Stephen M. Watt, Richard D. Jenks, Robert S. Sutor and Barry M. Trager, `The Scratchpad II type system: Domains and subdomains', Computing Tools for Scientific Problem Solving, ed., Alfonso M. Miola, pp. 63--82, Academic Press, London, UK, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....SML strictly separates types and type constructors of the core language from modules and functors of the module language. The functor based programming has (compared to the well known object oriented programming style) gained little popularity besides in parts of the computer algebra community [ Watt et al. 1988, Jenks and Sutor, 1992, Watt et al. 1994 ] However, this area is historically based on interpreted and dynamically typed languages where performance is not a primary goal. The situation is gradually changing by putting more emphasis on type systems [ Santas, 1993, Zippel, 1993 ] and by the ....

....allow a collection of exported entities (types, functions, values) to be parameterized by other such collections. This mechanism is e.g. called generic package (Ada [ Standard, 1983, Standard, 1994 ] parameterized domain (A# [ Watt et al. 1994 ] Axiom [ Jenks and Sutor, 1992 ] Scratchpad [ Watt et al. 1988 ] or functor (ML [ Milner, 1984, MacQueen, 1984, Milner et al. 1990 ] After instantiation of the arguments, the result is a package (Ada) domain (A#) or structure (ML) In this section, we will generally stick to the ML terminology. This approach differs from genericity by preprocessing ....

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Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II Type System: Domains and Subdomains. Technical report, Computer Algebra Group, Mathematical Sciences Department, IBM Research Division, Thomas J. Watson Research Center, Yorktown Heights, NY, 1988.

....other systems have been reported [16, 17] We will describe it briefly in this section in order to give a reader unacquainted with AXIOM a chance to understand some of the following sections. More detailed descriptions of the AXIOM type system and the underlying philosophy can be found in Refs. [10, 11, 59]. There is a three level hierarchy: Any object is member of one (and only one) domain which itself is member of a category. The easiest way to understand this hierarchy is to consider a concrete example: The object 5 is a member of the domain Integer which is a member of the category Ring. In the ....

S.M. Watt, R.D. Jenks, R.S. Sutor, and B.M. Trager. The Scratchpad II type system: Domains and subdomains. In A.M. Miola, editor, Computing Tools for Scientific Problem Solving. Academic Press, New York, 1990.

.... are related to types in Russel [15] signatures in ML [24, 25] type classes in Haskell [20] definition modules in Modula 2 [36] interface modules in Modula 3 [11] abstract types in Emerald [8] type modules in Trellis Owl [28] categories in Axiom [21] and its predecessor Scratchpad II [34, 35], and types in POOL I [4] In this section, we specify syntax and semantics of signatures, signature pointers, and signature references. We then show how signatures allow us to introduce subtype polymorphism into C independent of the inheritance mechanism. For the remainder of this section, we ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. "The Scratchpad II Type System: Domains and Subdomains." In Alfonso M. Miola (ed.): Computing Tools for Scientific Problem Solving. London: Academic Press, 1990, pp. 63--82.

.... are related to types in Russell [16] signatures in ML [25, 26] type classes in Haskell [17] definition modules in Modula 2 [37] interface modules in Modula 3 [12] abstract types in Emerald [9] type modules in Trellis Owl [29] categories in Axiom [22] and its predecessor Scratchpad II [35, 36], and types in POOL I [4] In this section, we specify syntax and semantics of signatures, signature pointers, and signature references. We then show how signatures allow the introduction of subtype polymorphism into C independent of the inheritance mechanism. For the remainder of this section, ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II type system: Domains and subdomains. In Alfonso M. Miola, editor, Computing Tools for Scientific Problem Solving, pages 63--82. Academic Press, London, Great Britain, 1990.

....ordered elements, not only must the elements understand the message, the method(s) implementing the message should insure that the relationship is irreflexive and transitive. Two systems which support this additional kind of specification are Theta [Liskov Wing 93] and Scratchpad [Watt et al. ] In these systems, the programmer may annotate method implementations and signatures with abstract properties such as transitive. The systems then enforce these restrictions, preventing the instantiation of a polymorphic data structure or function with types that do not support methods that ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II Type System: Domains and Subdomains. Technical report, Mathematical Sciences Department, IBM Thomas J. Watson Research Center.

