A complete transformation system for polymorphic higher-order unification:
Abstract: "Polymorphic higher-order unification is a method for unifying terms in the polymorphically typed [lambda]-calculus, that is, given a set of pairs of terms [formula], called a unification problem, finding a substitution [sigma] such that [sigma](S[subscript i]) and [sigma](t[subscript...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Saarbrücken
1991
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| Schriftenreihe: | Max-Planck-Institut für Informatik <Saarbrücken>: MPI I
91,228 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Polymorphic higher-order unification is a method for unifying terms in the polymorphically typed [lambda]-calculus, that is, given a set of pairs of terms [formula], called a unification problem, finding a substitution [sigma] such that [sigma](S[subscript i]) and [sigma](t[subscript i]) are equivalent under the conversion rules of the calculus for all i, 1 [<or =] i [<or =] n. I present the method as a transformation system, i.e. as a set of schematic rules U ==> U' such that any unification problem [delta](U) can be transformed into [delta](U') where [delta] is an instantiation of the meta-level variables in U and U'. By successive use of transformation rules one possibly obtains a solved unification problem with obvious unifier I show that the transformation system is correct and complete, i.e. if [delta](U) ==> [delta](U') is an instance of a transformation rule, then the set of all unifiers of [delta](U') is a subset of the set of all unifiers of [delta](U) and if U is the set of all unification problems that can be obtained from successive applications of transformation rules from an unification problem U, then the union of the set of all unifiers of all unification problems in U is the set of all unifiers of U. The transformation rules presented here are essentially different from those in Snyder and Gallier (1989) or Nipkow (1990). The correctness and completeness proofs are in lines with those of Snyder and Gallier (1989). |
| Beschreibung: | 22 Bl. |
Internformat
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| 100 | 1 | |a Hustadt, Ullrich |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A complete transformation system for polymorphic higher-order unification |c Ullrich Hustadt |
| 264 | 1 | |a Saarbrücken |c 1991 | |
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| 520 | 3 | |a Abstract: "Polymorphic higher-order unification is a method for unifying terms in the polymorphically typed [lambda]-calculus, that is, given a set of pairs of terms [formula], called a unification problem, finding a substitution [sigma] such that [sigma](S[subscript i]) and [sigma](t[subscript i]) are equivalent under the conversion rules of the calculus for all i, 1 [<or =] i [<or =] n. I present the method as a transformation system, i.e. as a set of schematic rules U ==> U' such that any unification problem [delta](U) can be transformed into [delta](U') where [delta] is an instantiation of the meta-level variables in U and U'. By successive use of transformation rules one possibly obtains a solved unification problem with obvious unifier | |
| 520 | 3 | |a I show that the transformation system is correct and complete, i.e. if [delta](U) ==> [delta](U') is an instance of a transformation rule, then the set of all unifiers of [delta](U') is a subset of the set of all unifiers of [delta](U) and if U is the set of all unification problems that can be obtained from successive applications of transformation rules from an unification problem U, then the union of the set of all unifiers of all unification problems in U is the set of all unifiers of U. The transformation rules presented here are essentially different from those in Snyder and Gallier (1989) or Nipkow (1990). The correctness and completeness proofs are in lines with those of Snyder and Gallier (1989). | |
| 650 | 4 | |a Lambda calculus | |
| 830 | 0 | |a Max-Planck-Institut für Informatik <Saarbrücken>: MPI I |v 91,228 |w (DE-604)BV008908578 |9 91,228 | |
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Datensatz im Suchindex
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| author | Hustadt, Ullrich |
| author_facet | Hustadt, Ullrich |
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| bvnumber | BV009033748 |
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| id | DE-604.BV009033748 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:28:57Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-29T |
| physical | 22 Bl. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
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| series | Max-Planck-Institut für Informatik <Saarbrücken>: MPI I |
| series2 | Max-Planck-Institut für Informatik <Saarbrücken>: MPI I |
| spelling | Hustadt, Ullrich Verfasser aut A complete transformation system for polymorphic higher-order unification Ullrich Hustadt Saarbrücken 1991 22 Bl. txt rdacontent n rdamedia nc rdacarrier Max-Planck-Institut für Informatik <Saarbrücken>: MPI I 91,228 Abstract: "Polymorphic higher-order unification is a method for unifying terms in the polymorphically typed [lambda]-calculus, that is, given a set of pairs of terms [formula], called a unification problem, finding a substitution [sigma] such that [sigma](S[subscript i]) and [sigma](t[subscript i]) are equivalent under the conversion rules of the calculus for all i, 1 [<or =] i [<or =] n. I present the method as a transformation system, i.e. as a set of schematic rules U ==> U' such that any unification problem [delta](U) can be transformed into [delta](U') where [delta] is an instantiation of the meta-level variables in U and U'. By successive use of transformation rules one possibly obtains a solved unification problem with obvious unifier I show that the transformation system is correct and complete, i.e. if [delta](U) ==> [delta](U') is an instance of a transformation rule, then the set of all unifiers of [delta](U') is a subset of the set of all unifiers of [delta](U) and if U is the set of all unification problems that can be obtained from successive applications of transformation rules from an unification problem U, then the union of the set of all unifiers of all unification problems in U is the set of all unifiers of U. The transformation rules presented here are essentially different from those in Snyder and Gallier (1989) or Nipkow (1990). The correctness and completeness proofs are in lines with those of Snyder and Gallier (1989). Lambda calculus Max-Planck-Institut für Informatik <Saarbrücken>: MPI I 91,228 (DE-604)BV008908578 91,228 |
| spellingShingle | Hustadt, Ullrich A complete transformation system for polymorphic higher-order unification Max-Planck-Institut für Informatik <Saarbrücken>: MPI I Lambda calculus |
| title | A complete transformation system for polymorphic higher-order unification |
| title_auth | A complete transformation system for polymorphic higher-order unification |
| title_exact_search | A complete transformation system for polymorphic higher-order unification |
| title_full | A complete transformation system for polymorphic higher-order unification Ullrich Hustadt |
| title_fullStr | A complete transformation system for polymorphic higher-order unification Ullrich Hustadt |
| title_full_unstemmed | A complete transformation system for polymorphic higher-order unification Ullrich Hustadt |
| title_short | A complete transformation system for polymorphic higher-order unification |
| title_sort | a complete transformation system for polymorphic higher order unification |
| topic | Lambda calculus |
| topic_facet | Lambda calculus |
| volume_link | (DE-604)BV008908578 |
| work_keys_str_mv | AT hustadtullrich acompletetransformationsystemforpolymorphichigherorderunification |