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SLE 2020
Sun 15 - Fri 20 November 2020 Online Conference
co-located with SPLASH 2020
Mon 16 Nov 2020 05:20 - 05:40 at SPLASH-III - Chair(s): Friedrich Steimann
Sun 15 Nov 2020 17:20 - 17:40 at SPLASH-III - Chair(s): Marjan Mernik

We describe a monadification process for attribute grammars for more concisely written attribute equations, closer to the style of inference rules used in traditional typing and evaluation specifications. Inference rules specifying, for example, a typing relation typically consider only typable expressions, whereas well-defined attribute grammars explicitly determine attribute values for any term, including untypable ones. The monadification approach lets one represent, for example, types as monadic optional/maybe values, but write non-monadic equations over the value inside the monad that only specify the rules for a correct typing, leading to more concise specifications. The missing failure cases are handled by a rewriting that inserts monadic return, bind, and failure operations to produce a well-defined attribute grammar that handles untypable trees. Thus, one can think in terms of a type T and not the actual monadic type M(T). To formalize this notion, typing and evaluation relations are given for the original and rewritten equations. The rewriting is total, preserves types, and a correctness property relating values of original and rewritten equations is given. A prototype implementation illustrates the benefits with examples such as typing of the simply-typed lambda calculus with Booleans, evaluation of the same, and type inference in Caml Light.

Sun 15 Nov
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Mon 16 Nov
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