A Rewriting System for Categorical Combinators with Multiple Arguments

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...

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...

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)

Dactl Rewriting Is Categorical

The graph-manipulating core of the general term graph rewriting language DACTL, namely contraction building and redirection, is reexamined from a categorical viewpoint. The essentials of this rather complex two-phase operational semantics is recast as a Grothendieck opfibration of a category of graph rewrites over a base of rewrite rules. This generalises previous attempts to categorise contrac...