Albert Meyer. Semantical paradigms: notes for an invited lecture. In Proceedings of the Third Annual IEEE Symposium on Logic in Computer Science, pages 236--253, July 1988. With two appendices by Stavros S. Cosmadakis.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....operations in the language up to some notion of behavioural equivalence. Since most languages that have been proposed in the literature are completely expressive in the first sense, this criterion does not offer a useful means to classify the expressiveness of languages. This is what Meyer [149] calls the Turing tarpit . The remaining two criteria have been investigated by De Simone in op. cit. and, since then, by several other authors. Indeed, this kind of expressiveness results has, to the best of our knowledge, only been developed for De Simone languages, and similar investigations ....

....use of the complementary benefits afforded by these semantic descriptions in establishing properties of processes. However, developing these three views of processes for each process description language from scratch and proving their coincidence is hard, subtle work; in addition, to quote from [149], giving denotational semantics to programming languages using the Scott Strachey approach involves an armamentarium of mathematical weapons otherwise unfamiliar in Computer Science . It would therefore be beneficial to develop systematic ways of giving denotational semantics to process ....

A. Meyer, Semantical paradigms: notes for an invited lecture, in Proceedings 3rd Symposium on Logic in Computer Science, Edinburgh, IEEE Computer Society Press, 1988, pp. 236--242.

....of classes with this property is described as being compositional . Another desirable property of a semantics of classes is that the denotation of any class is only as detailed as necessary for the semantics to be compositional. A semantics with this property is described as being fully abstract [Plo77, Sto88, MeC88]. Intuitively, the denotation of a class in a fully abstract semantics contains no unnecessary implementational details and, therefore, describes only the external behaviour of its objects. Consequently, only objects of classes with equal denotations in such a semantics will be behaviourally ....

....a semantics T which denotes a class by the set of traces its objects can undergo, a semantics D is fully abstract with respect to T if, for any context C , the following holds. Yelland s understanding of full abstraction is similar to that of Stoughton [Sto88] which, as pointed out by Meyer in [MeC88], is actually equivalent to compositionality. Stoughton s notion of contextual full abstraction is equivalent to the definition of full abstraction adopted in this paper. This approach can be used to show that a model of classes in Object Z is fully abstract. Adopting the definition of Event from ....

Meyer, A. and Cosmadakis, S.: Semanticalparadigms: Notes for an invited lecture. In Proceedings 3rd IEEE Symposium on Logic in Computer Science, pages 236-- 253, 1988.

....in [Plo85] FPC was considered as a programming language with a call by value operational semantics and a denotational semantics in pCpo (the category of cpos and partial continuous functions) and a computational soundness and adequacy result was proved. Related results can be found in [ML83, MC88] In [Fio94a] the author gave an axiomatic version of Plotkin s proof for an axiomatisation of absolute non trivial domain theoretic models of FPC. From 2 this result it follows that not only the standard model pCpo provides a computationally sound and adequate interpretation for FPC but so ....

A.R. Meyer and S.S. Cosmadakis. Semantical paradigms: Notes for an invited lecture. In 3 rd Press, 1988.

....these attitudes have suggested fruitful lines of research. Yet others point out that the semantics still serves its purposes fairly well, for example in proving the safety of evaluation schemes. At any rate, full abstraction is one of the main criteria in assessing programming language semantics [4]. A similar situation commonly arises in the semantics of type systems. In its simplest form, a semantics for a type system maps each type expression to a reasonable subset of the domain of values. Let us call these subsets types. In most A preliminary version of this paper was presented at the ....

....similar requirements implicit in the rest of the paper. Other notions of observation are also justifiable; for instance, we might care about the set of contexts C such that [ C[e] is a boolean value. Fortunately, many reasonable kinds of observation are equivalent to the one we choose (see [4] for an informal discussion of this point) Thus, full abstraction requires that, for all e and e , whenever [ C[e] if and only if [ C[e ] for all contexts C, it must also be the case that [ e] e ] An interesting refinement of this definition allows the ordering relation v to ....

