Rice's theorem

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Formal statement

Admissible numbering Partial computable functions Index sets

3 related topics

Introduction

Syntax Semantics Bugs Specification Dynamically typed programming languages

12 related topics

Examples

Natural number Total

2 related topics

Proof by Kleene's recursion theorem

Extensional Kleene's recursion theorem

2 related topics

Topics to explore

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Examples

Natural number
Total General recursive function

Proof by Kleene's recursion theorem

Extensional Rice's theorem
Kleene's recursion theorem

Proof by reduction from the halting problem

Strings String (computer science)
Reductio ad absurdum

Advanced semantic analysis

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Map overview Semantic statistics

Nodes36

Edges35

Triples14

Avg. degree1.94

Density0.055556

Components1

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Rice's theorem

Top relations

see also · 8

Rice's theorem → Curry, Halting, Kreisel, Lacombe, Rice's, Shapiro, Shoenfield, Tseitin

related to Introduction · 4

Rice's theorem → By Rice's, One, Rice's, The

Important terminology Word statistics

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Important terminology

program algorithm theorem non-trivial programs property problem displaystyle halting input one terminate rice's given since whether proof undecidable assume function

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
in Hoare logic.Another way of working around Rice's theorem is to search for methods that catch many bugs	instance of	this idea leads to correctness proofs of programs through proof annotations	0.80	text
without being complete	instance of	this idea leads to correctness proofs of programs through proof annotations	0.80	text
Rice's theorem	related to Introduction	Rice's	0.60	section
Rice's theorem	related to Introduction	One	0.60	section
Rice's theorem	related to Introduction	The	0.60	section
Rice's theorem	related to Introduction	By Rice's	0.60	section
Rice's theorem	see also	Halting	0.60	section
Rice's theorem	see also	Shapiro	0.60	section
Rice's theorem	see also	Kreisel	0.60	section
Rice's theorem	see also	Lacombe	0.60	section
Rice's theorem	see also	Shoenfield	0.60	section
Rice's theorem	see also	Tseitin	0.60	section

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Formal statement

Introduction

Examples

Proof by Kleene's recursion theorem

Key facts & relationships

Topics to explore

Overview

Introduction

Formal statement

Examples

Proof by Kleene's recursion theorem

Proof by reduction from the halting problem

Advanced semantic analysis

Map overview Semantic statistics

Rice's theorem

How this topic connects Entity context

Rice's theorem

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges