Safe recursion with higher types and BCK-algebra

Safe recursion with higher types and BCK-algebra

In previous work the author has introduced a lambda calculus SLR with modal and linear types which serves as an extension of Bellantoni–Cook’s function algebra BC to higher types. It is a step towards a functional programming language in which all programs run in polynomial time. In this paper we develop a semantics of SLR using BCK-algebras consisting of certain polynomial-time algorithms. It ...

Infinite Terms and Recursion in Higher Types

Systems of infinite terms defining functionals of finite type were first considered by Tait [10] and further developed by Feferman [3] initially in a proof-theoretic context. Later in unpublished notes Feferman introduced the system T of infinite o terms inductively generated from variables of all finite types and constants for the ordinary primitive recursive functions by application, abstract...

Higher-Order Algebra with Transfinite Types

Dual Bck - Algebra and Mv - Algebra

The aim of this paper is to study the properties of dual BCK-algebra and to prove that the MV -algebra is equvalent to the bounded commutative dual BCK-algebra.

Types and Recursion Schemes for Higher-Order Program Verification