Partial Categorical Multi-Combinators and Church-Rosser Theorems

An effective one-step Church-Rosser strategy for combinators

Parallelism and Concurrency Theorems for Rules with Nested Application Conditions

We present Local Church-Rosser, Parallelism, and Concurrency Theorems for rules with nested application conditions in the framework of weak adhesive HLR categories including different kinds of graphs. The proofs of the statements are based on the corresponding statements for rules without application conditions and two Shift-Lemmas, saying that nested application conditions can be shifted over ...

More Church-Rosser Proofs (in Isabelle/HOL)

The proofs of the Church Rosser theorems for and reduction in untyped calculus are formalized in Isabelle HOL an im plementation of Higher Order Logic in the generic theorem prover Isa belle For reduction both the standard proof and the variation by Takahashi are given and compared All proofs are based on a general theory of commutating relations which supports an almost geometric style of con ...

Separating Developments in -calculus

We introduce a proof technique in-calculus which can facilitate inductive reasoning on-terms by separating certain-developments from other-reductions. We present proofs based on this technique for several fundamental theorems in-calculus such as the Church-Rosser theorem, the standardisation theorem, the conservation theorem and the normalisation theorem. The appealing features of these proofs ...

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...