Presenting distributive laws. (English) Zbl 1394.68238
Heckel, Reiko (ed.) et al., Algebra and coalgebra in computer science. 5th international conference, CALCO 2013, Warsaw, Poland, September 3–6, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-40205-0/pbk). Lecture Notes in Computer Science 8089, 95-109 (2013).
Summary: Distributive laws of a monad \(\mathcal{T}\) over a functor \(F\) are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If \(\mathcal{T}\) is a free monad, then such distributive laws correspond to simple natural transformations. However, when \(\mathcal{T}\) is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages.
For the entire collection see [Zbl 1271.68041].
For the entire collection see [Zbl 1271.68041].
MSC:
68Q65 | Abstract data types; algebraic specification |
18C15 | Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads |
68Q45 | Formal languages and automata |
68Q55 | Semantics in the theory of computing |