Modules over Monads and Linearity
By André Hirschowitz, Marco Maggesi. 2006
43 citations recorded by the source corpus.
Inspired by the classical theory of modules over a monoid, we give a first account of 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, in the heterogeneous case where "terms" and variables therein could be of different types as well as in the homogeneous case. In this paper, we present basic constructions of modules and we show examples concerning in particular abstract syntax and lambda-calculus.
Subfields: Artificial Intelligence, Mathematical Physics
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Citations in the corpus
- Heterogeneous substitution systems revisited (2016, neutral): “In the meantime, monads and modules over monads, have been used by Hirscho-witz and Maggesi [16, 17] to define models of syntax, and to give a categorical characterization thereof.”
- Initial Semantics for Strengthened Signatures (2012, methodology): “For more details we refer to our paper [13] (Theorems 1 and 2).”
- Initiality for Typed Syntax and Semantics (2012, background): “Hirschowitz and Maggesi [9] prove initiality of the set of lambda terms modulo beta and eta conversion in a category of exponential monads.”