Denotational Semantics of HOFL

Abstract

In this chapter we exploit the domain theory from Chapter 8 to define the (lazy) denotational semantics of HOFL. For each type τ we introduce a corresponding domain (V _τ )_⊥ which is defined inductively over the structure of τ and such that we can assign an element of the domain (V _τ )_⊥ to each (closed and typable) term t with type τ. Moreover, we introduce the notion of environment, which assigns meanings to variables, and can be exploited to define the denotational semantics of (typable) terms with variables. Interestingly, all constructions we use are continuous, so that we are able to assign meaning also to any (typable) term that is recursively defined. We conclude the chapter by showing some important properties of the denotational semantics; in particular, that it is compositional.

Work out what you want to say before you decide how you want to say it. (Christopher Strachey’s first law of logical design)