Scott, D.S., C. Strachey, Toward a mathematical semantics for computer languages, Oxford University Technical Monograph PRG-6, August 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to prove many interesting example equivalences. 5. 1 Locality c : comm newint v in c comm c: This deceptively simple equivalence ( 3, Example 1] is not validated by the traditional models of imperative computation relying on a global store model, traceable back to Scott and Strachey [25]. It re ects the fact that a nonlocally de ned procedure cannot modify a local variable. It was rst proved in the possible worlds model of Reynolds and Oles, constructed using functor categories [4] PROOF. Jc : comm newint v in c : commK Jc : comm; v : var c : commK f ....

D. S. Scott, C. Strachey, Toward a mathematical semantics for computer languages, in: J. Fox (Ed.), Proceedings of the Symposium on Computers and Automata, Vol. 21 of Microwave Research Institute Symposia Series, Polytechnic Institute of Brooklyn Press, New York, 1971, pp. 19-46, also Technical Monograph PRG-6, Oxford University Computing Laboratory, Programming Research Group, Oxford.

....and that every monotone function f : D C# into a flat poset is, trivially, continuous. The lemma holds for monotone mappings # : D D which may be discontinuous, and with the same proof, using now ordinal recursion to define the sequence . 7 The fundamental paper is Scott Strachey [17], which started an extensive development of what is alternatively called the fixed point theory of programs, domain theory or denotational semantics, depending on what one does with it. See [19] for a good, elementary exposition of denotational semantics in the proper context. Part of the ....

D. S. Scott and C. Strachey. Towards a mathematical semantics for computer languages. In J. Fox, editor, Proceedings of the Symposium on computers and automata, pages 19--46, New York, 1971. Polytechnic Institute of Brooklyn Press.

....Scott and Strachey in the late 1960s. Since then, it has been widely studied by distinguished researchers and has been used as a method for the semantic analysis, description, evaluation as well as the implementation of various programming languages. The seminal paper on denotational semantics is [Scot71]. Other introductory papers including useful bibliography are [Tenn76] and [Moss90] Introductory books presenting in more depth the underlying theory and the techniques that have been developed include [Miln76] Stoy77] Gord79] Alli86] and [Schm86] An graduate level book with more ....

....representing monad morphisms. 3.3 Domain theory The theory of domains was established by Scott and Strachey, in order to provide appropriate mathematical spaces on which to define the denotational semantics of programming languages. Introductions of various sizes and levels can be found in [Scot71, Scot82, Gunt90, Gunt92]. Various kinds of domains are commonly used in denotational semantics, the majority of them based on complete partial orders (cpo s) The variation used in this thesis is one of the possible options. 3.3.1 Preliminaries Definition 3.22. A partial order, or poset, is a set D together with a ....

D. Scott and C. Strachey, "Towards a Mathematical Semantics for Computer Languages", in Proceedings of the Symposium on Computers and Automata, pp. 19--46, Brooklyn, NY, 1971, Polytechnic Press.

....example octal, decimal, roman, but in each case we are really concerned with what is denoted (a natural number) and not how the natural number is represented. The first examples of denotational specifications of program fragments were worked out by Scott and Strachey; see [Sco70b] Sco70a] and [SS71]. In pursuing the notion of mathematical models of programming languages, the question of what constitutes such a model of the calculus arose. The calculus allows syntactic expressions (which represent functions) to be applied to themselves. It was clear that a mathematical model should ....

D.S. Scott and C. Strachey. Towards a mathematical semantics for computer languages. Technical Report 6, Programming Research Group, Oxford University Computing Laboratory, 1971.

.... also possible to derive an SOS semantics from an axiomatic one, as witnessed by the developments in [8, 132] Axiomatic semantics and proof systems for programming and specification languages are often closely related to denotational semantics for them, particularly if the Scott Strachey approach [198] is followed. A paradigmatic example of the development of a semantic theory of processes in which operational, axiomatic, and denotational semantics coexist harmoniously, and may be used to highlight different aspects of process behaviours, is the theory of testing equivalence developed by De ....

....each other when restricted to the part of their behaviour that is fully specified. A divergent state s with no outgoing transition intuitively corresponds to a process whose behaviour is totally unspecified essentially an operational version of the bottom element in Scott s theory of domains [176, 198, 211]. The following precongruence result for . with respect to recursive GSOS languages including the inert constant Omega originates from [11, 12] Proposition 7.3 . is a precongruence with respect to the LTS with divergence over CREC( Sigma) associated with a recursive GSOS language including ....

