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Presenting distributive laws
 In CALCO
, 2013
"... Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebracoalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of wellbehaved structural operational semantics and, more recently, also fo ..."
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Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebracoalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of wellbehaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when 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 contextfree languages. 1
Symbolic Synthesis of Mealy Machines from Arithmetic Bitstream Functions
"... In this paper, we describe a symbolic synthesis method which given an algebraic expression that specifies a bitstream function f, constructs a (minimal) Mealy machine that realises f. The synthesis algorithm can be seen as an analogue of Brzozowski’s construction of a finite deterministic automaton ..."
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Cited by 4 (4 self)
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In this paper, we describe a symbolic synthesis method which given an algebraic expression that specifies a bitstream function f, constructs a (minimal) Mealy machine that realises f. The synthesis algorithm can be seen as an analogue of Brzozowski’s construction of a finite deterministic automaton from a regular expression. It is based on a coinductive characterisation of the operators of 2adic arithmetic in terms of stream differential equations. 1