Modular monadic semantics is a high-level and modular form of denotational semantics. It is capable of capturing individual programming language features as small building blocks which can be combined to form a programming language of arbitrary complexity. Interactions between features are isolated in such a way that the building blocks are invariant. This paper explores the theory and application of modular monadic semantics, including the building blocks for individual programming language features, equational reasoning with laws and axioms, modular proofs, program transformation, modular interpreters, and semantics-directed compilation. We demonstrate that modular monadic semantics makes programming languages easier to specify, reason about, and implement than the alternative of using conventional denotational semantics. Our contributions include: (a) the design of a fully modular interpreter based on monad transformers, including important features missing from several earlier efforts, (b) a method to lift monad operations through monad transformers, including difficult cases not achieved in earlier work, (c) a study of the semantic implications of the order of monad transformer composition, (d) a formal theory of modular monadic semantics that justifies our choice of liftings based on a notion of naturality, and (e) an implementation of our interpreter in Gofer, whose constructor classes provide just the added power over Haskell type classes to allow precise and convenient expression of our ideas. A note to reviewers: this paper is rather long. Short of resorting to “Part I / Part II”, the one way we see to shorten it would be to remove Section 4 and its Appendix B, which would amount to eliminating contribution (e) above. This would shorten the paper by about 12 pages.

: This draft 1 provides the most recent collection of definitions and explanations on the GSF formalism. The basic motivation for this draft has been to provide the formal base and the intuitive introduction for GSFs as required in the context of the system LDL. Thus, certain aspects like comparison with other formalims, particular questions of implementation are not in the centre of this presentation. Date: 10.11.95 13:51 Contents 1 Overview 2 2 Introduction of GSFs 3 3 Basic formalization 8 4 GSFs as a specification language 13 5 References 18 1 This draft is in an early stage. I would be very grateful for comments. Most of the contents is not my personal achievement but rather newly formulated and assembled presentation of notions, terms and results already earlier published by Gnter Riedewald, Uwe Lmmel and me. However, for insufficiencies and incorrectness in the draft I am responsible only. Ralf Lmmel: Grammars of Syntactical Functions 2 1 Overview Not yet available. 2...