D. Scott and C. Strachey, Towards a mathematical semantics for computer languages, in Proceedings Symposium on Computers and Automata, vol. 21 of Microwave Research Institute Symposia Series, 1971.

.... logic seems useful in many areas, including the foundations of mathematics (e.g. type theory [111] extracting programs from correctness proofs of algorithms, describing proof strategies (as in LCF tactics [89] modeling traditional programming languages (as in Scott Strachey semantics [139]) and studying the foundations of the programming process. One important advantage of higher order programming over traditional imperative programming is its capability for structuring programs (see [94] for some cogent arguments and examples) However, a language with sufficiently powerful ....

Dana Scott and Christopher Strachey. Towards a mathematical semantics for computer languages. In Proceedings, 21st Symposium on Computers and Automata, pages 19--46. Polytechnic Institute of Brooklyn, 1971. Also Programming Research Group Technical Monograph PRG--6, Oxford.

....and has had major impact on the other models and upon practical specification systems. That is the technique of denotational semantics developed by Scott 2Not to be confused with the Vienna Development Method or VDM to be described later. Figure 4: Vienna Definition Language Model and Strachey (Scott, 1971). In this case, similar to the functional model of Mills, we view a program as function from one domain to another. A fundamental idea is that we view memory as simply a function from a set of identifiers to a set of values. Thus the state of a computation at any time is simply a function mi ....

Scott D. and Strachey C., Towards a mathematical semantics for computer languages, In Symp. Computers and Automata, pages 19-46. Polytechnic Inst. of Brooklyn.

....a source language has loops or (function) procedures, then term rewriting or copy rule semantics is employed throughout [42, 45] Other operational styles split in natural [55] or structural [58] operational or state machinelike [32, 33] Denotational semantics has started with D. Scott s work [65, 64], and typical compiling correctness proofs can be found in [47] The authors in [37, 63, 50, 51] use an algebraic denotational style for clearer modular proofs, based on state transformations resp. predicate transformers. Mechanical proofs are often based on interpreter semantics, a further ....

D. Scott and Ch. Strachey. Toward a mathematical semantics for computer languages. pages 19-46. April 1971.

....reverse engineering techniques have been developed to extract the information directly from the source code. Textual Analysis, Lexical Analysis, Syntactic Analysis, Control Flow Analysis, Data Flow Analysis, Program Dependence Graph [3] Slicing [13] Clich Recognition, Abstract Interpretation [12], Dynamic Analysis [10] Partial Evaluation [8] and Static and Dynamic Feature Analysis [1] are some examples of such posterior techniques. Posterior techniques are difficult to apply; time consuming and costly while writing down and representing understanding information at the time of ....

Scott, D. S. & C. Strachey (1971). Towards a Mathematical Semantics for Computer Languages. Computers and Automata. Polytechnic Institute of Brooklyn Press, pp. 19-46.

....loops or (function) procedures, then term rewriting or copy rule semantics is employed throughout [Lan73, LS87] Other operational styles split in natural [NN92] or structural [Plo81] operational or state machine like [Gur91, Gur95] Denotational semantics has started with D. Scott s work [Sco70, SS71] and typical compiling correctness proofs can be found in [MS76] The authors in [HJS93, Sam93, MO97, MOW00] use an algebraic denotational style for clearer modular proofs, based on state transformations resp. predicate transformers. Mechanical proofs are often based on interpreter semantics, a ....

D. Scott and Ch. Strachey. Toward a mathematical semantics for computer languages. pages 19-46. April 1971.

....is another innovation associated with VDM. In the Logic of Partial Functions, each type is extended with an extra value that denotes nontermination. Similar approaches to describing nonterminating behaviour had been tried before, most notably by Scott with his Logic of Computable Functions [SS71] However, Scott s approach was somewhat different. While the Logic of Partial Functions is a true three valued logic, The Logic of Computable Functions could be more accurately described as a two valued logic for reasoning about three valued terms. VDM was the first application of three valued ....

....More recently, logics in which every type not just the booleans is extended with an additional value have been developed for reasoning about partial functions. The most 55 well known of these are Jones s Logic of Partial Functions [BCJ84] and Scott s Logic of Computable Functions [SS71] Scott s logic could perhaps be more accurately described as a two valued logic for reasoning about types extended with an extra element. This section introduces a three valued logic for reasoning about programs only the boolean type is extended with a distinguished value. The three valued ....