[Article contains additional citation context not shown here]

Albert Meyer. Semantical paradigms: notes for an invited lecture. In Proceedings of the Third Annual IEEE Symposium on Logic in Computer Science, pages 236--253, July 1988. With two appendices by Stavros S. Cosmadakis.

....use of the complementary benefits afforded by these semantic descriptions in establishing properties of processes. However, developing these three views of processes for each process description language from scratch and proving their coincidence is hard, subtle work; in addition, to quote from [54], giving denotational semantics to programming languages using the Scott Strachey approach involves an armamentarium of mathematical weapons otherwise unfamiliar in Computer Science . We thus believe that it would be beneficial to develop systematic ways of giving denotational semantics to ....

A. Meyer, Semantical paradigms: Notes for an invited lecture, in Third Annual Symposium on Logic in Computer Science Edinburgh, IEEE Computer Society Press,

....criterion to judge the appropriateness of denotational models for programming and specification languages is that they be in agreement with operational intuition about program behaviour. Of the good fit criteria for such models that have been discussed in the literature (cf. e.g. the reference [19] for a discussion) the most desirable one is that of full abstraction. Intuitively, a denotational model for a programming or specification language is fully abstract with respect to a notion of operationally based (or behavioural) equivalence or preorder iff it is in complete agreement with it. ....

A. Meyer, Semantical paradigms: Notes for an invited lecture, in Proceedings 3 Annual Symposium on Logic in Computer Science, Edinburgh, IEEE Computer Society Press, 1988, pp. 236--242.

....defined by a signature together with a set of structured rules. The operational semantics are given as a labeled transition system on the set of closed terms. It is difficult to define structured operational rule in sufficient generality to cover all the ways used in the literature (e.g. [Blo88a, Mey88, Plo81, Bar81] as well as many places in concurrency theory) and simultaneously avoid pathologies in particular cases. The results in this thesis, among other work, show that the properties of a system defined by structured rules can be quite sensitive to the form of the rules. In general, though, a structured ....

Albert R. Meyer. Semantical paradigms: Notes for an invited lecture, with two appendices by Stavros Cosmadakis. In Third Annual Symposium on Logic in Computer Science [IEE88], pages 236--253.

.... d = Lemma 7 If c : s is a derivable judgement of PCF and c is a canonical form, then [ c : s] 6= Most of the rest of this section is devoted to a proof of a kind of converse to the Soundness Theorem which we will call computational adequacy (the term is suggested by Albert Meyer [Mey88], although his definition includes soundness) For PCF , it can be stated as follows: Theorem 8 (Computational Adequacy. Suppose e : s is derivable in PCF . If [ e : s] 6= then e c for some canonical form c. We focus on explaining how the methods that one uses for results such as ....

A. R. Meyer. Semantical paradigms: notes for an invited lecture. In Y. Gurevich, editor, Logic in Computer Science, pages 236--253, IEEE Computer Society, July 1988.

....0 ae; oe) Finally, we conclude (21) as required, because the relation l is transitive. 2 Clearly, operational equivalence is also the largest adequate congruence on static terms. It follows that it coincides with Morris style contextual equivalence, sometimes known as observational congruence (Meyer and Cosmadakis 1988), where we take convergence of programs as our means of observation. Instead of the usual definition of contextual equivalence in terms of variable 54 capturing contexts, one can equivalently define it as the relation between static terms which are related by a compatible and adequate relation; ....

Meyer, A. R. and S. S. Cosmadakis (1988, July). Semantical paradigms: Notes for an invited lecture. In Proceedings of the 3rd IEEE Symposium on Logic in Computer Science, pp. 236--253.

