Nominal Unification

Nominal Unification (2003)

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by Christian Urban , Andrew Pitts , Murdoch Gabbay

Venue:	Theoretical Computer Science
Citations:	46 - 18 self

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Datum	Value	Source
TITLE	Nominal Unification	INFERENCE
AUTHOR NAME	Christian Urban	SVM HeaderParse 0.1
AUTHOR AFFIL	University of Cambridge, Cambridge	SVM HeaderParse 0.2
AUTHOR ADDR	UK	SVM HeaderParse 0.1
AUTHOR NAME	Andrew Pitts	SVM HeaderParse 0.1
AUTHOR AFFIL	University of Cambridge, Cambridge	SVM HeaderParse 0.2
AUTHOR ADDR	UK	SVM HeaderParse 0.1
AUTHOR NAME	Murdoch Gabbay	SVM HeaderParse 0.1
AUTHOR AFFIL	University of Cambridge, Cambridge	SVM HeaderParse 0.2
AUTHOR ADDR	UK	SVM HeaderParse 0.1
ABSTRACT	We present a generalisation of first-order unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms #-equivalent, i.e. equal up to renaming bound names. For the applications we have in mind, we must consider the simple, textual form of substitution in which names occurring in terms may be captured within the scope of binders upon substitution. We are able to take a `nominal' approach to binding in which bound entities are explicitly named (rather than using nameless, de Bruijn-style representations) and yet get a version of this form of substitution that respects #-equivalence and possesses good algorithmic properties. We achieve this by adapting an existing idea and introducing a key new idea. The existing idea is terms involving explicit substitutions of names for names, except that here we only use explicit permutations (bijective substitutions). The key new idea is that the unification algorithm should solve not only equational problems, but also problems about the freshness of names for terms. There is a simple generalisation of the classical first-order unification algorithm to this setting which retains the latter's pleasant properties: unification problems involving #-equivalence and freshness are decidable; and solvable problems possess most general solutions.	user correction - Legacy Corrections
YEAR	2003	INFERENCE
VENUE	Theoretical Computer Science	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2004	INFERENCE
VOLUME	323	INFERENCE
CITATIONS	27 found	ParsCit 1.0