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Dana S. Scott and Christopher Strachey. Towards a mathematical semantics for computer languages. In Jerome Fox, editor, Proceeding of the Symposium on Computers and Automata, volume 21 of Microwave Research Institute Symposia Series, pages 19--46, Brooklyn, United States, 1971. Polytechnic University, Microwave Research Institute, Wiley-Interscience.

....versus Goto Unlike earlier languages, Algol 60 included both lexically nested procedures (blocks) and unconditional jumps (gotos) The combination of these two constructs posed a challenge to both semanticists and implementors alike. On one hand, the contemporary mathematical theory of semantics [89, 90] could not accommodate imperative facilities such as gotos. On the other hand, the ability to jump outside of blocks (and hence jump to new lexical scopes) complicated the implementation of procedures and the representation of labels. In an attempt to solve the above problems, two lines of ....

....explicitly enables both an implementation of procedure calls as jumps and a stack based implementation strategy of languages with higher order procedures. 2.1. 2 Goto as Procedure Call The idea of defining the semantics of programming languages mathematically was proposed by Scott and Strachey [89, 90, 100]. Intuitively, the goal of the approach is to use well established mathematical concepts, e.g. functions, lattices, etc, in order to describe the semantics of programming languages. In the absence of gotos and blocks, the semantics of an Algol like language is defined by mapping each statement S ....

Scott, D. and Strachey, C. Toward a mathematical semantics for computer languages. In Proceedings of the Symposium on Computers and Automata (1971). Also Technical Monograph PRG-6, Oxford University, Computing Laboratory, Programming Research Group.

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Scott, D.S., C. Strachey, Toward a mathematical semantics for computer languages, Oxford University Technical Monograph PRG-6, August 1971.

....we just want to remind the reader what we are unifying. We will go a little more into details with the metric approaches to semantics, since these are less well known than the partial order based ones. 2. 1 Pre orders for semantics The Scott approach It has been customary since [Scott 70a] and [Scott Strachey 71] to model the domain of possible outcomes of a function computed by some algorithm, with a pre order (or more precisely with a partial order) Consider for example a function f which is supposed to output a Boolean. If we have called f , but not yet gotten an answer we are in a state of having no ....

Scott, D.S., C. Strachey, Toward a mathematical semantics for computer languages, Oxford University Technical Monograph PRG-6, August 1971.

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D. Scott and C. Strachey. Towards a mathematical semantics for computer languages. In Proceedings Symposium Computers and Automata, May 1971.

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D. Scott and C. Strachey. Towards a mathematical semantics for computer languages. In J. Fox, editor, Proc. Symp. Computers and Automata, pages 19--46. Wiley, New York, 1972.

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SCOTT, D., AND STRACHEY, C. Towards a mathematical semantics for computer languages. In Computers and Automata. Wiley, 1971, pp. 19--46.

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D. S. Scott and C. Strachey. Toward a mathematical semantics for computer languages. In J. Fox, editor, Proceedings of the Symposium on Computers and Automata, New York, 1971. Polytechnic Institute of Brooklyn Press.

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D. S. Scott and C. Strachey. Towards a mathematical semantics for computer languages. In Proc. Symposium on Computers and Automata, Microwave Research Institute Symposia Series, vol. 21, 1971.

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Dana S. Scott and Christopher Strachey. Towards a mathematical semantics for computer languages. In Proceedings, 21st Symposium on Computers and Automata, pages 19--46. Polytechnic Institute of Brooklyn, 1971. Also, Programming Research Group Technical Monograph PRG--6, Oxford University.

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D. S. Scott and C. Strachey. Toward a mathematical semantics for computer languages. In J. Fox, editor, Proceedings of the Symposium on Compute= rs and Automata, New York, 1971. Polytechnic Institute of Brooklyn Press.

No context found.

D. S. Scott and C. Strachey. Towards a mathematical semantics for computer languages. In Proc. Symposium on Computers and Automata, Microwave Research Institute Symposia Series, vol. 21, 1971.

No context found.

Scott, D. and Strachey, C., Towards a mathematical semantics for computer languages, Proceeding of 21st Symposium on Computers and Automata, 19--46, Polytechnic Institute of Brooklyn, 1971.

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Scott, D. S. and Strachey, C. Towards a Mathematical Semantics for Computer Languages. Computers and Automata. Polytechnic Institute of Brooklyn Press, pp. 19-46, 1971.

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D. Scott and C. Strachey. Towards a mathematical semantics for computer languages. Technical Report PRC6, Oxford Univ., 1971.

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