....believe that if Lemma 7.11 generalises to arbitrary cartesian V, the formal approximation relations can be extracted. It seems that so straightforward an adequacy theorem would not be available if one instead axiomatised Cppo (the category of small pointed cpos and continuous functions) see [MC88]. The essential difficulty is that the least element does not correspond to non termination at higher types. Again, although pCpo is equivalent to Cppo they are conceptually different. The first seems computationally more natural, fitting with standard formulations of recursion theory that ....

A.R. Meyer and S.S. Cosmadakis. Semantical paradigms: Notes for an invited lecture. In 3 rd LICS Conf., pages 236--253. IEEE, Computer Society Press, 1988.

....the model as a guide, we develop a sound logic for the language. 1 Introduction The denotational semantics most appropriate for a programming language depends crucially upon the observations one makes about computations. In general, an observation is some important behavior of the interpreter [8]. For example, in the arithmetic, higher order programming language PCF [11, 13] one usually chooses to observe the results of arithmetic expressions that a term of integer type reduces to a numeral. One may also extend the notion of observation to arbitrary terms, saying that two terms are ....

....will proceed no further (e.g. LISP [15] If we observe termination at higher type, A V fails to be adequate since the meanings of the two terms above are both . To regain adequacy, one could change the interpreter to reduce inside abstractions; Wadsworth [16] and Cosmadakis and Meyer [4, 8] give examples of such interpreters. We take the opposite approach and try to build a model that reflects the behavior of the interpreter. We are willing to add new constants to PCF, as long as we do so conservatively; the interpreter s behavior should not change on terms without the new ....

[Article contains additional citation context not shown here]

A. R. Meyer. Semantical paradigms: notes for an invited lecture, with two appendices by Stavros Cosmadakis. In 3 rd Symp. Logic in Computer Science, pages 236--255, IEEE, 1988.

....free term variables, we write [ M] h as shorthand for [ 0 M : s] h. The model is adequate: Theorem 5.1 For any closed PCF poly rec 1 term M of type num, M n iff [ M] n. The proof uses the Girard Tait method of reducibility following Amadio s proof in [6] and Cosmadakis proof in [21] (see also [34] We include a sketch of the proof in Appendix B. 5.3 Syntactic representation of pre ep pairs and functors The ep pairs and functors of the semantics can be encoded in PCF poly rec 1. Given type expressions s and s 0 , a pair of closed terms t : s s 0 and t 0 : s 0 ....

A. R. Meyer. Semantical paradigms: Notes for an invited lecture, with two appendices by Stavros S. Cosmadakis. In Proceedings, Third Annual Symposium on Logic in Computer Science, pages 236--255. IEEE, 1988.

....1992 ] The first gives an exposition of the state of the art up to Berry and Curien s work on sequential algorithms. The second, based on an invited talk given at the 1991 Durham Symposium, complements the first and brings it more or less up to date. A short paper of Meyer and Cosmadakis [ Meyer and Cosmadakis, 1988 ] gives a highly readable introduction to full abstraction problems in general. An excellent book length treatment of most of the material surveyed in this chapter is the second edition of Curien s book [ Curien, 1993a ] Stoughton s book [ Stoughton, 1988 ] presents a language independent theory ....

....1) to contexts of type (1) 2) or (3) as the case may be, we infer that D[N ] V . But D[N ] j MC 1 [N ] Delta Delta Delta Cm [N ] by condition (C) so we have NC 1 [N ] Delta Delta Delta Cm [N ] j C[N ] V . Meyer refers to the Context Lemma as the Operational Extensionality Theorem [ Meyer and Cosmadakis, 1988 ] The gist of the Context Lemma 304 C. H. L. Ong is this: terms of the language pcf are determined by their applicative behaviour. Hence, it is quite appropriate to call pcf an applicative or functional programming language. The proof we have presented is due to Berry [ Berry, 1979 ] Milner ....

A. R. Meyer and S. C. Cosmadakis. Semantical paradigms: notes for an invited lecture. In Proc. 3rd Annual IEEE Symp. Logic in Computer Science. Computer Society Press, 1988.

