Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
Notions of computation and monads
Information and Computation
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Semantics of Name and Value Passing
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
de Bruijn notation as a nested datatype
Journal of Functional Programming
Explicit substitutions and higher-order syntax
MERLIN '03 Proceedings of the 2003 ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Substitution in non-wellfounded syntax with variable binding
Theoretical Computer Science - Selected papers of CMCS'03
A unified category-theoretic formulation of typed binding signatures
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Pseudo-distributive laws and axiomatics for variable binding
Higher-Order and Symbolic Computation
Mathematical quotients and quotient types in Coq
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
HOL2P - a system of classical higher order logic with second order polymorphism
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Mechanized metatheory for the masses: the PoplMark challenge
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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Inspired by the classical theory of modules over a monoid, we introduce the natural notion of module over a monad. The associated notion of morphism of left modules (''linear'' natural transformations) captures an important property of compatibility with substitution, not only in the so-called homogeneous case but also in the heterogeneous case where ''terms'' and variables therein could be of different types. In this paper, we present basic constructions of modules and we show how modules allow a new point of view concerning higher-order syntax and semantics.