Honsell, F., Lenisa, M.,\Final Semantics for untyped -calculus", LNCS 902,1995, pp.249-265. 17  Home/Search   Document Not in Database   Summary   Related Articles   Check

....coherence, and strongly stable functions as morphisms. Lambda theories are consistent extensions of the lambda calculus that include fi conversion. They arise by syntactical considerations, a lambda theory may correspond to a possible operational semantics of lambda calculus (see e.g. 2] 3] [23]) as well as by semantic ones, a lambda theory may be the theory of a model of lambda calculus (see e.g. 3] 9] The problem of the completeness incompleteness of a semantics can be stated as follows: are the set of the lambda theories determined by a semantics equal or strictly included within ....

Honsell F. and M. Lenisa, Final semantics for untyped -calculus, LNCS 902, Springer-Verlag, Berlin (1995), 249--265.

....semantics is incomplete. 1. Introduction Lambda theories are consistent extensions of the lambda calculus that are closed under derivation. They arise by syntactical considerations, a lambda theory may correspond to a possible operational (observational) semantics of lambda calculus (see e.g. [2, 3, 24]) as well as by semantic ones, a lambda theory may be the theory of a model of lambda calculus (see e.g. 3, 10] Since the lattice of lambda theories is a very rich and complex structure (see e.g. 3, 10, 24, 25, 49] syntactical techniques are usually difficult to use in the study of lambda ....

.... to a possible operational (observational) semantics of lambda calculus (see e.g. 2, 3, 24] as well as by semantic ones, a lambda theory may be the theory of a model of lambda calculus (see e.g. 3, 10] Since the lattice of lambda theories is a very rich and complex structure (see e.g. [3, 10, 24, 25, 49]) syntactical techniques are usually difficult to use in the study of lambda theories. Therefore, semantic methods have been extensively investigated. Computational motivations and intuitions justify Scott s view of models (see [44, 45] as partially ordered sets (sets of observations or ....

F. Honsell and M. Lenisa, "Final semantics for untyped -calculus", LNCS 902, Springer-Verlag, Berlin (1995), pp. 249-265

....dynamics is the notion of cofree system. In addition to the references mentioned above, work on (final) coalgebraic semantics includes [Tur96] which gives a systematic comparison of final coalgebra and initial algebra semantics for concurrent languages; Rei95] on object oriented programming; [HL95], on a model for the lambda calculus; Len96] on a higher order concurrent language; Jac96a] on behaviour refinement in object oriented programming. The following papers are using non wellfounded sets as the starting point for semantics: Rut92] Acz94] and [FHL94] on processes and ....

F. Honsell and M. Lenisa. Final semantics for untyped -calculus. In M. DezaniCiancaglini and G. Plotkin, editors, Proceedings of the 2nd Conference on Typed Lambda Calculus and Applications, volume 902 of Lecture Notes in Computer Science, pages 249--265. Springer-Verlag, 1995. 52

....Applications of corecursion This paper is not concerned with applications of corecursion or final coalgebra theorems. but there are a number of recent papers on this topic, especially in the area of semantics for features of programming languages. For examples of this, see Honsell and Lenisa [6], Lenisa [7] Rutten [9] and Rutten and Turi [11, 12] Foundations of recursion To get a feeling for the kind of results we are after, consider the following well known results pertaining to recursion: A) Let A be any set, let f : A Theta N A, and let a 2 A. Then there is a unique function ....

Honsell, Furio and Marina Lenisa. 1995. Final Semantics for Untyped -calculus. In M. Dezani and G. Plotkin (eds.) TLCA '95. Springer LNCS 902, Berlin, pp. 249--265.

....path ffl Gamma ffl Gamma ffl Gamma Delta Delta Delta are necessarily mapped to Omega by the corresponding unique decorations. Notice that, besides applications in the semantics of programming languages (eg, Aczel, 1988; Mukai, 1991; Rutten and Turi, 1993; Aczel, 1994; Baldamus, 1994; Honsell and Lenisa, 1995; Hartonas, 1997) non well founded sets have been extensively used in Situation Theory (eg, Barwise and Etchemendy, 1987) where they are better known as hypersets. Correspondingly, models of the universe of non well founded sets are also called hyperuniverses. Foundations of Final ....

Honsell, F. and Lenisa, M. (1995). Final semantics for untyped -calculus. In Dezani-Ciancaglini, M. and Plotkin, G., editors, Typed Lambda calculi and applications: second international conference, volume 902 of LNCS. Springer-Verlag.

....versus observation. It may be found in process theory [50] data type theory [21, 25, 5, 40] including the theory of classes and objects in objectoriented programming [61, 30, 37, 35] semantics of programming languages [46] denotational versus operational [64, 67, 6] and of lambda calculi [58, 59, 20, 31], automata theory [53] system theory [65, 34] natural language theory [10, 62] and many other fields. We assume that the reader is familiar with definitions and proofs by (ordinary) induction. As a typical example, consider for a fixed data set A, the set A = list(A) of finite sequences ....

F. Honsell and M. Lenisa. Final semantics for untyped -calculus. In M. Dezani-Ciancaglini and G. Plotkin, editors, Typed Lambda Calculi and Applications, number 902 in Lect. Notes Comp. Sci., pages 249--265. Springer, Berlin, 1995.

....to the calculus the techniques which have been developed for CCS like languages. In this paper we address the problem of extending to the calculus the final semantics approach originally introduced by Aczel, Rutten and Turi [2, 15, 14] for CCS like languages and further generalized to calculus [8] and higher order concurrent imperative languages [9] The gist of the final semantics paradigm [2] is to view the interpretation function from syntax to semantics as a final mapping in a suitable category. To this end the semantics has to be construed as a terminal coalgebra for a suitable ....