....executable and observable are designated as programs, and their behaviour is defined; ii) Two arbitrary terms are defined to be equivalent iff they have the same behaviour in every program context. The resulting notion of program equivalence is usually referred to as observational congruence [Mey88]. Observational congruence for the first order object calculus with subtyping Ob 1 : has been defined in [GR96] thus: Two programs are observationally congruent iff they have the same termination behaviour in all contexts of type boolean. Following earlier work on functional languages, in op. ....

....A 0 . b A ff b 0 A 0 a 0 A 0 b 0 A 0 ) and (ii) b A ff b 0 A 0 ) 9 a 0 A 0 . a A ff a 0 A 0 a 0 A 0 b 0 A 0 ) If aA b A we say that aA and b A are bisimilar. A natural notion of equivalence for the object calculus is that of observational congruence [Mey88] where two terms are considered equivalent if they Aceto, H uttel, Ing olfsd ottir and Kleist (Eq Object) where A j [l i :B i i2I ] Gamma; x i :A b i b 0 i : B i 8i 2 I Gamma [l i = x i :A)b i i2I ] l i = x i :A)b 0 i i2I ] A (Eq Select) Gamma a b : l i :B i ....

[Article contains additional citation context not shown here]

A.R. Meyer. Semantical paradigms: Notes for an invited lecture. In Proceedings 3 th Annual Symposium on Logic in Computer Science, Edinburgh, pages 236--242. IEEE Computer Society Press, 1988.

....we sometimes briefly say that we choose a new location and leave it to the reader to spell out precisely what is meant by new in a particular case. 6 Computational Adequacy In this section we will show that our denotational semantics is computationally adequate. Computational adequacy means [12] that the observable behavior beh(P ) of a program P can be (easily) derived from its denotational meaning [ P ] Concretely, we will show that for every n 2 Z n 2 beh(P ) P ] s init = n where s init is the constant 0 store, i.e. the (unique) store in Stores ; This implies that beh(P ) ....

Albert R. Meyer. Semantical paradigms: Notes for an invited lecture, with two appendices by Stavros Cosmadakis. In Proc. 3 rd IEEE Symp. on Logic in Computer Science, pages 236--253, Edinburgh, 1988.

....N , if, for any context C[ Delta] such that C[M ] and C[N ] are complete programs, C[M ] i v c l implies C[N ] i v c l . Two terms M and N are observationally congruent, written M j v obs N , if M v N and N v M . Observational congruences can be difficult to prove using only the definition [12]. For example, consider the terms N 1 = x Pi(y Piy) c 3 and N 2 = x Pic 3 . If N 1 is applied to an 2 Using this rationale, variables might also be considered values, if it were not for the fact that variables may be replaced by terms that require further evaluation. For example, f gets ....

....a simple typable context using only numerals distinguishes their transforms. 1 Other techniques exist for verifying congruences: one may rely upon either an adequate or fully abstract denotational semantics or upon an equational system sound for j v obs yet strong enough to prove the congruence [12, 20]. Either method rests upon a nontrivial adequacy or soundness proof. Plotkin [18] claims both methods can be used to prove M1 j v obs M2 , using either pre domains [22] or Moggi s p [16] but I have not worked through the proofs of adequacy of the pre domain semantics or soundness of p for j v ....

Albert R. Meyer. Semantical paradigms: notes for an invited lecture, with two appendices by Stavros Cosmadakis. In 3 rd Symp. Logic in Computer Science, pages 236--255, IEEE, 1988.

....to the concerned variables, thus greatly simplifying the conception of distributed cc programming languages (cf. SKL90] 1. 2 Comparison with related work The notion that lattice models of the calculus have something to do with concurrency is part of the folklore of domain theory (see, e.g. [Mey88], Blo90] However, to our knowledge the appropriate notions of concurrent computation has not been worked out in such detail before, and the notion of join as fair parallel composition, and agents as information transducers, not been exposed before. This work is most closely related to [AO89] ....

