Central Problems of Equational Reasoning 22.06.2010 Theory 1 - - - PowerPoint PPT Presentation

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15 Foundation of Programming Languages and Software Engineering: The Word Problem The Word Problem Summer Term 2010 Robert Elssser Robert Elssser Central Problems of Equational Reasoning 22.06.2010 Theory 1 - Foundation of Programming

SLIDE 1

15 Foundation of Programming Languages

and Software Engineering: The Word Problem The Word Problem

Summer Term 2010 Robert Elsässer Robert Elsässer

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Central Problems of Equational Reasoning

22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 2

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The Word Problem

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Solving the Word Problem

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An Undecidable Word Problem

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The Reduction Relation Generated by ∑ Id i i ∑-Identities

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Example

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Composing Relations

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Notations for Reduction Relations

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Terminology for Reduction Relations (1)

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Terminology for Reduction Relations (2)

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Deciding the Word Problem

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Church-Rosser and Confluence are Equivalent

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Church-Rosser and Confluence are Equivalent

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Proof (cont.)

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Existence and Uniqueness of Normal Forms

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Another Lemma

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Relating ↔ɛ and ≈ɛ: Auxiliary Lemma

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Proof of (3)

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Relating ↔ɛ and ≈ɛ

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Proof (cont.)

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Deciding the Word Problem

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Computing Normal Forms (1)

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Computing Normal Forms (2)

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