A co-induction principle for recursively defined domains:
Abstract: "This paper establishes a new property of predomains recursively defined using the cartesian product, disjoint union, partial function space and convex powerdomain constructors. We prove that the partial order on such a recursive predomain D is the greatest fixed point of a certain mo...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
1992
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| Schriftenreihe: | Computer Laboratory <Cambridge>: Technical report
252 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "This paper establishes a new property of predomains recursively defined using the cartesian product, disjoint union, partial function space and convex powerdomain constructors. We prove that the partial order on such a recursive predomain D is the greatest fixed point of a certain monotone operator associated to D. This provides a structurally defined family of proof principles for these recursive predomains: to show that one element of D approximates another, it suffices to find a binary relation containing the two elements that is a post-fixed point for the associated monotone operator. The statement of the proof principles is independent of any of the various methods available for explicit construction of recursive predomains Following Milner and Tofte [9], the method of proof is called co- induction. It closely resembles the way bisimulations are used in concurrent process calculi [8]. Two specific instances of the co- induction principle already occur in work of Abramsky [1, 2] in the form of 'internal full abstraction' theorems for denotational semantics of SCCS and the lazy lambda calculus. In the first case post-fixed binary relations are precisely Abramsky's partial bisimulations, whereas in the second case they are his applicative bisimulations. The co-induction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in (strict or lazy) higher order functional programming languages. |
| Beschreibung: | 25 S. |
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| 245 | 1 | 0 | |a A co-induction principle for recursively defined domains |
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| 490 | 1 | |a Computer Laboratory <Cambridge>: Technical report |v 252 | |
| 520 | 3 | |a Abstract: "This paper establishes a new property of predomains recursively defined using the cartesian product, disjoint union, partial function space and convex powerdomain constructors. We prove that the partial order on such a recursive predomain D is the greatest fixed point of a certain monotone operator associated to D. This provides a structurally defined family of proof principles for these recursive predomains: to show that one element of D approximates another, it suffices to find a binary relation containing the two elements that is a post-fixed point for the associated monotone operator. The statement of the proof principles is independent of any of the various methods available for explicit construction of recursive predomains | |
| 520 | 3 | |a Following Milner and Tofte [9], the method of proof is called co- induction. It closely resembles the way bisimulations are used in concurrent process calculi [8]. Two specific instances of the co- induction principle already occur in work of Abramsky [1, 2] in the form of 'internal full abstraction' theorems for denotational semantics of SCCS and the lazy lambda calculus. In the first case post-fixed binary relations are precisely Abramsky's partial bisimulations, whereas in the second case they are his applicative bisimulations. The co-induction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in (strict or lazy) higher order functional programming languages. | |
| 650 | 7 | |a Computer software |2 sigle | |
| 650 | 7 | |a Mathematics |2 sigle | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Abstract data types (Computer science) | |
| 650 | 4 | |a Recursive functions | |
| 830 | 0 | |a Computer Laboratory <Cambridge>: Technical report |v 252 |w (DE-604)BV004055605 |9 252 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006933522 | ||
Datensatz im Suchindex
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| author | Pitts, Andrew M. 1956- |
| author_GND | (DE-588)1069892432 |
| author_facet | Pitts, Andrew M. 1956- |
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| author_sort | Pitts, Andrew M. 1956- |
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| bvnumber | BV010411591 |
| ctrlnum | (OCoLC)27028379 (DE-599)BVBBV010411591 |
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| id | DE-604.BV010411591 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:03Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006933522 |
| oclc_num | 27028379 |
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| physical | 25 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| record_format | marc |
| series | Computer Laboratory <Cambridge>: Technical report |
| series2 | Computer Laboratory <Cambridge>: Technical report |
| spelling | Pitts, Andrew M. 1956- Verfasser (DE-588)1069892432 aut A co-induction principle for recursively defined domains Cambridge 1992 25 S. txt rdacontent n rdamedia nc rdacarrier Computer Laboratory <Cambridge>: Technical report 252 Abstract: "This paper establishes a new property of predomains recursively defined using the cartesian product, disjoint union, partial function space and convex powerdomain constructors. We prove that the partial order on such a recursive predomain D is the greatest fixed point of a certain monotone operator associated to D. This provides a structurally defined family of proof principles for these recursive predomains: to show that one element of D approximates another, it suffices to find a binary relation containing the two elements that is a post-fixed point for the associated monotone operator. The statement of the proof principles is independent of any of the various methods available for explicit construction of recursive predomains Following Milner and Tofte [9], the method of proof is called co- induction. It closely resembles the way bisimulations are used in concurrent process calculi [8]. Two specific instances of the co- induction principle already occur in work of Abramsky [1, 2] in the form of 'internal full abstraction' theorems for denotational semantics of SCCS and the lazy lambda calculus. In the first case post-fixed binary relations are precisely Abramsky's partial bisimulations, whereas in the second case they are his applicative bisimulations. The co-induction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in (strict or lazy) higher order functional programming languages. Computer software sigle Mathematics sigle Mathematik Abstract data types (Computer science) Recursive functions Computer Laboratory <Cambridge>: Technical report 252 (DE-604)BV004055605 252 |
| spellingShingle | Pitts, Andrew M. 1956- A co-induction principle for recursively defined domains Computer Laboratory <Cambridge>: Technical report Computer software sigle Mathematics sigle Mathematik Abstract data types (Computer science) Recursive functions |
| title | A co-induction principle for recursively defined domains |
| title_auth | A co-induction principle for recursively defined domains |
| title_exact_search | A co-induction principle for recursively defined domains |
| title_full | A co-induction principle for recursively defined domains |
| title_fullStr | A co-induction principle for recursively defined domains |
| title_full_unstemmed | A co-induction principle for recursively defined domains |
| title_short | A co-induction principle for recursively defined domains |
| title_sort | a co induction principle for recursively defined domains |
| topic | Computer software sigle Mathematics sigle Mathematik Abstract data types (Computer science) Recursive functions |
| topic_facet | Computer software Mathematics Mathematik Abstract data types (Computer science) Recursive functions |
| volume_link | (DE-604)BV004055605 |
| work_keys_str_mv | AT pittsandrewm acoinductionprincipleforrecursivelydefineddomains |