L. Cardelli, S. Martini, J. C. Mitchell, and A. Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4-- 56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770). 66  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the presence of Bot introduces some surprising intricacies. In particular, a type variable bounded by Bot is actually a synonym for Bot; such bottom variables must be treated specially at several points. 1 Introduction The typed lambda calculus Kernel Fun [CW85] and its wilder sibling, F [CG92, Ghe90, CMMS94] have become standard tools for the foundational study of programming languages combining subtyping and impredicative polymorphism. Their syntax and semantics have been investigated in detail, and they have formed the basis for a number of experimental language designs. Moreover, many ways of ....

.... First, as discussed in the introduction, the definition extends the original Kernel Fun variant of F [CW85] in which the upper bounds B in the subtyping rule for polymorphic functions are required to be identical, rather than the more powerful but less tractable variant of Curien and Ghelli [CG92, CMMS94]. The principal reason for this restriction is that it allows us to define meets and joins of all pairs of types, which may fail to exist in Full F [Ghe90] Second, we give an algorithmic presentation of subtyping, in which the rules of transitivity and general reflexivity are omitted, and ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

.... been built and has type (List Int) new r: List Int) cons Int [33 tl r] r l: List Int) Polymorphism and subtyping are combined by giving each bound type variable in a package value an upper bound, as in the polymorphic calculus with bounded quantification, System F [CW85, CMMS94] For example, the type X T [X X] describes a channel that can be used to transmit a type X and two values of types X and X, but also stipulates that the only legal values of X are subtypes of T. Just as functions in Pict have no special status being regarded as output channels on ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

....respect to F 41 10 PER semantics 45 11 Conclusions 59 2 1 Introduction System F bounded is a type system which was defined by Canning, Cook, Hill, Olthoff, and Mitchell [CCH 89] to model the basic features of object oriented languages. F bounded properly generalizes system F [CW85, CG92, CMMS94] an extension of the polymorphic lambda calculus (syst eme F, Rey74, Gir72] with subtyping. The key ingredient of F is the bounded type abstraction (or bounded polymorphism) It allows one to define a function which works for every type A 0 that is a subtype of a bound A, and whose result ....

....for further studies about system F bounded . Another contribution of this paper is the presentation of an explicit semantic interpretation of system F bounded . Our interpretation is a classical realizability interpretation based on partial equivalence relations, in the tradition of [BL90, CL91, CMMS94, Ghe90] and others. However, most of these papers focus on semantic frameworks , i.e. on the definition of a general notion of a semantic interpretation for system F , in the style of [BMM90] rather than on the definition of a specific interpretation. As a consequence, most proofs become quite ....

[Article contains additional citation context not shown here]

L. Cardelli, S. Martini, J. C. Mitchell, and A. Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4-- 56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770). 64

.... of the single points (1) and (2) results in a system analogous to the system F defined in [8] and studied in [12, 18] with the difference that such papers consider the decidable version derived from the Kernel fun system [7] while Fibonacci uses a richer version derived from the system F [13, 11]. This more expressive system is essential when developing modules with multiple interfaces (Section 4) The dependent type mechanism (3) isolated from the others, is described in [10] where it is interpreted in terms of existential types. Nevertheless, the Fibonacci version is more general, ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

....Two points are worth noting. First, we use the original Kernel Fun rule for comparing quantifiers [CW85] in which the upper bounds B in the subtyping rule for polymorphic functions are required to be identical, rather than the more powerful but less tractable variant of Curien and Ghelli [CG92, CMMS94]. 1 The principal reason for this restriction is that it allows us to define meets and joins of all pairs of types, which may fail to exist in Full F [Ghe90] Second, for simplicity, we use an algorithmic presentation of subtyping, in which the rules of transitivity and general reflexivity ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

....the presence of Bot introduces some surprising intricacies. In particular, a type variable bounded by Bot is actually a synonym for Bot; such bottom variables must be treated specially at several points. 1 Introduction The typed lambda calculus Kernel Fun [CW85] and its wilder sibling, F [CG92, Ghe90, CMMS94] have become standard tools for the foundational study of programming languages combining subtyping and impredicative polymorphism. Their syntax and semantics have been investigated in detail, and they have formed the basis for a number of experimental language designs. Moreover, many ways of ....

