Signatures and models for syntax and operational semantics in the presence of variable binding [article]

Ambroise Lafont
2019 arXiv   pre-print
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable category of models.This characterization, in the spirit of Initial Semantics, gives a justification of the recursion principle. Languages with variable binding, such as the pure lambda calculus, are monads on the category of sets specified through the
more » ... l algebraic signatures. The first extensions to syntaxes with equations that we consider are quotients of these algebraic signatures. They allow, for example, to specify a binary commutative operation. But some equations, such as associativity, seem to remain out of reach. We thus introduce the notion of 2-signature, consisting in two parts: a specification of operations through a usual signature as before, and a set of equations among them. We identify the class of algebraic 2-signatures for which the existence of the associated syntax is guaranteed. Finally, we takle the specification of the operational semantics of a programming language such as lambda calculus with beta-reduction. To this end, we introduce the notion of reduction monad and their signatures, then we generalize them to get the notion of operational monad.
arXiv:1910.09162v4 fatcat:dmbqxqqn3zbzlmt5gyz7hnuzvm