J. M. Spivey and B. A. Sufrin. Type inference in Z. In [39], 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....As a trivial example, consider the expression dom first . As explained in the Reference Manual, this is in fact an abbreviated notation for the expression dom[A; B] first [C ; D ] where A, B , C and D are implicit generic actual parameters (which are usually inferred from the context [52]) And, in fact, provided C 2 D A and D B , we have dom[A; B] first [C ; D ] C 2 D . Thus, some typing information must be presented during proof. As a second example, given X = and Y = it is tempting to conclude T X = T Y . This need not be the case. Recall the definition of ....

J. M. Spivey and B. A. Sufrin. Type inference in Z. In [39], 1990.

....but it has since been found convenient to have types available for use in defining values, especially for schema negation. A formal system of type inference rules is needed to determine the type annotations, analogous to the type inference algorithms implemented in typechecking tools [16]. Every typechecker we have tried, f uzz and CADiZ included, currently fails to determine the unique assignment of type annotations in some cases where one exists. We must either show that typechecking algorithms can be made to determine the unique assignment of type annotations wherever there is ....

J.M. Spivey and B.A. Sufrin. Type inference in Z. In D. Bjrner, C.A.R. Hoare, and H. Langmaack, editors, Proceedings of VDM and Z -- Formal Methods in Software Development, volume 428 of Lecture Notes in Computer Science. Springer-Verlag, 1990.

....can not be done in a schema, and ffl a schema can be used as a type, whereas a library can not. The library extension to Z is discussed in greater detail in [2] A typechecker for the library extension to Z has been developed by extending the hippo typechecker for Z developed by Sufrin et al. [9]. The specification presented in this paper has been mechanically checked with the typechecker. 3 Grammar transformations In this section we introduce some of the libraries that define the grammar transformations that are used within the specification of the parser for the language based editor. ....

J.M. Spivey and B.A. Sufrin. Type inference in Z. In D. Bjrner, C.A.R. Hoare and H. Langmaack (editors), VDM and Z -- Formal Methods in Software Development, Volume 428 of Lecture Notes in Computer Science, pages 426--438. VDM-Europe, SpringerVerlag, 1990.

....for typechecking polymorphic functional languages, as explained by Cardelli [1] and by Hancock [2] are readily adaptable to typecheck Z specifications and their generic constructs. They are based around Milner s unification algorithm [6] Spivey and Sufrin gave an account of typechecking Z [12], focusing on the inference of implicit generic instantiations. They deliberately omitted any discussion of the typechecking of schemas. We have found some schemas that are awkward to typecheck but could be well typed. An investigation of the typechecking of schemas is particularly important in ....

J.M. Spivey and B.A. Sufrin. Type inference in Z. In D. Bjrner, C.A.R. Hoare, and H. Langmaack, editors, VDM'90: VDM and Z---Formal Methods in Software Development, LNCS 428, pages 426--451. Springer, 1990.

....to use. It would reduce some duplication of effort, it would allow the arguments of cut to be type checked automatically, and would permit generic parameters to be calculated when necessary. Stephen Brien s thesis [Bri95] presents typeinference rules for Z (in the style of [Spi88] and [SS90] with each type inference corresponding to a logical inference in W . Using the two systems together could form the basis of a more unified tool. This work with W has also suffered from the fact that it has been undergoing change during the course of the work. It was necessary to fix on one ....

J. M. Spivey and B. A. Sufrin. Type inference in Z. In D. Bjørner, C. A. R. Hoare, and H. Langmaack, editors, VDM'90: VDM and Z---Formal Methods in Software Development, volume 428 of Lecture Notes in Computer Science, pages 426--451. Springer-Verlag, 1990.

....union operation union(x; y; z) z = x [ y can be used in the mode fzg ) fx; yg. The algorithms for mode analysis in the context of animating Z specifications are given in [18, 19] Z s type system consists of a class of base types and can be simply extended to include a hierarchy of subtypes [13, 14] which are defined in terms of the base types. Operations like a are only guaranteed to return a sequence if the two arguments are also sequences, but sequences themselves are defined in terms of the base type P(N Theta A) where A is the type of the elements of the sequence. Subtype analysis ....

J. M. Spivey and B. A. Sufrin. Type inference in Z. In D. Bjørner, C. A. R. Hoare, and H. Langmaack, editors, VDM and Z -- Formal Methods in Software Development, volume 428 of Lecture Notes in Computer Science, pages 426--438. VDM-Europe, Springer-Verlag, 1990.

....regards to the specification of large systems. Although Object Z is largely based on Z, there are important differences such as the notion of class, class type and class inheritance. Type checking Z specifications has been previously investigated and several type checkers have been developed [18]. To our best knowledge, currently there is no type checker implemented for Object Z. Although specifiers could use a Z type checker for type checking Object Z specifications, a large part of their specifications cannot be checked because that class types in Object Z is new to Z. From the ....

Spivey, J.M. and Sufrin, B.A., "Type Inference in Z", in Proceedings of the 4th Annual Z User Meeting, Nicholls, J.E. (ed.), Springer-Verlag, pages 6-31, 1990.

....manner as the existential quantifier. For brevity, the constraint part of the quantifiers is deleted. The production rules for Decl are as follows: Decl : VarList : Type j Decl ; Decl VarList : VarName j VarList ; VarName IZRC V1.0 April 13, 1995 8 where Type represents the common types[14], and VarName represents the conventional variable names in Z. 3.2 The subset of the Refinement Calculus(RC) Unlike Z, we could not find the official abstract syntax of the Refinement Calculus in the literature. However, there is a complete BNF grammar for a method which is very close to the ....

Spivey J. M., Sufrin B. A., Type Inference in Z, Proceedings, VDM'90, LNCS 428, Springer-Verlag, pp. 426-451, April 1990

....Z specification technique. Z is a formal language based on set theory and first order logic, developed by the Programming Research Group at Oxford [Spi92, Hay93] It has been successfully used in software development and there are lot of works around Z extensions for the specification of real time [Eng94, Fid92, Rud93, SS90] and distributed systems [CM92] Our aim in this work is to check what kind of properties can be proved with Z and to indicate the weaknesses that must be fought for a successful usability in the domain of real time and concurrent systems. The rest of the paper is organized as follows: section 1 ....

J. M. Spivey and B. A. Sufrin. Type inference in Z. In Bjørner et al. [BHL90], pages 426--438.

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J. M. Spivey and B. A. Sufrin. Type inference in Z. In Bjørner et al. [32], pages 426--438. See also [341].

No context found.

J.M. Spivey and B.A. Sufrin. Type inference in Z. In D. Bjørner, C.A.R. Hoare, and H. Langmaack, editors, VDM and Z -- Formal Methods in Software Development, volume 428 of Lecture Notes in Computer Science, pages 426--438. VDM-Europe, Springer-Verlag, 1990. See also [279].

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