R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proc. POPL, pages 328--342. ACM Press, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....simply typed calculus with constants, and SPCF. Fully abstract models of both of these languages have been described before (Padovani [7] has given a syntactic construction of the minimal model , whilst SPCF has been modelled using observably sequential functions by Cartwright and Felleisen [2], and sequential algorithms (with Curien) 3] However, the bistable model is simpler, and can be straightforwardly extended with recursive types, for instance, or used in a call by value setting. More importantly, it represents a link between the intensional notion of sequentiality represented ....

....Suppose a b. Let X = fhf(b) g(a)i j f 2 F g 2 G f gg. Then 1 (X) ff(b) j f 2 Fg and 2 (X) fg(a) j g 2 Gg and hence by property (ii) hf;gi2X (f(b) g(a) f2F f(b) g2G g(a) 4. 1 Full abstraction for SPCF We shall now show that a bistable bicpo model of SPCF [2] (that is, PCF with a catch operator) with a single error i.e. is fully abstract, using our result for the model of . SPCF can also be viewed as an extension of with an additional ground type, nat (with a constant 0 and combinators succ; pred : 0 ) 0) recursion combinators Y : ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proceedings of POPL '92, 1992.

....with some abstract structure, e.g. the notion of a strict monad over DCPO de ned in [36] Call by value monads are, however, de ned over call by value models, not over categories. There is a good reason for this: constructing categories suitable for sequential languages like VPCF (see, e.g. [3, 4, 6]) has been open for many years (although recent announcements [2, 15, 26] suggest that a categorical framework can be constructed) Moreover, by de ning call by value monads over models, we can state and prove our results independent of the details of the construction of any particular model. ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Conference Record of the Nineteenth Annual ACM Symposium on Principles of Programming Languages, pages 328-342. ACM, 1992.

.... model based on strongly stable functions [BE91] The fourth is the Berry Curien model based on sequential algorithms [BC82] Of these, we can say that the standard Cartwright and Felleisen s model without error values turns out to be equivalent to the sequential algorithms model [CF92, Cur92a]. The main result in [CF92, Cur92a] is that the sequential algorithms model with errors is fully abstract for SPCF, an extension of PCF with a catch construct and errors. This is a ne result, but SPCF has a rather di erent avour to model gives a good account of functional computation at higher ....

.... stable functions [BE91] The fourth is the Berry Curien model based on sequential algorithms [BC82] Of these, we can say that the standard Cartwright and Felleisen s model without error values turns out to be equivalent to the sequential algorithms model [CF92, Cur92a] The main result in [CF92, Cur92a] is that the sequential algorithms model with errors is fully abstract for SPCF, an extension of PCF with a catch construct and errors. This is a ne result, but SPCF has a rather di erent avour to model gives a good account of functional computation at higher types, but fails to capture ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proc. POPL, pages 328-342. ACM Press, 1992.

.... extension of the simply typed calculus; if we add local control operators (If : then : else) and non local control operators (such as callcc, or any of a variety of equivalent forms) the result is (a nitary version of) a prototypical functional programming language, called SPCF in [9]. A semantic characterisation of observational equivalence in SPCF has been described, initially by Cartwright and Felleisen using observably sequential functions , and then by Cartwright, Curien and Felleisen using sequential algorithms [10] Although no connection appears to have been made ....

....and each one except for PCF has an e ectively presentable fully abstract semantics obtainable by collapsing the games model under its intrinsic preorder. 1. 2 Observably sequential functions and Sequential Algorithms Observably sequential functions were proposed by Cartwright and Felleisen [9] as an alternative notion of sequential functional, based on the fact that adding untrappable errors to a functional language radically changes its observational equivalence. Errors allow observable distinctions to be made between terms which are extensionally equivalent in PCF (for instance, ....

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R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. Technical Report 91 - 167, Rice University Department of Computer Science, 1991.

....obtain observational equivalence by enriching calculus with a simple non deterministic operator (in place of constants) Corollary 6.6. 22 suggests an analogy with the full abstraction result for PCF using error generator and escape handlers recently studied by Cartwright, Felleisen and Curien [CF92,Cur92]. Intuitively, in both cases the symbols or operators with which the calculus is enriched are used to explore the internal structure of terms. We leave for future investigations whether this analogy can be made deeper. Chapter 7 Conclusions and Future Work In this thesis we have investigated ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proc. POPL 92, pages 328--342. Association for Computing Machinery, 1992.

....some abstract structure, e.g. the notion of a strict monad over DCPO defined in [36] Call by value monads are, however, defined over call by value models, not over categories. There is a good reason for this: constructing categories suitable for sequential languages like VPCF (see, e.g. [3, 4, 6]) has been open for many years (although recent announcements [2, 15, 26] suggest that a categorical framework can be constructed) Moreover, by defining call by value monads over models, we can state and prove our results independent of the details of the construction of any particular model. ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Conference Record of the Nineteenth Annual ACM Symposium on Principles of Programming Languages, pages 328--342. ACM, 1992.

