operational theory for a linear PCF: the (typed) linear - calculus extended with booleans, conditional and non-termination. An operational semantics is given which corresponds in a precise way to the process of fi-reduction which originates from proof theory. Using this operational semantics I define notions of observational equivalence (sometimes called contextual equivalence). Surprisingly, the linearity of the language forces a reworking of the traditional notion of a context (the details are given in an appendix). A co-inductively defined notion, applicative bisimularity, is developed and compared with observational equivalence using a variant of Howe's method. Interestingly the equivalence of these two notions is greatly complicated by the linearity of the language. These equivalences ar...