Gordin Plotkin and Martn Abadi. A logic for parametric polymorphism. In Proc. LICS'98, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the interaction of recursion and freshness is semantically quite challenging, and was investigated in Part I. In this paper we go one step further and introduce second order quantification in the logic, from which we can define least and greatest fixpoints of formulas, almost along standard lines [14]. Structurally, our logic consists of a collection of left right rules for logical operators, including essentially the standard rules of classical sequent calculus, plus the ones for temporal and spatial operators. In addition, there are special rules about the worlds: they add meaning to the ....

G. Plotkin and M. Abadi. A logic for parametric polymorphism. In M. Bezem and J. F. Groote, editors, International Conference on Typed Lambda Calculi and Applications, number 664 in Lecture Notes in Computer Science, pages 361--375, Utrecht, The Netherlands, March 1993. Springer-Verlag. TLCA'93.

....terms with that type in the predicative calculus. These sets frequently admit interesting and intuitive descriptions. Some such characterizations of polymorphic types were given by Reynolds [Rey83] Even more results have been described, including what Wadler called Theorems for Free [ACC93, PA93, Wad89] As an example, the type 8X:X)X contains only a single term (up to equivalence) the polymorphic identity function. This is to be expected, as it agrees with our intuitive understanding of uniform computations of the type 8X:X)X. Given an element x of an unknown type X, since the only ....

..... Such a partial recursive function is said to realize f . The re exive graph category PER has the category of PERs over IN and PER morphisms for the vertex category. The edge category of PER is motivated by the relational parametricity identi ed by Bainbridge et.al. BFSS90] and used in [BAC95, PA93] An edge R: A B is a relation between natural numbers satisfying the following. An nRm mBm = n Such a relation R is called a saturated relation. A square from an edge R: A B to R : A B is a pair hf; gi where f : A A g: B B are PER morphisms that have ....

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G. Plotkin and M. Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications - TLCA '93, LNCS, pages 361-375. Springer-Verlag, 1993.

....the interaction of recursion and freshness is semantically quite challenging, and was investigated in Part I. In this paper we go one step further and introduce second order quantification in the logic, from which we can define least and greatest fixpoints of formulas, almost along standard lines [19]. Structurally, our logic consists of a collection of left right rules for logical operators, including essentially the standard rules of classical sequent calculus, plus the ones for temporal and spatial operators. In addition, there are special rules about the worlds: they add meaning to the ....

.... formula, where the index is 0) We can then easily derive the following inference rules: g; u : AfBg Z) AfCg g; u : B Z) C (MontonL) g u : B Z) C; g u : AfBg Z) AfCg; MontonR) We then define least and greatest fixpoint operators in a style similar to F algebraic encodings [19]. Y:AfY g = 8Y: AfY g Z) Y ) Y Y:AfY g = X: AfXg These definitions turn out to enjoy the expected properties of recursive formulas, in the form of the derivable left and right rules in Figure 16. For example, the derivable rule ( R) corresponds to a coinduction principle. The ....

G. Plotkin and M. Abadi. A logic for parametric polymorphism. In M. Bezem and J. F. Groote, editors, International Conference on Typed Lambda Calculi and Applications, number 664 in Lecture Notes in Computer Science, pages 361--375, Utrecht, The Netherlands, March 1993. Springer-Verlag. TLCA'93.

....type instances has been John Reynolds Figure 1: Generic list structure notion of relational parametricity [Rey83] which requires that relations between instances be preserved in a suitable sense by generic programs. This has led to numerous further developments, e.g. [MR92, ACC93, PA93]. Relational parametricity is a beautiful and important notion. However, in our view it is not the whole story. In particular: It is a pointwise notion, which gets at genericity indirectly, via a notion of uniformity applied to the family of instantiations of the program, rather than ....

....notion of uniformity applied to the family of instantiations of the program, rather than directly capturing the idea of a program written at the generic level, which necessarily cannot probe the structure of an instance. It is closely linked to strong extensionality principles, as shown e.g. in [ACC93, PA93], whereas the intuition of generic programs not probing the structure of instances is prima facie an intensional notion a constraint on the behaviour of processes. An interestingly di erent analysis of genericity with di erent formal consequences was proposed by Giuseppe Longo, Kathleen Milsted ....

G. Plotkin, M. Abadi. A Logic for Parametric Polymorphism, TLCA'93 Conf. Proc., LNCS, 1993.

....to that of SOL has not been previously available. In a sense, IA is to Idealized Algol what SOL is to polymorphic lambda calculus. Like SOL, it adds types and features that explicitly represent data abstraction. However, while SOL can be faithfully encoded in polymorphic lambda calculus [55], the data abstraction features of IA are more re ned than those expressible in Idealized Algol. The corresponding encoding does not preserve equivalences. Thus, IA is a proper extension. Related work In the earlier work of the author [56, 32] a global state based semantics was de ned ....

.... Z : Z Z serves as the required relation S. The rst step in the above proof shows that the identi cation of behaviorally equivalent implementations is a necessary condition for the identity extension property. The basic reference for parametricity is Reynolds [62] while Plotkin and Abadi [55] de ne a logic for reasoning about parametricity. The notion of existential quanti cation is from [43] but its parametricity semantics discussed above seems new. The idea of simulation relations for implementations dates back to Milner [40] and appears in various sources including [9, 33, 26, ....

G. Plotkin and M. Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications - TLCA '93, LNCS, pages 361-375. Springer-Verlag, 1993.

