TY - GEN

T1 - Incremental checking of well-founded recursive specifications modulo axioms

AU - Schernhammer, Felix

AU - Meseguer, José

PY - 2011

Y1 - 2011

N2 - 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 conuence 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.

AB - 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 conuence 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.

KW - Conuence

KW - Modularity

KW - Order-sorted rewriting modulo axioms

KW - Sufficient completeness

KW - Termination

KW - Well-founded recursive theory

UR - http://www.scopus.com/inward/record.url?scp=80052164663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052164663&partnerID=8YFLogxK

U2 - 10.1145/2003476.2003481

DO - 10.1145/2003476.2003481

M3 - Conference contribution

AN - SCOPUS:80052164663

SN - 9781450307765

T3 - PPDP'11 - Proceedings of the 2011 Symposium on Principles and Practices of Declarative Programming

SP - 5

EP - 16

BT - PPDP'11 - Proceedings of the 2011 Symposium on Principles and Practices of Declarative Programming

T2 - 13th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming, PPDP 2011

Y2 - 20 July 2011 through 22 July 2011

ER -