Semantic Lego

Denotational semantics (Sch86) is a powerful framework for describing programming languages; however, its descriptions lack modularity: conceptually independent language features influence each others' semantics. We address this problem by presenting a theory of modular denotational semantics. Following Mosses (Mos92), we divide a semantics into two parts, a computation ADT and a language ADT (abstract data type). The computation ADT represents the basic semantic structure of the language. The language ADT represents the actual language constructs, as described by a grammar. We define the language ADT using the computation ADT; in fact, language constructs are polymorphic over many different computation ADTs. Following Moggi (Mog89a), we build the computation ADT from composable parts, using monads and monad transformers. These techniques allow us to build many different computation ADTs, and, since our language constructs are polymorphic, many different language semantics. We automate these ideas in scSEMANTIC LEGO (SL), a modular language construction set written in Scheme. SL generates interpreters automatically from composable parts and is a useful tool for programming language design.

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