....a sample Lisp like syntax, and a small example. A larger example can be found in the next section. To explain the behavior of these constructs we roughly sketch a possible implementation in Common Lisp (see [Steele 1984] For a detailed description of the Scratchpad II type system see [Watt et al. 1987]. For the explanation of the language constructs below we adopt the notion of Scratchpad II. What we called an abstract data type in the previous sections is called a category in Scratchpad II. Instead of a concrete data type the notion of a (computational) domain is used. One purpose of using ....

Watt, S.M., Jenks, R.D., Sutor, R.S., Trager, B.M., 1987: The Scratchpad II Type System: Domains and Subdomains. Manuscript, Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, NY.

.... It is related to types in Russel [11] ML s signatures [19, 20] Haskell s type classes [16] definition modules in Modula 2 [26] interface modules in Modula 3 [8] abstract types in Emerald [6] type modules in Trellis Owl [21] categories in Axiom [17] and its predecessor Scratchpad II [24, 25], and types in POOL I [3] The type system of C with signatures comes closest to those of Axiom and POOL I. Russel, ML, Haskell, and Modula 2 don t have class types, Modula 3 only has interfaces for modules but not for classes. Emerald has first class types instead of classes, and Trellis Owl ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. "The Scratchpad II Type System: Domains and Subdomains." In Alfonso M. Miola (ed.): Computing Tools for Scientific Problem Solving. London: Academic Press, 1990, pp. 63--82.

....(types of) languages. Therefore, we do not critique these languages but only give a summary of their object models using our terminology. For lack of a better sorting criterion, we simply present the languages in alphabetical order. 4. 1 Axiom Axiom [JS92] like its predecessor Scratchpad II [WJST90, SJ87] is an abstract data type language with parameterized modules (domains and packages) and module interfaces (categories) Domains are implementations of categories. Packages are domains that simply package functions and, therefore, do not have a representation type. Both domains and ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II type system: Domains and subdomains. In Alfonso M. Miola, editor, Computing Tools for Scientific Problem Solving, pages 63--82. Academic Press, London, Great Britain, 1990. 143

.... is related to types in Russell [10] ML s signatures [17, 18] Haskell s type classes [11] definition modules in Modula 2 [24] interface modules in Modula 3 [7] abstract types in Emerald [4] type modules in Trellis Owl [19] categories in Axiom [15] and its predecessor Scratchpad II [22, 23], and types in POOL I [1] To associate an implementation with a signature type, we introduce the notion of a signature pointer into the language. For an assignment of an object pointer to a signature pointer, the compiler verifies that the class implements all the member functions declared in ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II type system: Domains and subdomains. In Alfonso M. Miola, editor, Computing Tools for Scientific Problem Solving, pages 63--82. Academic Press, London, Great Britain, 1990.

....typed and provides subtyping. Abstract types can have multiple implementations; there is no facility for data abstraction. The main innovation of Emerald is that objects can be moved between machines. To help achieve that full run time type information is provided. 3. 5 Scratchpad II Scratchpad [32, 34], a language designed for computer algebra, allows to write parameterized classes and provides a construct similar to parameterized signatures called category. Semantically, however, a category is not an abstract type containing objects but a higher order type containing class types. In addition, ....

Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II Type System: Domains and Subdomains. Manuscript, Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1987.

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Stephen M. Watt, Richard D. Jenks, Robert S. Sutor and Barry M. Trager, `The Scratchpad II type system: Domains and subdomains', Computing Tools for Scientific Problem Solving, ed., Alfonso M. Miola, pp. 63--82, Academic Press, London, UK, 1990.

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Stephen M. Watt, Richard D. Jenks, Robert S. Sutor, and Barry M. Trager. The Scratchpad II Type System: Domains and Subdomains. Technical report, Computer Algebra Group, Mathematical Sciences Department, IBM Research Division, Thomas J. Watson Research Center, Yorktown Heights, NY, 1988.

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