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Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the λσcal ..."
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Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the λσcalculus of explicit substitutions.
A study of substitution, using nominal techniques and FraenkelMostowki sets
"... FraenkelMostowski (FM) set theory delivers a model of names and alphaequivalence. This model, now generally called the ‘nominal ’ model, delivers inductive datatypes of syntax with alphaequivalence — rather than inductive datatypes of syntax, quotiented by alphaequivalence. The treatment of name ..."
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Cited by 3 (0 self)
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FraenkelMostowski (FM) set theory delivers a model of names and alphaequivalence. This model, now generally called the ‘nominal ’ model, delivers inductive datatypes of syntax with alphaequivalence — rather than inductive datatypes of syntax, quotiented by alphaequivalence. The treatment of names and alphaequivalence extends to the entire sets universe. This has proven useful for developing ‘nominal ’ theories of reasoning and programming on syntax with alphaequivalence, because a sets universe includes elements representing functions, predicates, and behaviour. Often, we want names and alphaequivalence to model captureavoiding substitution. In this paper we show that FM set theory models captureavoiding subsitution for names in much the same way as it models alphaequivalence; as an operation valid for the entire sets universe which coincides with the usual (inductively defined) operation on inductive datatypes. In fact, more than one substitution action is possible (they all agree on sets representing