Relating Nominal and Higher-Order Pattern Unification
نویسنده
چکیده
Higher-order pattern unification and nominal unification are two approaches to unifying modulo some form of α-equivalence (consistent renaming of bound names). Though the higher-order and nominal approaches superficially dissimilar, there is a natural concretion (or name-application) operation for nominal terms that can be used to simulate the behavior of higher-order patterns. We describe a form of nominal terms called nominal patterns that includes concretion and for which unification is equivalent to a special case of higher-order pattern unification, and then show how full higher-order pattern unification can be reduced to nominal unification via nominal patterns.
منابع مشابه
Relating the solutions of nominal unification and pattern unification
Levy and Villaret proposed a translation of nominal unification problems to higher-order pattern unification problems and showed that unifiability is preserved by this translation. We take this further by showing correspondences between solutions of corresponding pattern unification problems and nominal unification problems. The notions of correspondence are non-trivial, and require careful def...
متن کاملNominal Unification Revisited
Nominal unification calculates substitutions that make terms involving binders equal modulo alphaequivalence. Although nominal unification can be seen as equivalent to Miller’s higher-order pattern unification, it has properties, such as the use of first-order terms with names (as opposed to alphaequivalence classes) and that no new names need to be generated during unification, which set it cl...
متن کاملA Nominal Unification from a Higher-Order Perspective
Nominal logic is an extension of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to lambda-terms, in nominal terms, bindable names, called atoms, and instantiable variables are considered as distinct entities. Moreover, atoms are capturable by instantiations, breaking a fundamental principle of the lambda-calculus. Despite these diffe...
متن کاملNominal Unification from a Higher-Order Perspective
Nominal logic is an extension of first-order logic with equality, namebinding, renaming via name-swapping and freshness of names. Contrarily to lambda-terms, in nominal terms, bindable names, called atoms, and instantiable variables are considered as distinct entities. Moreover, atoms are capturable by instantiations, breaking a fundamental principle of the lambda-calculus. Despite these differ...
متن کاملPermissive nominal terms and their unification: an infinite, co-infinite approach to nominal techniques
Nominal terms extend first-order terms with binding. They lack some properties of firstand higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005