Effect polymorphism in higher-order logic


Title: Effect polymorphism in higher-order logic
Author: Andreas Lochbihler
Submission date: 2017-05-05
Abstract: The notion of a monad cannot be expressed within higher-order logic (HOL) due to type system restrictions. We show that if a monad is used with values of only one type, this notion can be formalised in HOL. Based on this idea, we develop a library of effect specifications and implementations of monads and monad transformers. Hence, we can abstract over the concrete monad in HOL definitions and thus use the same definition for different (combinations of) effects. We illustrate the usefulness of effect polymorphism with a monadic interpreter for a simple language.
Change history: [2018-02-15]: added further specifications and implementations of non-determinism; more examples (revision bc5399eea78e)
  author  = {Andreas Lochbihler},
  title   = {Effect polymorphism in higher-order logic},
  journal = {Archive of Formal Proofs},
  month   = may,
  year    = 2017,
  note    = {\url{http://isa-afp.org/entries/Monomorphic_Monad.html},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Used by: CryptHOL
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.