....simple reason is that the ordering in question is not the extensional ordering but rather the stable ordering. In the case of the model associated with sequential algorithms, the morphisms are not even functions 4 . Recently, drawing on their intuitions as programmers, Cartwright and Felleisen [ Cartwright and Felleisen, 1992; Cartwright et al. 1994 ] introduced a continuous, order extensional model for pcf which is based on what they call observably sequential functions. Curien [ Curien, 1992 ] immediately realized that the observably sequential functions were a natural extensional refinement of sequential ....

....by an appropriate higher type procedure definable in CDS. The main result of this work is that the model based on sequential algorithms is fully abstract for CDS. 4. 4 Observable algorithms and pcf with error values Recently, drawing on their intuitions as programmers, Cartwright and Felleisen [ Cartwright and Felleisen, 1992 ] invented the observably sequential functions to construct a fully abstract denotational semantics for a sequential extension of pcf which they call spcf. Curien [ Curien, 1992 ] immediately realized that the observably sequential functions were a natural extensional refinement of sequential ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction (preliminary version). In Proc. 19th ACM Symp. Principles of Programming Languages, pages 328--342. ACM Press, 1992.

.... for sequential languages such as PCF [Plo77, BCL85] The known constructions of fully abstract models for PCF [Mil77, Ber78, Mul87] are not natural, yet there are natural fully abstract models for an extension of PCF with parallel facilities [Plo77] and, more recently, with control facilities [CF92, Cur92] There is currently no definition of sequential functions suitable for defining a natural extensional semantic model for PCF. The first definitions of sequential functions, given by Milner [Mil77] and Vuillemin [Vui73] were limited to functions on products of flat domains. Kahn and ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Nineteenth Annual ACM Symposium on Principles of Programming Languages, pages 328--342. ACM Press, January 1992.

....3 that are excluded from all practical programming languages. Thus, programming languages using this framework for underlying model of computation, can formulate sequential constructs to make the language complete with respect to the new models. We present a study of one such language SPCF [CF91, CF92] 4 in this thesis. We also show how our reformulation of domain theory facilitates the invention of new constructs to make the languages more expressive. Aside from these fundamental contributions, we develop new techniques to describe domains. We also develop techniques to show full ....

....category of OS domains with OS functions. The main result of this Chapter is the formation of such a ccc. 3 A boolean function that needs to evaluate both the arguments in parallel to produce the answer. The full description is given in the next chapter. 4 SPCF stands for sequential PCF [CF92] PCF is a language based on simply typed lambda calculus [Plo77] 6 Chapter 5 describes universal domains based on OS domains. These universal domains satisfy the goal of the thesis, namely, providing a satisfactory model of computation where termination properties are not ignored. We show ....

[Article contains additional citation context not shown here]

Robert Cartwright and Matthias Felleisen. Observable sequentiality and full abstraction. In Conference Record of the Nineteenth Annual ACM Symposium on Principles of Programming Languages, pages 328--342, January 1992.

.... Berry s bidomains model based on stable functions [2] and the Bucciarelli Ehrhard model based on strongly stable functions [5] The fourth is the Berry Curien model based on sequential algorithms [3] Cartwright and Felleisen s model turns out to be equivalent to the sequential algorithms model [6, 9]) Of these, we can say that the standard model gives a good account of functional computation at higher types, but fails to capture sequentiality, while the sequential algorithms model gives a good analysis of sequential computation, but fails to capture functional behaviour. In each case, the ....

R. Cartwright and M. Felleisen, Observable Sequentiality and Full Abstraction, Proc. POPL 1992.

.... model based on strongly stable functions [BE91] The fourth is the Berry Curien model based on sequential algorithms [BC82] 1 Of these, we can say that the standard 1 Cartwright and Felleisen s model without error values turns out to be equivalent to the sequential algorithms model [CF92, Cur92a]. The main result in [CF92, Cur92a] is that the sequential algorithm model with errors is fully abstract for SPCF, an extension of PCF with a catch construct and errors. This is a fine result, but SPCF has a rather different flavour to model gives a good account of functional computation at ....

.... stable functions [BE91] The fourth is the Berry Curien model based on sequential algorithms [BC82] 1 Of these, we can say that the standard 1 Cartwright and Felleisen s model without error values turns out to be equivalent to the sequential algorithms model [CF92, Cur92a] The main result in [CF92, Cur92a] is that the sequential algorithm model with errors is fully abstract for SPCF, an extension of PCF with a catch construct and errors. This is a fine result, but SPCF has a rather different flavour to model gives a good account of functional computation at higher types, but fails to capture ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proc. POPL, pages 328--342. ACM Press, 1992.

