Incremental Checking of Well-Founded Recursive Specifications Modulo Axioms

Schernhammer, Felix; Mseguer, Jose

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https://hdl.handle.net/2142/32095 Copy

Description

Title

Incremental Checking of Well-Founded Recursive Specifications Modulo Axioms

Author(s)

• Schernhammer, Felix
• Mseguer, Jose

Issue Date

2011-05-10

Keyword(s)

well-founded recursive theory, order-sorted rewriting modulo axioms, termination, confluence, sufficient completeness

Date of Ingest

2012-06-29T20:44:44Z

Abstract

We introduce the notion of well-founded recursive order-sorted equational logic (OS) theories modulo axioms. Such theories define functions by well-founded recursion and are inherently terminating. Moreover, for well-founded recursive theories important properties such as confluence and sufficient completeness are modular for so-called fair extensions. This enables us to incrementally check these properties for hierarchies of such theories that occur naturally in modular rule-based functional programs. Well-founded recursive OS theories modulo axioms contain only commutativity and associativity-commutativity axioms. In order to support arbitrary combinations of associativity, commutativity and identity axioms, we show how to eliminate identity and (under certain conditions) associativity (without commutativity) axioms by theory transformations in the last part of the paper.

Type of Resource

text

Genre of Resource

Technical Report

Language

en

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http://hdl.handle.net/2142/32095

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