A. Pravato, S. Ronchi della Rocca and L. Roversi, "Categorical Semantics of the call-by-value Lambda Calculus", TACS '95, Springer Lecture Notes in Computer Science 902 (1995), pp. 381-396.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....counterpart of call by value lazy programming languages, reflecting closer the actual practice of language implementation. In fact, the subtleties of parameter passing can be caught by the formal calculus, and analyzed using both proof theoretical and model theoretical tools in an elegant way [6, 10, 11]. What we will show here is that B is the type theory of the call by value calculus, in the following sense: we will consider the full language of the logic B , including disjunction, and take the B axioms and rules as defining a subtype relation. Then we will consider a type assignment system ....

....hinted above, with a key restriction on the types that can be assumed for variables in a basis. It turns out that, within this system, types are preserved under fi v conversion. Moreover, the filter structure of the type theory is an instance of call by value syntactical model (a generalisation, [6, 10, 11] of the notion of syntactical model due to Hindley and Longo [7] 2 The minimal relevant logic B as a type discipline The minimal relevant logic B is a propositional calculus. To see B as a type discipline, we interpret propositions as types: the constant for truth is interpreted as a ....

[Article contains additional citation context not shown here]

A. Pravato, S. Ronchi della Rocca and L. Roversi, "Categorical Semantics of the call-by-value Lambda Calculus", TACS '95, Springer Lecture Notes in Computer Science 902 (1995), pp. 381-396.

....to M 2 the counter example used in Theorem 8.1.1 of [1] can be applied, inducing that M 1 too is not fully abstract. An example of model for lazy (but this time call by value) computation built using a modal construction in the category of coherence spaces and linear functions, can be found in [16]. The paper is structured as follows: Section 2 introduces the syntax and the operational semantics of the lazy calculus and the concept of lazy regular models. Section 3 speaks about the approximation property satisfied by each lazy regular model. In Section 4 we introduce two lazy regular ....

A. Pravato, S. Ronchi della Rocca, and L. Roversi. Categorical semantics of the call-by-value lambdacalculus. In Proceeding of the Second International Conference of Typed Lambda Calculi and Application, TLCA'95, LNCS 902, pages 302 -- 318, Edinburgh, U.K., 1995. Springer-Verlag.

....used in Theorem 8.1.1 of Abramsky Ong (1993) can be applied, inducing that M 1 too is not fully abstract. An example of model for lazy (but this time call by value) computation built using a modal construction in the category of coherence spaces and linear functions, can be found in Pravato, Ronchi della Rocca Roversi (1995). 2 LAZY MODELS In this section we will define the lazy calculus and its models. Moreover, we will introduce a class of models, particularly suitable for our purposes. Let be the set of terms of the pure (i.e. without constants) calculus built out from a denumerable set Var of variables. i.e. ....

Pravato, A., Ronchi della Rocca, S. & Roversi, L. (1995), Categorical semantics of the call-by-value lambda-calculus, in `Proceeding of the Second International Conference of Typed Lambda Calculi and Application, TLCA'95, LNCS 902', Edinburgh, U.K., Springer-Verlag, pp. 302 --318.

....structure is used in Section 5 and in Section 6 to define a categorical model for the fi v calculus. In Section 7 problems involving the extensionality are treated, while in Section 8 two instances of the categorical model are introduced. An earlier, partial version of this paper was in [15]. In the paper we will assume a basic knowledge about category theory, Scott Domains and Coherence Spaces. 2 Modeling the call by value calculus The call by value lambda calculus, or fi v calculus, is a restriction of the classical one, based on the concept of value. In particular, the ....

....7.5. All the total models we know turn out to be Cbv categories. Let we refer again the model P , in the Scott domain setting, based on the domain equation D (D D) studied in [4] and that one in the coherence space setting based on the domain equation D (D Gammaffi D) studied in [15]. Remark 4.4 together with the fact that enough values becomes enough points in the fi calculus setting and that a cartesian closed category is a particular Cbv category, implies that every model of the fi calculus is a total model of the fi v calculus too. The above discussion brings us to ....

A. Pravato, S. Ronchi della Rocca, and L. Roversi. Categorical semantics of the call-by-value lambda-calculus. In LNCS 902: Proceedings of TLCA '95, Edinburgh, U.K., pages 302 -- 318. Springer-Verlag, 1995.

No context found.

A. Pravato, S. Ronchi della Rocca and L. Roversi, "Categorical Semantics of the call-by-value Lambda Calculus", TACS '95, Springer Lecture Notes in Computer Science 902 (1995), pp. 381-396.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC