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Nominal rewriting
 Information and Computation
"... Nominal rewriting is based on the observation that if we add support for alphaequivalence to firstorder syntax using the nominalset approach, then systems with binding, including higherorder reduction schemes such as lambdacalculus betareduction, can be smoothly represented. Nominal rewriting ma ..."
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Cited by 33 (14 self)
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Nominal rewriting is based on the observation that if we add support for alphaequivalence to firstorder syntax using the nominalset approach, then systems with binding, including higherorder reduction schemes such as lambdacalculus betareduction, can be smoothly represented. Nominal rewriting maintains a strict distinction between variables of the objectlanguage (atoms) and of the metalanguage (variables or unknowns). Atoms may be bound by a special abstraction operation, but variables cannot be bound, giving the framework a pronounced firstorder character, since substitution of terms for variables is not captureavoiding. We show how good properties of firstorder rewriting survive the extension, by giving an efficient rewriting algorithm, a critical pair lemma, and a confluence theorem
Nominal unification from a higherorder perspective
 In Proceedings of RTA’08
"... Abstract. Nominal Logic is an extension of firstorder logic with equality, namebinding, nameswapping, and freshness of names. Contrarily to higherorder logic, bound variables are treated as atoms, and only free variables are proper unknowns in nominal unification. This allows “variable capture”, ..."
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Cited by 12 (3 self)
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Abstract. Nominal Logic is an extension of firstorder logic with equality, namebinding, nameswapping, and freshness of names. Contrarily to higherorder logic, bound variables are treated as atoms, and only free variables are proper unknowns in nominal unification. This allows “variable capture”, breaking a fundamental principle of lambdacalculus. Despite this difference, nominal unification can be seen from a higherorder perspective. From this view, we show that nominal unification can be reduced to a particular fragment of higherorder unification problems: higherorder patterns unification. This reduction proves that nominal unification can be decided in quadratic deterministic time. 1
AN EFFICIENT NOMINAL UNIFICATION ALGORITHM
"... Abstract. Nominal Unification is an extension of firstorder unification where terms can contain binders and unification is performed modulo αequivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearlyreduce nominal unification problems to ..."
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Cited by 7 (1 self)
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Abstract. Nominal Unification is an extension of firstorder unification where terms can contain binders and unification is performed modulo αequivalence. Here we prove that the existence of nominal unifiers can be decided in quadratic time. First, we linearlyreduce nominal unification problems to a sequence of freshness and equalities between atoms, modulo a permutation, using ideas as Paterson and Wegman for firstorder unification. Second, we prove that solvability of these reduced problems may be checked in quadratic time. Finally, we point out how using ideas of Brown and Tarjan for unbalanced merging, we could solve these reduced problems more efficiently. 1.
Nominal) Unification by Recursive Descent with Triangular Substitutions
 In Proc. of the 1st Interactive Theorem Prover Conference (ITP), volume 6172 of LNCS
, 2010
"... Abstract. We mechanise termination and correctness for two unification algorithms, written in a recursive descent style. One computes unifiers for first order terms, the other for nominal terms (terms including αequivalent binding structure). Both algorithms work with triangular substitutions in a ..."
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Cited by 3 (1 self)
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Abstract. We mechanise termination and correctness for two unification algorithms, written in a recursive descent style. One computes unifiers for first order terms, the other for nominal terms (terms including αequivalent binding structure). Both algorithms work with triangular substitutions in accumulatorpassing style: taking a substitution as input, and returning an extension of that substitution on success. This style of algorithm has performance benefits and has not been mechanised previously. The algorithms use nested recursion so the termination proofs are nontrivial; the termination relation is also slightly different from usual.
Nominal Matching and AlphaEquivalence (Extended Abstract)
"... Nominal techniques were introduced to represent in a simple and natural way systems that involve binders. The syntax includes an abstraction operator and a primitive notion of name swapping. Nominal matching is matching modulo αequality, and has applications in programming languages and theorem pro ..."
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Nominal techniques were introduced to represent in a simple and natural way systems that involve binders. The syntax includes an abstraction operator and a primitive notion of name swapping. Nominal matching is matching modulo αequality, and has applications in programming languages and theorem proving, amongst others. In this paper we describe efficient algorithms to check the validity of equations involving binders, and also to solve matching problems modulo αequivalence, using the nominal approach.
Unification
, 2013
"... Warmup: do these terms unify? P ∧Q ≈? (true ∨ false) ∧ (false ⇒ true) int → T1 ≈? T2 → (T3 × T4) j(a, g(X, f(Y)), h(Y)) ≈? j(X, g(Y,Z), h(b)) ..."
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Warmup: do these terms unify? P ∧Q ≈? (true ∨ false) ∧ (false ⇒ true) int → T1 ≈? T2 → (T3 × T4) j(a, g(X, f(Y)), h(Y)) ≈? j(X, g(Y,Z), h(b))
CurryHoward
"... for incomplete firstorder logic derivations using oneandahalf level terms ..."
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for incomplete firstorder logic derivations using oneandahalf level terms