Nominal unification with atom and context variables

  • Automated deduction in higher-order program calculi, where properties of transformation rules are demanded, or confluence or other equational properties are requested, can often be done by syntactically computing overlaps (critical pairs) of reduction rules and transformation rules. Since higher-order calculi have alpha-equivalence as fundamental equivalence, the reasoning procedure must deal with it. We define ASD1-unification problems, which are higher-order equational unification problems employing variables for atoms, expressions and contexts, with additional distinct-variable constraints, and which have to be solved w.r.t. alpha-equivalence. Our proposal is to extend nominal unification to solve these unification problems. We succeeded in constructing the nominal unification algorithm NomUnifyASC. We show that NomUnifyASC is sound and complete for these problem class, and outputs a set of unifiers with constraints in nondeterministic polynomial time if the final constraints are satisfiable. We also show that solvability of the output constraints can be decided in NEXPTIME, and for a fixed number of context-variables in NP time. For terms without context-variables and atom-variables, NomUnifyASC runs in polynomial time, is unitary, and extends the classical problem by permitting distinct-variable constraints. 1998 ACM Subject Classification F.4.1 Mathematical Logic

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Author:Manfred Schmidt-SchaußORCiDGND, David SabelORCiDGND
Parent Title (German):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik ; 59
Series (Serial Number):Technical report Frank / Johann-Wolfgang-Goethe-Universität, Fachbereich Informatik und Mathematik, Institut für Informatik (59)
Publisher:Institut für Informatik, Fachbereich Mathematik und Informatik Goethe-Universität Frankfurt am Main, Germany
Place of publication:Frankfurt am Main
Document Type:Working Paper
Year of Completion:2018
Year of first Publication:2018
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2018/01/29
Tag:automated deduction; functional programming; lambda calculus; nominal unification
Page Number:25
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):License LogoCreative Commons - Namensnennung 4.0