.... First, as discussed in the introduction, the definition extends the original Kernel Fun variant of F [CW85] in which the upper bounds B in the subtyping rule for polymorphic functions are required to be identical, rather than the more powerful but less tractable variant of Curien and Ghelli [CG92, CMMS94]. The principal reason for this restriction is that it allows us to define meets and joins of all pairs of types, which may fail to exist in Full F [Ghe90] Second, we give an algorithmic presentation of subtyping, in which the rules of transitivity and general reflexivity are omitted, and ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

....metatheory. The properties of the latter system are developed in detail. 1 Introduction The search for type theoretic foundations for object oriented languages has driven the development of numerous typed lambda calculi combining polymorphism and subtyping. The prototype of these systems is F [CW85, CG92, CMMS94]. However, in the recent literature, many have observed that F in its pure form is an inadequate framework for object oriented programming. The problem is that the only way in which subtyping in F can be used in typing terms is via the subsumption rule, which wastes some of the information ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

....term can be characterized by a single least element. We consider alternative formulations and give an algorithm computing minimal types for the slightly weaker Kernel Fun variant of F . 1 Introduction F is a typed lambda calculus combining subtyping and second order bounded quantification [4, 5, 7, 3]. Besides its utility as a vehicle for theoretical investigations, it has come to be seen as a good basis for the design of programming languages incorporating subtyping and polymorphism. The extension of F with bounded existential quantifiers to support programming with abstract data types is ....

....defined modulo ff conversion and substitution is always capture free. This convention allows us to ignore the type and environment formation rules that would otherwise be needed to assure that every type variable in a judgement is bound and that no variable appears twice in the environment. See [5, 3] for more detailed presentations of the system. The usual presentation of F is not syntax directed: given a typing or subtyping statement, there may be different proofs of its validity, and given a term and an environment, there can be proofs of different typings. However, an important property of ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

.... already been built and has type (List Int) new r: List Int) cons Int[33 tl r] r l: List Int) Polymorphism and subtyping are combined by giving each bound type variable in a package value an upper bound, as in the polymorphic calculus with bounded quantification, System F [CW85, CMMS94] For example, the type X T[X X] describes a channel that can be used to transmit a type X and two values of types X and X, but also stipulates that the only legal values of X are subtypes of T. Just as functions in Pict have no special status being regarded as output channels on which ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

No context found.

L. Cardelli, S. Martini, J. C. Mitchell, and A. Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4-- 56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770). 66

No context found.

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

....extension of the system. This problem is strictly related to the undecidability of subtyping in F [Pie94, Ghe93a] Languages of the Fun family, with their extensions, are the main foundational tool used to model object oriented languages with expressive and strong types (see, for example, [DT88, CHO88, CCHO89, CHC90, Mit90, CMMS94, Ghe91, Bru91, MHF93, GM94, Bru94, ESTZ94, HP95, BSvG95, FM94, EST95, AC94, BCGS91]) The main results of this paper are as follows. ffl We define an algorithm to perform subtype checking in a strongly recursive extension of kernel Fun, which is the first one presented in the literature, and we prove that it is correct and complete. The algorithm is non obvious, and its ....

....completeness. In Section 8 we outline our conclusions and areas of future research. 2 Kernel Fun As we are interested in the problem of subtyping recursive types, we only present the syntax of types and of the subtyping judgements of kernel Fun (for a more complete introduction to the system see [CW85, Ghe90, CG92, CMMS94]) The syntax is as follows: Types T : j t j 8t T:T j T T Pre Judgements P : Gamma B Env j Gamma B T j Type j Pi B T T Judgements J : Gamma Env j Gamma T Type j Pi T T Environments Gamma : j Gamma; t T BiEnvironments Pi : j Pi; t; t) T ; T ) 8t ....

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1-2):4-56, 1994. A preliminary version appeared in TACS'91 (Sendai, Japan, pp. 750-770).

.... our treatment to add high level update to (a second order fragment of) the primitive object model proposed by Pierce and Turner [1994] In Sections 2, 3, and 4, we introduce the syntax, equational theory, and semantics of a positive variant of the calculus F of second order bounded quantification [Cardelli et al. 1994, Curien and Ghelli, 1992] Section 5 gives a small example, showing how updateable records can be encoded in this system. Section 6 presents an example at some length, showing how the equational laws of positive F can be used to prove nontrivial facts about a small object oriented program. This ....

....1994, Pierce and Steffen, 1995] and partial functions, extending our simple example to a full scale model of object oriented programming. Although our development is self contained, readers may like to compare our system with standard bounded quantification calculi [Curien and Ghelli, 1992, Cardelli et al. 1994] and semantic models of subtyping [Bruce and Longo, 1990, Breazu Tannen et al. 1991] In Section 6, familiarity with the literature on type theoretic models of object oriented programming languages [Fisher and Mitchell, 1994, Abadi and Cardelli, 1994, Bruce, 1994, Pierce and Turner, 1994, ....

[Article contains additional citation context not shown here]

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

No context found.

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

No context found.

Luca Cardelli, Simone Martini, John C. Mitchell, and Andre Scedrov. An extension of system F with subtyping. Information and Computation, 109(1--2):4--56, 1994. A preliminary version appeared in TACS '91 (Sendai, Japan, pp. 750--770).

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