Categorical combinators

Categorical Combinators

Our main aim is to present the connection between 2-calculus and Cartesian closed categories both in an untyped and purely syntactic setting. More specifically we establish a syntactic equivalence theorem between what we call categorical com-binatory logic and j-calculus with explicit products and projections, with fl and q-rules as well as with surjective pairing. "Combinatory logic" is of cou...

Implementing SASL using Categorical Multi-combinators

Categorical multi-combinators form a rewriting system developed with the aim of providing efficient implementations of lazy functional languages. The core of the system of categorical multi-combinators consists of only two rewriting laws with a very low pattern-matching complexity. This system allows the equivalent of several -reductions to be performed at once, and avoids the generation of tri...

Syntactic Multicategories and Categorical Combinators for Linear Logic (abstract)

Partial Categorical Multi-Combinators and Church-Rosser Theorems

Categorical Multi Combinators form a rewriting system developed with the aim of providing e cient implementations of lazy functional languages The core of the system of Categorical Multi Combinators consists of only four rewriting laws with a very low pattern matching complexity This system allows the equivalent of several reductions to be performed at once as functions form frames with all the...

Interaction Combinators

It is shown that a very simple system of interaction com-binators, with only 3 symbols and 6 rules, is a universal model of distributed computation, in a sense that will be made precise. This paper is the continuation of the au-thor's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading.