Dami, L. 1998. A lambda-calculus for dynamic binding. Theoretical Computer Science 192, 2, 201--231.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....two classes of variable (one treated statically and one dynamically) or one class of variable, with some other way of specifying which are rebound in any particular marshal unmarshal instance. Two classes were used in some related systems, though not motivated by marshalling [LLMS00, LF93, Dam98, Jag94] discussed further in 5) The disadvantages of the two class choice are: a) it is less flexible than our use of marks, in which di#erent marshals and unmarshals can refer to di#erent marks, e.g. in the examples of 3.6; and (b) if the types or usage forms of the two classes di#er, ....

....et al. forbid arguments of higher order functions from using dynamically scoped variables) 32 5 RELATED WORK 5. 2 Dynamic Rebinding and # marsh Turning to static scoping with explicit rebinding, the quasi static scoping Scheme extension of Lee and Friedman [LF93] and the #N calculus of Dami [Dam98] both have two classes of variable with a rebinding primitive that specifies new bindings for individual variables. Jagannathan s Rascal language [Jag94] maintains both a static environment and a public environment, corresponding again to two variable classes. The barrier, reify, and reflect ....

Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, 1998.

....two classes of variable (one treated statically and one dynamically) or one class of variable, with some other way of specifying which are rebound in any particular marshal unmarshal instance. Two classes were used in some related systems, though not motivated by marshalling [LLMS00, LF93, Dam98, Jag94] discussed further in 5) The disadvantages of the two class choice are: a) it is less flexible than our use of marks, in which different marshals and unmarshals can refer to different marks, e.g. in the 3.6 examples; and (b) if the types or usage forms of the two classes differ, then ....

.... Lisp community (to avoid this in a typed setting Lewis et al. forbid arguments of higher order functions from using dynamically scoped variables) Turning to static scoping with explicit rebinding, the quasi static scoping Scheme extension of Lee and Friedman [LF93] and the #N calculus of Dami [Dam98] both have two classes of variable with a rebinding primitive that specifies new bindings for individual variables. Jagannathan s Rascal language [Jag94] maintains both a static environment and a public environment, corresponding again to two variable classes. The barrier, reify, and reflect ....

Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, 1998.

....as containing the pure form calculus presented here as a sublanguage. Neither Schneider s form calculus nor the Piccola calculus are typed. Abadi s calculus of explicit substitutions [ACCL90] makes environment explicit, but does not turn them into first class values. Dami s calculus of names, #N[Dam98], replaces variables by names, and has a similar flavour to our form calculus, but still does not treat environments as first class values. Nishizaki s environment calculus [Nis00] treats environments as first class values, and supports a polymorphic, ML style type system with a corresponding ....

Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, February 1998.

....are that resolution of optional arguments does not rely on types anymore, and full compliance with the call by value semantics. From a technical point of view, the contribution of this paper is a reduction system combining currying, labeled and optional arguments. Works by others [Lam88, Dam98] did not consider the full combination of currying and commutation (some kind of non commuting closure operation is needed between passing groups of parameters) and the Objective Label approach had to rely on types for optional parameters. More practically, we give here the rst formal account ....

Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192:201-231, 1998.

....as source code and lambda terms as compiled code . This separation is done by assuming two disjoint variable name spaces: one for lambda terms and one for contexts. As a consequence, in their system, reduction and ll reduction are two disjoint relations without non trivial interaction. Dami [2] also announced a system for dynamic binding similar to that of Lee and Friedman. While these approaches would be useful for representing source code as a data structure, they do not allow contexts of the language itself to be treated as rst class values inside the language. Kahrs [9] have ....

Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201-31, February 1998. Special issue on Coordination. 21

....the variable x remains to be free. So, unlike substitution, hole lling may introduce new and intended bound variables. Recently there have been several attempts to formalize the notion of context and thereby make computing with contexts possible. For example, Talcott [16] Lee Friedman [8] Dami [5], Hashimoto Ohori [7] Sands [13] Mason [9] and Bognar de Vrijer [3] made notable contributions. However, as far as we know, there is as yet no proposal of a language which has contexts as rst class values and which is at the same time pure in the following sense. We understand that a functional ....

....that (i) each context may have at most one hole in it, and (ii) as we have explained in section 1, the application of the reduction is allowed only when the redex has no hole in it. Our calculus does not have such restrictions and reduction and hole lling always commute. Dami s calculus N [5] is a very simple and powerful calculus with named variables. It is possible to represent both contexts and hole lling in N . However, this is done by a translation of calculus into N . Therefore, it is hard to read the translated terms as contexts. On the other hand, Mason [9] introduces a ....

Dami, L., A Lambda-Calculus for Dynamic Binding, pp. 201-231, Theoretical Computer Science 192, 1998. 15

....the variable x remains to be free. So, unlike substitution, hole filling may introduce new and intended bound variables. Recently there have been several attempts to formalize the notion of context and thereby make computing with contexts possible. For example, Talcott [16] Lee Friedman [8] Dami [5], Hashimoto Ohori [7] Sands [13] Mason [9] and Bognar de Vrijer [3] made notable contributions. However, as far as we know, there are as yet no proposal of a language which has contexts as first class values and which is at the same time pure in the following sense. We understand that a ....

....(i) each context may have at most one hole in it, and (ii) as we have explained in section 1, the application of the fi reduction is allowed only when the fi redex has no hole in it. Our calculus does not have such restrictions and fi reduction and hole filling always commute. Dami s calculus N [5] is a very simple and powerful calculus with named variables. It is possible to represent both contexts and hole filling in N . However, this is done by a translation of fi calculus into N . Therefore, it is hard to read the translated term as contexts. On the other hand, Mason [9] introduces a ....

Dami, L., A Lambda-Calculus for Dynamic Binding, pp. 201-231, Theoretical Computer Science, 192, 1998.

....requires the propagation of extensions of one part to the other. This propagation, however, can be reduced in many cases, if we replace the polyadic communication of tuples by monadic communication of forms. Dami has tackled a similar problem in the context of the # calculus, and has proposed #N [Dam94, Dam98], a calculus in which parameters are identified by names rather than positions. The resulting flexibility and extensibility can also be seen in HTML forms, whose fields are encoded as named (rather than positional) parameters in URLs, and in Python [vR96] where functions can be defined to take ....

Dami, L. A Lambda-Calculus for Dynamic Binding. Theoretical Computer Science, 192:201--231, February 1998.

.... source code and lambda terms as compiled code . This separation is done by assuming two disjoint variable name spaces: one for lambda terms and one for contexts. As a consequence, in their system, fi reduction and fill reduction are two disjoint relations without non trivial interaction. Dami [2] also announced a system for dynamic binding similar to that of Lee and Friedman. While these approaches would be useful for representing source code as a data structure, they do not allow contexts of the language itself to be treated as first class values inside the language. Kahrs [9] have ....

L. Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--31, February 1998. 21

....produce a more interesting system. Relationship with other systems. There are several formal systems for manipulating names and bindings: A t Kaci and Garrigue s label selective calculus [2] calculus [1] for explicit substitutions of Abadi et al. Dami s calculus for dynamic binding N [4], and calculi for rstclass environments [12, 17] Although none of them can directly represent the notion of rst class contexts, similar features except for typed macros appear to be also directly representable in those systems. The precise relationship between the context calculus and those ....

Laurent Dami. A lambda-calculus for dynamic binding. In Theoretical Computer Science, 192(2), February 1998. special issue on Coordination.

....determined by the attribute assigned to the symbol [2] which is especially designed for mobile programming 58 CHAPTER 2. A CALCULUS WITH CODE MOBILITY languages. The naming resolution is the critical mechanism in CORBA. In general, a calculus with first class environments [75] and context calculi [27, 48] would be useful for the problem. 2.7.2 Hierarchical Locations The notion of location adopted in our calculus is flat, but many other mobile calculi [19, 82, 85] and mobile systems such as Telescript [41] have hierarchical location. From the practical view point, there are several bases to ....

Laurent Dami. A Lambda-Calculus for Dynamic Binding. Theoretical Computer Science, 192(2), 1998.

....to derive a homomorphic model of functional languages by considering as a combinator. His axioms are derived from the oe calculus axioms, while ours are constructed during the proof of equational correspondence of the calculus. Two recent publications refer to the notion of dynamic binding. Dami [7] presents a calculus for dynamic binding: N , the calculus with names, is an extension of the calculus in which arguments are passed to functions along named channels. 57 An embedding of the calculus is given as a translation into N . An application of the N calculus that is relevant to this ....

Laurent Dami. A Lambda-Calculus for Dynamic Binding. Theoretical Computer Science, Accepted for publication.

....on the length of computations see for example [1] Thanks to this lemma, it then suffices to check a restricted class of applicative contexts and the proof of the laws above becomes easy. Complete developments and more detailed discussions for record extension constructs can be found in [12, 14]. 6 Interpreting Types This section illustrates the usefulness of both subsumption and labelled reductions for the semantics of types : subsumption is a natural foundation for interpreting subtyping, and labelled terms are a natural foundation for interpreting recursive types, following the ....

Laurent Dami. A Lambda-Calculus for Dynamic Binding. To appear in Theoretical Comp. Sc., special issue on Coordination, 1997.

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Laurent Dami. A Lambda-Calculus for Dynamic Binding. To appear in Theoretical Comp. Sc., special issue on Coordination, 1997.

....reflexive, transitive closure is written , and the symmetric closure of is written = Theorem 2.1 (Confluence) The language is confluent: whenever a b and a c there is a d such that b d and c d. Proof. Standard Tait technique using parallel reductions; see for example [22,9]. 2 Definition 2.2 [Convergence] A term a converges (a ) iff 9v 2 V; a v. Otherwise a diverges (a ) 3 Operational Subsumption The idea of operational subsumption is a simulation relation based on observation of errors. In the abstract framework of [10] we had to build a complex machinery ....

....a diverges (a ) 3 Operational Subsumption The idea of operational subsumption is a simulation relation based on observation of errors. In the abstract framework of [10] we had to build a complex machinery in order to define the notion of erroneous terms . Here this can be much simpler: like in [9], we have a rule ( which removes a abstraction if its body is an error; this rule is admissible because it does not break confluence (Theorem 2.1 above) As a result it suffices to observe reductions to as a basis for subsumption. Definition 3.1 [Error terms] ay ( 9n; a n 1 E ....

Laurent Dami. A Lambda-Calculus for Dynamic Binding. Theoretical Comp. Sc. 192(2):201-231, Feb 1998.

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Dami, L. 1998. A lambda-calculus for dynamic binding. Theoretical Computer Science 192, 2, 201--231.

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Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, 1998.

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L. Dami. A Lambda-Calculus for Dynamic Binding. Theoretical Computer Science, 192:201--231, 1998.

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Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, February 1998.

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Laurent Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, 1998.

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L. Dami. A Lambda-Calculus for Dynamic Binding. Theoretical Computer Science, 192:201--231, Feb. 1998.

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L. Dami. A lambda-calculus for dynamic binding. Theoretical Computer Science, 192(2):201--231, 1998.

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