....such an exception mechanism is a way to modify evaluation in H to formalise the notion of demand for the next character in a stream. Another motivation is to obtain a fully abstract denotational semantics; this is the purpose of Cartwright and Felleisen s recent extension of PCF with exceptions [3]. We consider a language HX obtained from H by adding just one exception, the canonical term bang. Raising an exception is represented by a program evaluating to bang, which is present at every type. For the sake of brevity, we say the program has banged. Program bang bangs. In general, if a ....

Robert Cartwright and Matthias Felleisen. Observable sequentiality and full abstraction. In Proc. of the 19th ACM Symp. on Principles of Programming Languages, pages 328--342, 1992.

....Computations proceed by dialogues of questions and answers composed of filling cells . Cartwright and Felleisen, subsequently built a fully abstract model for SPCF an extension of PCF that remains sequential but includes errors and a simple control operator out of question answer trees [CF92] Curien pointed out that they had defined on a subtly different version of sequential algorithms [Cur92, CCF94] While this result is not for PCF itself, the model is quite interesting in many respects. A fourth approach that is closely related to sequential algorithms is game semantics. ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Conference Record 19th ACM Symposium on Principles of Programming Languages, pages 328--342. ACM, New York, 1992.

....is based on a game in which each play describes the interaction between a functional and its arguments during a computation. This approach is influenced by the work of Kleene [Kle78] Gandy [Gan67] Kahn and Plotkin [KP78] Berry and Curien [BC82, Cur86, Cur92] and Cartwright and Felleisen [CF92]. We characterize the computable elements in this model in two different ways: a) by recursiveness requirements for the game, and (b) as definability with the schemata (S1) S8) S11) which is related to definability in PCF. It turns out that both definitions give the same class of computable ....

.... 1; 1:2 5 O ; 1; 1:1; 3; 1:2; 5 14 P ; 1; 14 14 Hence the value of this play is p[p 1 ; p 2 ] 14. 3 2.4 Decision trees Now we consider another representation of the sequential strategies. In this representation, the form being similar to that used by Cartwright and Felleisen [CF92] for sequential algorithms and by Bucciarelli [Buc93] for Kleene s oracles, only the relevant part of the strategy is shown. For instance if for some strategy p( 1 then in no play there will be a P view starting with ; 2. Hence a value of p on those views is irrelevant. More formally we ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In 19th ACM Symposium on Principles of Programming Languages, pp. 328--342, ACM Press, 1992.

....T n ) F f[ f ( t) P; j t 2 (T 1 ; T n )g and the data type is completely defined. It should be noted that a similar reasoning using furthermore the fact that our programs are only of first order shows, that the semantics is fully abstract in the sense of Definition 2. 1 of [CF92] We noticed already w.r.t. the cbn semantics in Subsection 5.4 that since the reduction semantics is defined as least upper bound of semantic approximations, data terms are possibly only approximated to arbitrary precision, but never actually reached as final results. Obviously this is ....

R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Conference Record of the 19th Annual ACM Symposium on Principles of Programming Languages, POPL, pages 328--342, 1992.

.... Berry s bidomains model based on stable functions [5] and the Bucciarelli Ehrhard model based on strongly stable functions [8] The fourth is the Berry Curien model based on sequential algorithms [6] Cartwright and Felleisen s model turns out to be equivalent to the sequential algorithms model [9, 12]) Of these, we can say that the standard model gives a good account of functional computation at higher types, but fails to capture sequentiality, while the sequential algorithms model gives a good analysis of sequential computation, but fails to capture functional behaviour. In each case, the ....

R. Cartwright and M. Felleisen, Observable Sequentiality and Full Abstraction, Proc. POPL 1992.

....construction by using a more restrictive formulation of functions than the continuous functions. We recently developed a subspace of the continuous functions called the observably sequential functions that encompasses all of the functions definable in practical deterministic programming languages [5, 6, 12]. The observably sequential functions exclude continuous func tions that cannot be evaluated without multiple threads of control. In practice, non sequential functions are unimportant in deterministic computation. We are not aware of any practical deterministic language that can define ....

.... some x oe a, f has a sequentiality index; and error sensitive: if R is the sequentiality index of f for the input a and the output position Q, error Q 1 2 (f(a [ ferror R 1 g) and error Q 2 2 f(a [ ferror R 2 g) Every OS function has a unique evaluation strategy manifest in its graph [5]. If an OS function f has two sequentiality indices R; R 0 for input a and open position Q in f(a) it is easy to show that f is not continuous. 4 Since the sequentiality indices for an OS function f are unique, it makes sense to introduce a function si f , where si f (a; Q) is the ....

Robert Cartwright and Matthias Felleisen. Observable sequentiality and full abstraction. In Conference Record of the Nineteenth Annual ACM Symposium on Principles of Programming Languages, pages 328--342, January 1992.

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R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proc. POPL, pages 328--342. ACM Press, 1992.

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