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This paper presents 3MT, a framework for modular mechanized meta-theory of languages with effects. Using 3MT, individual language features and their corresponding definitions -- semantic functions, theorem statements and proofs-- can be built separately and then reused to create different languages with fully mechanized meta-theory. 3MT combines modular datatypes and monads to define denotational semantics with effects on a per-feature basis, without fixing the particular set of effects or language constructs.

One well-established problem with type soundness proofs for denotational semantics is that they are notoriously brittle with respect to the addition of new effects. The statement of type soundness for a language depends intimately on the effects it uses, making it particularly challenging to achieve modularity. 3MT solves this long-standing problem by splitting these theorems into two separate and …