Effect Polymorphism in Higher-Order Logic (Proof Pearl)

The notion of a monad cannot be expressed within higher-order logic (HOL) due to type system restrictions. I show that if a monad is restricted to values of a fixed type, this notion can be formalised in HOL. Based on this idea, I develop a library of effect specifications and implementations of mon...

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Bibliographic Details
Published inJournal of automated reasoning Vol. 63; no. 2; pp. 439 - 462
Main Author Lochbihler, Andreas
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.08.2019
Springer Nature B.V
Subjects
Artificial Intelligence
Computer Science
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Polymorphism
Symbolic and Algebraic Manipulation
Isabelle/HOL
Effects
Equational reasoning
Monad transformer
Monad
Polymorphism
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Summary:The notion of a monad cannot be expressed within higher-order logic (HOL) due to type system restrictions. I show that if a monad is restricted to values of a fixed type, this notion can be formalised in HOL. Based on this idea, I develop a library of effect specifications and implementations of monads and monad transformers. Hence, I can abstract over the concrete monad in HOL definitions and thus use the same definition for different (combinations of) effects. I illustrate the usefulness of effect polymorphism with a monadic interpreter.
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-018-9476-2