Checking Sufficient Completeness by Inductive Theorem Proving

Meseguer, José

doi:10.1007/978-3-031-12441-9_9

Cited by 3 publications

(1 citation statement)

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“…Therefore, even if the original goal to be proved is a Σ-multiclause, some of its subgoals may be Σ -multiclauses -obtained, for example, by application of the ICC simplification rule (see Section 4). Second, the extra generality of the theory E supports the verification of sufficient completeness properties as inductive theorems for specifications E outside the scope of tree-automata techniques such as [37], a topic developed elsewhere [55]. 18 A crucial property of a total RPO order modulo B 0 , for B 0 any combination of associativity and/or commutativity axioms, is that it defines a total order on B 0 -equivalence classes of ground terms [66,65].…”

Section: Multiclauses and Inductive Theoriesmentioning

confidence: 99%

Inductive Reasoning with Equality Predicates, Contextual Rewriting and Variant-Based Simplification

Meseguer

Skeirik

2020

Lecture Notes in Computer Science

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An inductive inference system for proving validity of formulas in the initial algebra T E of an order-sorted equational theory E is presented. It has 20 inference rules, but only 9 of them require user interaction; the remaining 11 can be automated as simplification rules. In this way, a substantial fraction of the proof effort can be automated. The inference rules are based on advanced equational reasoning techniques, including: equationally defined equality predicates, narrowing, constructor variant unification, variant satisfiability, order-sorted congruence closure, contextual rewriting, ordered rewriting, and recursive path orderings. All these techniques work modulo axioms B, for B any combination of associativity and/or commutativity and/or identity axioms. Most of these inference rules have already been implemented in Maude's NuITP inductive theorem prover.

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