## Recursive Definitions of Partial Functions and Their Computations |

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### Contents

GENERAL PRESENTATION AND DISCUSSION | 1 |

THE MODEL FORMAL DEFINITIONS | 29 |

RELATIONS BETWEEN COMPUTED FUNCTIONS | 48 |

5 other sections not shown

### Common terms and phrases

a'recursive chain closed Chapter computation of F(x computed function Continuous Functionals correct term D+)k D+)n defined inductively Dom(g equation example f e Pfn(D Fixpoint Computations fixpoint of f fixpoint Theorem full computation function f function variable given functions Hence individual constant induction hypothesis integers key occurrences least element least fixpoint least strong fixpoint least upper bound least weak fixpoint Lemma Let f lub(K mf(S monotonic functional monotonic mapping monotonically structured recursive monotonically structured system n-tuple notation occurrences of F ordinal Paragraph parallel if-then-else partially ordered set pf(S pfn(D Proof prove Psubst recursive definition F(x safe innermost computation safe innermost substitutions safe simplification Section 1.5 sequence of terms set of partial standard computation standard innermost computation standard simplification rule standard simplification schema strict partial ordering strong value structural induction structured recursive definition subcomputation subset subterm system of recursive term variable trivial tuple Weak Values