Albert Meyer. Semantical paradigms: Notes for an invited lecture. In IEEE LICS, pages 236--253, 1988.

....and Information, Stanford University. of research. Yet others point out that the semantics still serves its purposes fairly well, for example in proving the safety of evaluation schemes. At any rate, full abstraction is one of the main criteria in assessing programminglanguage semantics [Mey88]. A similar situation commonly arises in the semantics of type systems. In its simplest form, a semantics for a type system maps each type expression to a reasonable subset of the domain of values. Let us call these subsets types. In most semantics, some programs that behave identically in all ....

....leave similar requirements implicit in the rest of the paper. Other notions of observation are also justifiable; for instance, we might care about the set of contexts C such that [ C[e] is a boolean value. Fortunately, many reasonable kinds of observation are equivalent to the one we choose (see [Mey88] for an informal discussion of this point) Thus, full abstraction requires that, for all e and e , whenever [ C[e] if and only if [ C[e ] for all contexts C, it must also be the case that [ e] e ] An interesting refinement of this definition allows the ordering relation v to ....

[Article contains additional citation context not shown here]

Albert Meyer. Semantical paradigms: notes for an invited lecture. In Proceedings of the Third Annual IEEE Symposium on Logic in Computer Science, pages 236--253, July 1988. With two appendices by Stavros S. Cosmadakis.

....to be considered equivalent if they can be interchanged in any context without affecting the visible results of the computation. More precisely: two modules P and Q are observationally congruent (P j obs Q) iff for every context C[ Delta] C[P ] and C[Q] exhibit the same observational behaviour [68]. Needless to say, reasoning about programs (and their computational equivalence) in terms of their denotation will be worthwhile only when the notion of semantic equivalence is a good approximation of the relation of computational equivalence. These intuitive arguments can be formalized as ....

....reasoning about programs (and their computational equivalence) in terms of their denotation will be worthwhile only when the notion of semantic equivalence is a good approximation of the relation of computational equivalence. These intuitive arguments can be formalized as suggested in [39] and [68], in terms of the two notions of compositionality and full abstraction. Compositionality ensures that two semantically equivalent programs are also observationally equivalent; full abstraction guarantees that any distinction made at the semantic level has also an observational counterpart. ....

[Article contains additional citation context not shown here]

A. Meyer. Semantical Paradigms: Notes for an Invited Lecture. In Proceedings 3rd Annual Symposium on Logic in Computer Science, pages 236--242. IEEE Computer Society, 1988.

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Albert Meyer. Semantical paradigms: notes for an invited lecture. In Proceedings of the Third Annual IEEE Symposium on Logic in Computer Science, pages 236--253, July 1988. With two appendices by Stavros S. Cosmadakis.

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A. Meyer and S. Cosmadakis. Semantical paradigms: Notes for an invited lecture. In Proceedings 3rd IEEE Symposium on Logic in Comp. Science, pages 236--253, 1988.

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A. R. Meyer and S. S. Cosmadakis, Semantical Paradigms: Notes for an Invited Lecture. Proceedings of the Third Annual Symposium on Logic in Computer Science, 1988. pp. 236-253.

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--298. Meyer, A. and S. Cosmadakis (1988). Semantical paradigms: Notes for an invited lecture. In Proceedings LICS'88, pp. 236--253. Meyer, A. and K. Sieber (1988). Towards fully abstract semantics for local variables. In Proceedings POPL'88, pp. 236--253.

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A. R. Meyer and S. S. Cosmadakis, Semantical Paradigms: Notes for an Invited Lecture. Proceedings of the Third Annual Symposium on Logic in Computer Science, 1988. pp. 236-253.

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Meyer, A. R. (1988). Semantical paradigms: Notes for an invited lecture, with two appendices by Stavros S.

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