Abstract:
We exhibit Semantic Lego, a modular system for constructing programming language implementations from denotational-style building blocks. We present languages as abstract data types, show that ADTs have advantages over interpreters, and incrementally construct semantics for them using type transformations and liftings. We derive specific type transformations (third order) and liftings (monads) from more fundamental considerations and show that monads transform rather than compose. Semantic Lego extends Moggi, Wadler, and Steele's earlier work and has applications to language extensibility, the construction of interpreters and compilers, and the study of semantic models.
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