Isomorphism types of index sets of partial recursive functions

Isomorphism Types of Index Sets of Partial Recursive Functions

1. Let [qo, qi,q2, ■ • ■ J be a Kleene enumeration of partial recursive functions. If / is such a function, denote by 9f its index set, 9f= {ra|g„^/}. Insofar as the indices of a partial recursive function correspond to the different sets of "instructions" for computing its values, it is natural to ask how much of the "complexity" of the function is reflected by its index set; for example, one ...

Topological Size of Sets of Partial Recursive Functions

Relativized Topological Size of Sets of Partial Recursive Functions

Calude, C., Relativized topological size of sets of partial recursive functions (Note), Theoretical Computer Science 87 (1991) 347-352. In [ 11, a recursive topology on the set of unary partial recursive functions was introduced and recursive variants of Baire topological notions of nowhere dense and meagre sets were defined. These tools were used to measure the size of some classes of partial ...

Mutually Recursive Partial Functions

We provide a wrapper around the partial-function command which supports mutual recursion. Our results have been used to simplify the development of mutually recursive parsers, e.g., a parser to convert external proofs given in XML into some mutually recursive datatype within Isabelle/HOL.

Partial Recursive Functions and Finality

We seek universal categorical conditions ensuring the representability of all partial recursive functions. In the category Pfn of sets and partial functions, the natural numbers provide both an initial algebra and a final coalgebra for the functor 1 + −. We recount how finality yields closure of the partial functions on natural numbers under Kleene’s μ-recursion scheme. Noting that Pfn is not c...