Applications of Innitary Lambda Calculus

Innitary Lambda Calculus

In a previous paper we have established the theory of trans nite reduction for orthogonal term rewriting systems. In this paper we perform the same task for the lambda calculus. From the viewpoint of in nitary rewriting, the Bohm model of the lambda calculus can be seen as an in nitary term model. In contrast to term rewriting, there are several di erent possible notions of in nite term, which...

Non-Newtonian Fuzzy numbers and related applications

Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, inc...

Lambda-calculus, types and models

Rewriting Calculus with(out) Types

The last few years have seen the development of a new calculus which can be considered as an outcome of the last decade of various researches on (higher order) term rewriting systems, and lambda calculi. In the Rewriting Calculus (or Rho Calculus, ρCal), algebraic rules are considered as sophisticated forms of “lambda terms with patterns”, and rule applications as lambda applications with patte...

A Mixed Modal/Linear Lambda Calculus with Applications to Bellantoni-Cook Safe Recursion

This paper introduces a simply-typed lambda calculus with both modal and linear function types. Through the use of subtyping extra term formers associated with modality and linearity are avoided. We study the basic metatheory of this system including existence and inference of principal types. The system serves as a platform for certain higher-order generalisations of Bellantoni-Cook's function...