....regardless of the type at which it is applied. In particular, a parametric, polymorphic function can neither branch on nor otherwise analyze its type argument. In many type theories (such as the polymorphic lambda calculus) all polymorphic functions must be parametric. It has long been recognized [10, 12, 8, 3] that in type theories in which all polymorphism is parametric, many properties of polymorphic functions can be determined solely by inspection of their types. For instance, in the polymorphic lambda calculus, any function having the type 8ff: ff ff must be the identity function. In an This ....

Gordon Plotkin and Mart'in Abadi. A logic for parametric polymorphism. In International Conference on Typed Lambda Calculi and Applications, pages 361--375, 1993.

....principle for this encoding provable in U . This weakness has been encountered before. In fact, it is conjectured that it is impossible to encode primitive recursion in System F using equality [21] A stronger equational theory for U , perhaps one incorporating a parametricity principle [19], might solve this problem. However, a simpler way to support primitive recursion would be to include a primitive for primitive recursion directly in the language [12, 18, 3, 4] 4.2 Impredicativity and Non termination Another issue with this encoding is that the target language must have ....

Gordon Plotkin and Martn Abadi. A logic for parametric polymorphism. In International Conference on Typed Lambda Calculi and Applications, pages 361{ 375, 1993.

....the general properties of these categories, e.g. define coproducts, products, etc. 36 . Besides full completeness, parametricity is another quality filter for models of polymorphic functions. In particular, in [Plo93] a logic for linear parametric models has been suggested, in the line of [PA93]. It would be interesting to develop further this approach, and see whether this logic holds on our linear PER models. Longo s genericity ( LMS92] can be viewed as a form of parametricity, in that it amounts to a uniformity property of polymorphic functions w.r.t. their input types. This issue ....

G.Plotkin, M.Abadi. A Logic for Parametric Polymorphism, TLCA'93 Conf. Proc., LNCS, 1993.

.... categories has been found for this hierarchy [Weh99] The next steps will be the development of general structural recursion for the hierarchy in style of this paper, and the development of higher dimensional parametricity to derive program transformations similar to the analysis for system F [Wad93, BFSS90, PA93]. I am currently working on applications exploring the expressive power of dimension three. Preliminary results deal with simply typed lambda calculus, internalisation of algebraic data specifications and examples from Okasakis purely functional data types [Oka98] A challenge is to internalise ....

Gordon Plotkin and Martin Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications TLCA `93, pages 361--375, LNCS 664, March 1993. Springer Verlag.

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Gordon Plotkin and Martn Abadi. A logic for parametric polymorphism. In M. Bezem and J.F. Groote, editors, Typed Lambda Calculi and Applications, volume 664 of Lecture Notes in Computer Science, pages 361--375. Springer-Verlag, March 1993.

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G.D. Plotkin and M. Abadi. A logic for parametric polymorphism . Proc. International Conference on Typed Lambda Calculi and Applications . Springer-Verlag.

....recursive type S: the two halves of the isomorphism in and out are not linear. After considering these typed version of the Scott numerals, we may wish to check that they are in fact isomorphic to the standard natural numbers. A direct argument uses many of the datatype constructions studied in [1]: M j N by unfolding j X8R: 1 R) X R) R) since R j (1 R) j X8R: 1 R) Theta (X R) R) by uncurrying j X8R: 1 X) R) R) turning a Theta into a j X: 1 X) as 1 X j R: 1 X) Similarly, we can give Scott versions for other familiar datatypes using covariant ....

Gordon Plotkin and Mart'in Abadi. A logic for parametric polymorphism. To appear in Proceedings of the International Conference on Typed Lambda Calculi and Applications, March 1993.

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Gordin Plotkin and Martn Abadi. A logic for parametric polymorphism. In Proc. LICS'98, 1998.

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Plotkin, G. and Abadi, M., A Logic for Parametric Polymorphism, LICS'98, 42--53, IEEE Press, 1998.

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G. Plotkin, M. Abadi. A Logic for Parametric Polymorphism, TLCA'93 Conf. Proc., LNCS, 1993.

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G. Plotkin and M. Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications, Lecture Notes in Computer Science 664, pages 361--375. Springer-Verlag, 1993.

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G. D. Plotkin and M. Abadi. A Logic for Parametric Polymorphism. In Proceedings of the Conference on Typed Lambda Calculus and its Applications, Utrecht, 1993.

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Gordon Plotkin and Martin Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications, volume 664 of Lecture Notes in Computer Science, pages 361-375, 1993.

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G. Plotkin and M. Abadi. A logic for parametric polymorphism. In TLCA '93 [129], pages 361--375. (pp. 5, 70, 122, 123)

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Plotkin, G. and Abadi, M., A Logic for Parametric Polymorphism, LICS'98, 42-53, IEEE Press, 1998.

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Gordon Plotkin and Martin Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications, volume 664 of Lecture Notes in Computer Science, pages 361-375, 1993.

No context found.

Plotkin, G. and Abadi, M., A Logic for Parametric Polymorphism, LICS'98, 42--53, IEEE Press, 1998.

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G. D. Plotkin and M. Abadi. A Logic for Parametric Polymorphism. In Proceedings of the Conference on Typed Lambda Calculus and its Applications, Utrecht, 1993, Lecture Notes in Computer Science Vol. 664 (Springer-Verlag, Berlin, 1993) pp 361-375.

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Plotkin, G. and Abadi, M., A Logic for Parametric Polymorphism, LICS'98, 42--53, IEEE Press, 1998.

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Gordon Plotkin and Martin Abadi. A logic for parametric polymorphism. In Typed Lambda Calculi and Applications, volume 664 of Lecture Notes in Computer Science, pages 361-375, 1993.

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