F.Honsell and M.Lenisa. Final semantics for untyped -calculus. In TLCA '95, LNCS 902, Springer, 1995.

....In this paper we show that a syntactical final approach to semantics can be applied successfully to higher order concurrent languages. Such languages are usually modeled by means of recursive domains of metric processes (see e.g. 2] This paper builds on [13] and is a companion to [10], where the final approach is applied to calculus. More specifically, using final syntactical coalgebras, we provide compositional semantics to a particular concurrent language with higher order imperative features, called L pas2 . This language is obtained by adding a parallel operator to the ....

F.Honsell, M.Lenisa, Final Semantics for untyped -calculus, M.Dezani et al. eds, TLCA'95 Springer LNCS Vol.902:249--265, Edinburgh, 1995.

....tools has yet appeared in the literature. Work supported by EC WG Gentzen . Preprint submitted to Elsevier Preprint 22 April This paper can be seen as a further chapter in the general programme of investigating the denotational semantics of calculi, some of whose earlier chapters are [3,8,9,13,10,11]. We feel that also in this case semantical investigations provide very fruitful insights. More specifically, we use semantical techniques for deriving logical tools for reasoning on the observational equivalence, p , induced by any perpetual strategy p . This is the equivalence obtained by ....

....characterization of p . We give a coinductive (applicative) characterization of the observational equivalence p , by showing that, in testing for p , we can restrict ourselves to applicative contexts. This allows us to derive a co induction principle for establishing p in the line of [11]. We discuss various proof methods for establishing this (see e.g. 15,16] We give details only of a semantical proof based on logical relations, which generalizes Pitts technique for lazy strategies. This proof makes use of a mixed induction coinduction principle for establishing p , based ....

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F.Honsell, M.Lenisa, Final Semantics for untyped -calculus, in: M.Dezani et al. eds., TLCA'95 Conference Proceedings, Springer LNCS, 902 (1995) 249--265.

....possible operational (obser vational) semantics of calculus. Although researchers have mainly focused on only three such operational semantics, namely those given by head reduction, head lazy reduction or call by value reduction, the class of theories is, in effect, unfathomly rich, see e.g. [6,14,13,9] for interesting examples of this complexity. Brute force, purely syntactical techniques are usually extremely difficult to use in the study of theories. Therefore, since the seminal work of Dana Scott on D1 in 1969 [18] semantical tools have been extensively investigated. A large number of ....

....do not match all the possible operational semantics of calculus. For example, in most existing categories of domains, models have too many functions, and hence many interesting theories, such as those arising from observing termination under some natural sequential reduction strategy (see e.g. [13]) do not have fully abstract denotational models [14,5,8] An example of such a strategy is the one which tries non deterministically to reduce a term to a closed term. In the case of CPOs, the sequentiality embedded in these strategies clashes with the necessary existence of Scott continuous ....

F. Honsell and M. Lenisa. Final semantics for untyped -calculus. In LNCS, volume 902, pages 249--265. Springer-Verlag, 1995.

....applicative (bisimulation) and the contextual equivalences. This purely syntactical method is based itself on a coinductive argument. Introduction This paper is part of a general project aiming at finding elementary proof principles for reasoning rigorously on infinite computational objects, see [4, 9] for the case of higher order functions, and [8] for the case of higher order processes. In this paper, as in [4, 9] we focus on the behaviour of terms when these are evaluated according to various reduction strategies. We address the problem of showing the coincidence of the applicative ....

....argument. Introduction This paper is part of a general project aiming at finding elementary proof principles for reasoning rigorously on infinite computational objects, see [4, 9] for the case of higher order functions, and [8] for the case of higher order processes. In this paper, as in [4, 9], we focus on the behaviour of terms when these are evaluated according to various reduction strategies. We address the problem of showing the coincidence of the applicative (bisimulation) equivalence with the observational (operational, contextual) equivalence for various reduction strategies, ....

[Article contains additional citation context not shown here]

F.Honsell, M.Lenisa, Final Semantics for untyped -calculus, M.Dezani et al. eds, TLCA'95 Springer LNCS, 902:249--265, Edinburgh, 1995.

....and the contextual equivalences are analyzed. The first is based on intersection types, the second is based on a mixed induction coinduction principle. Introduction This paper is part of a general project on finding elementary proof principles for reasoning rigorously on possibly infinite objects [8, 13]. Often, in dealing with infinite or circular objects, pure structural induction can be applied only after cumbersome encodings. Thus, alternative reasoning principles are called for, such as coinduction and mixed induction coinduction principles (see [16, 8] In this paper, we focus on the ....

....rigorously on possibly infinite objects [8, 13] Often, in dealing with infinite or circular objects, pure structural induction can be applied only after cumbersome encodings. Thus, alternative reasoning principles are called for, such as coinduction and mixed induction coinduction principles (see [16, 8]) In this paper, we focus on the behaviour of terms when they are evaluated according to a given reduction strategy. In particular, we introduce two general semantic techniques for deriving the coincidence of the applicative equivalence with the observational (operational, contextual) ....

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F.Honsell, M.Lenisa, Final Semantics for untyped -calculus, M.Dezani et al. eds, TLCA'95 Springer LNCS, 902:249--265, Edinburgh, 1995.

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Honsell, F., Lenisa, M.,\Final Semantics for untyped -calculus", LNCS 902,1995, pp.249-265. 17

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