An effective operator, continuous but not partial recursive

An Effective Operator, Continuous but Not Partial Recursive

Introduction. It is known that under many conditions, effective operators will be partial recursive, ([MS], [KLS], [L]). On the other hand, certain pathological examples have been constructed by Friedberg [F] and Pour-El [P] to show that effective operators are not always partial recursive. Pour-El has observed that although it is well known that all partial recursive operators are continuous, ...

not intervention but participation

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Leads-to Properties and the But-not-yet Operator

We deene a predicate transformer, in terms of which nite disjunctions of leads-to properties can be rewritten as single leads-to properties. Although disjunctions of leads-to properties do not typically arise naturally in progress speciications, an example shows how they may be introduced through the use of nested implications of leads-to properties; such implications allow subtle dependencies ...

An Operator Embedding Theorem for Complexity Classes of Recursive Functions

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.