Pot81 Garrel Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.  Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Simulating Expansions Without Expansions - Di Cosmo, KESNER (1993) (1 citation) (Correct)
....into a rewrite rule was also from left to right, as a contraction. But in 1980, J.W. Klop discovered [Klo80] that, if added to the usual confluent rewrite rules for pure calculus, this interpretation of SP breaks confluence 1 . Anyway, this first negative result was shortly after mitigated in [Pot81] for the simply typed calculus with j and SP contractions, by providing a first proof of confluence and strong normalization, later on simplified in different ways (see [Tro86] or [GLT90] for example) From then on, the contraction rule for SP was not considered harmful in a typed framework, ....
G. Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Reasoning about Redundant Patterns - Kesner (1997) (Correct)
....by abstraction, and a term M of product type must really be a pair, built via the pair constructor. The j and the sp axioms have traditionally been turned into contractions carrying the same name. Such an interpretation is well behaved in the simply typed calculus, as it preserves confluence [Pot81] But surprisingly, 3 The Journal of Functional and Logic Programming 1997 4 Kesner Reasoning about Redundant Patterns x1 recursion together with the sp axiom oriented as a contraction causes confluence to fail [Nes89] Moreover, the contractive interpretation of the j p axiom for patterns ....
Garrel Pottinger. The Church-Rosser theorem for the typed lambda-calculus with surjective pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Provable Isomorphisms of Types - Kim Bruce Roberto (1990) (7 citations) (Correct)
....in the axioms to the right is not Church Rosser. It is possible, though, to derive for this equality theory another notion of reduction that has the Church Rosser property; in the following we will refer to this latter one when talking about reduction, normal forms, and so on for # 1 #### (see [Pot81], CDC91] Definition 2.5 Let A, B # Tp. Then A and B are provably isomorphic (A # =p B) i# there exist closed # terms M : A # B and N : B # A such that # 1 ##### M N = I B and # 1 ##### N M = I A . We then say that M and N are invertible terms, and that M is an inverse of N, in # ....
Garrel Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Confluence Properties of Extensional and Non-Extensional.. - Kesner (1996) (17 citations) (Correct)
....as an expansion, called # expansion or b # expansion, depending on whether some other restrictions are imposed to its application. The # axiom has traditionally been turned into a contraction. Such an interpretation is well behaved in the simply typed # calculus as it preserves confluence [35], but it is not in many other # calculi [6, 12] Fortunately, expansions can be combined with many other higher order reduction rules [11, 2, 15, 24, 12, 13] all these combinations preserve confluence and strong normalization. For that, application of the # expansion has to be restricted by some ....
G. Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Jour. of Formal Logic, 22(3):264--268, 1981.
A Confluent Reduction for the Extensional Typed.. - Di Cosmo, Kesner (1993) (1 citation) (Correct)
....into a rewrite rule was also from left to right, as a contraction. But in 1980, J.W. Klop discovered [Klo80] that, if added to the usual confluent rewrite rules for pure calculus, this interpretation of SP breaks confluence 1 . Anyway, this first negative result was shortly after mitigated in [Pot81] for the simply typed calculus with j and SP contractions, by providing a first proof of confluence and strong normalization, later on simplified in different ways (see [Tro86] or [GLT90] for example) From then on, the contraction rule for SP was not considered harmful in a typed framework, ....
Garrel Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Reasoning about Layered, Wildcard and Product Patterns - Kesner (1994) (Correct)
.... abstraction, and a term M of product type has to be really a pair, built via the pair constructor. The (j) and the (sp) axioms have traditionally been turned into contractions carrying the same name. Such an interpretation is well behaved in the simply typed calculus as it preserves confluence [Pot81]. But surprisingly, recursion together with the (sp) axiom oriented as contraction causes confluence to fail [Nes89] Moreover, the contractive interpretation of the (b j) axiom for patterns breaks confluence, as the following example shows: Example 1.2 hx; yi : A Theta B:hx; yi fi Gamma ....
Garrel Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
A Brief History of Rewriting With Extensionality - Di Cosmo (1996) (2 citations) (Correct)
....1976 Huet uses ## long normal forms for higher order unification [Hue76] 1979 Mints reverses # and SP [Min79] 197 Many people suggest expansions: Martin Lof, Meyer, Statman, etc. 1980s: the contraction 1980 Klop s counterexample to CR for # SP [Klo80] 1981 Pottinger shows CR for typed ### SP [Pot81] 1986 Lambek Scott, Obtulowicz: typed ### SP T is not CR [LS86] 1987 Poigne Voss try completion for ### SP T sums and recursion [PV87] 1989 Nesmith: Klop s counterexample holds for simply typed # calculus fixpoints [Nes89] 1991 Curien Di Cosmo: completion for polymorphic ### SP T [CDC95] ....
Garrel Pottinger. The Church Rosser Theorem for the Typed lambdacalculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Confluence of Extensional and Non-Extensional λ-calculi.. - Kesner (Correct)
....way round as an expansion, called j expansion or b j expansion depending on whether some other restrictions are imposed to its application. The j axiom has traditionally been turned into a contraction. Such an interpretation is well behaved in the simply typed calculus as it preserves confluence [Pot81]. However, j contraction does not preserve confluence in many other calculi [CDC91, DCK94, Kes97b] Fortunately, expansions can be combined with many other higher order reduction rules, such as expansive surjective pairing [DCK93, Aka93, Dou93, JG95] recursion [DCK93, Dou93] sums [DCK93, ....
Garrel Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Provable Isomorphisms of Types - Bruce, Di Cosmo, Longo (1991) (7 citations) (Correct)
No context found.
Pot81 Garrel Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
Simulating Expansions Without Expansions - Di Cosmo, Kesner (1993) (1 citation) (Correct)
No context found.
G. Pottinger. The Church Rosser Theorem for the Typed lambda-calculus with Surjective Pairing. Notre Dame Journal of Formal Logic, 22(3):264--268, 1981.
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