On creative sets and indices of partial recursive functions

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 ...

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 ...

On Modal Logics of Partial Recursive Functions

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both...

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.