Plotkin, G. (1975), `Call-by-name, call-by-value and the #-calculus', Theoretical Computer Science 1, 125--159.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Algol; this prevents the state from being treated, semantically, as if it were first class. 3.1. Other Transforms We should emphasise that the preceding analysis is not dependent on the Fischer transform. Instead of a continuation first transform, we could use a continuation second transform [19, 22, 26] without a#ecting the validity of the technical results, but a continuation first transform admits a briefer presentation and we can contrast continuation transformers and continuations, rather than two types of continuations. More explicitly, the continuation second version of (3) is = ....

....give values to. The transform is ##k, h#. ##k 1 , h 1 #. #. ##m. #. #. #h #m #k h 1 , h 1 h##. Here, linear # redexes do not correspond to any computational steps in the source language, but instead serve to arrange code (they are socalled administrative redexes [22]) After eliminating these redexes we have ##k, h#. #m. #e. H h#) y) x. So (5) is transformed into a term which given return and handler continuations, throws away the value of x, binds e to the value of y, and then runs the body of the handler with the given continuations. Notice that the ....

Plotkin, G. D.: 1975, `Call-by-Name, Call-by-Value and the #-calculus'. Theoretical Computer Science 1(2), 125--159.

....then k y : s [pc] pc e : s] y. While proving that this CPS translation is operationally correct is beyond the scope of this paper, the translation is substantially identical to other translations that have been shown to be correct. We expect that the simulation techniques due to Plotkin [33] could be adapted to prove similar correctness results for this transformation. 6. Related Work The constraints imposed by linearity can be seen as a form of resource management [19] in this case limiting the set of possible future computations. Linearity has been more widely used in the ....

Plotkin, G. D.: 1975, `Call-by-name, Call-by-value and the -calculus'. Theoretical Computer Science 1, 125-159.

....from Algol; this prevents the state from being treated, semantically, as if it were rst class. 3.1. Other Transforms We should emphasise that the preceding analysis is not dependent on the Fischer transform. Instead of a continuation rst transform, we could use a continuation second transform [17, 20, 24] without a ecting the validity of the technical results, but a continuation rst transform admits a briefer presentation and we can contrast continuation transformers and continuations, rather than two types of continuations. More explicitly, the continuation second version of (3) is = D:D ....

.... ; h 2 i: k 2 x) h m: hk 3 ; h 3 i: hk 4 ; h 4 i: k 4 x) hh 3 ; h 3 i) hm hk 1 ; h 1 i; h 1 i ; h 1 i) hk; e: H hk; hii: Here, linear redexes do not correspond to any computational steps in the source language, but instead serve to arrange code (they are socalled administrative redexes [20]) After eliminating these redexes we have hk; hi: m: e: H hk; hi) y) x: So (5) is transformed into a term which given return and handler continuations, throws away the value of x, binds e to the value of y, and then runs the body of the handler with the given continuations. Notice that the ....

Plotkin, G. D.: 1975, `Call-by-Name, Call-by-Value and the -calculus'. Theoretical Computer Science 1(2), 125-159.

.... 0 : As the intended meaning of a parallel composition is a function, Boudol adds the following rule (MkN)L Gamma (ML)k(NL) The internal convergence test is achieved using, besides standard call by name abstraction, call by value abstraction, originally considered by Landin [41] and Plotkin [57]. To see how this works, let us extend the set Val of values inductively so that it includes all terms of the shape V kN or MkV , where V is a value. We use two sorts of variables to distinguish between call by value and call by name abstraction, namely v; w; for call by value variables and x; ....

G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", Theor. Comp. Sci. 1, 1975, 125-159.

....computer science applications. These lambda calculi share the same syntax, and the CBV calculus was formulated to have the desirable properties of the CBN calculus, the most notable of these being the satisfaction of the Church Rosser Theorem. Much of the material in these notes was gleaned from Plotkin (1975). Encylopedic references are Barendregt (1984) and Hindley and Seldin (1986) An introduction to the type free lambda calculus is Barendregdt (1977) Introductions to typed lambda calculus can be found in Hindley and Seldin (1986) and Revesz (1988) An historical account of the development of the ....

.... V ConstApply(a; b) when defined 3V (M N ) V (M 0 N ) if M V M 0 4V (M N ) V (M N 0 ) if M is a value and N V N 0 Informally, if M N N (M V N ) then N is obtained from M by contracting the leftmost CBN (CBV) redex of M that is not contained in the body of an abstraction. Theorem [Plotkin (1975)] For any term M and value N , N M N iff M N N . The same result holds when N and N are replaced by V and V . 2 Rather that using N and V , closed terms can be reduced to WHNF (i.e. values) by corresponding (partial) evaluation functions eval N ; eval V : ClosedTerms P ....

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Plotkin, G. D., "Call-by-Name, Call-by-Value, and the -Calculus", Theoretical Computer Science 1: 125159, 1975.

.... of standard reduction s Delta (standard) is often defined in intensional geometric terms (e.g. 31] To formalize this notion directly, we would have to enrich the datatype of terms to speak of redex positions, as is done by Huet [20] Instead we adapt Plotkin s notion of standard sequence [34]. Standard reduction (figure 5) is defined as the least congruence closed under prefixing by weak head reductions. s Delta is of arbitrary length. 8 We leave implicit the sequence of redexes contracted (this may be computed by recursion) and its left to right character, avoiding mention of ....

Plotkin, G.: 1975, `Call-by-name, call-by-value, and the -calculus'. Theoretical Computer Science 1.

....LKQ) For the CBN CPS calculus, see appendix. We only consider the implication ( and negation( as logical connective. This is enough to explain the subject. 2 There are many presentation of CPS transforms in the literature. Among the others, we focus on the CBV CPS transform of Plotkin[15]. To illustrate the isomorphism, we utilize the intuitionistic decoration method. Roughly speaking, this is because calculus is isomorphic to intuitionistic logic. Recall that the target language of the Plotkin s CPS transform is the calculus. The intuitionistic decoration method itself is also ....

G. D. Plotkin, "Call-by-name, call-by-value and the -calculus," Theoretical Computer Science,1(2)(Dec. 1975) pp. 125--159, . 17

....it turns out that strong systems of union types do not give filter models, while weaker systems allow for a satisfactory logical analysis of some extended calculi. Here we will follow a different path. Instead of extending the calculus, we will consider Plotkin s call by value calculus [9], whose syntax is the same as that of the K calculus, but the fi rule is replaced by a restricted form: fi v ) x:M)N Gamma M [N=x] if N is not an application. The idea is that a term that is an application needs to be further evaluated before it can be passed on as an argument. By rule (fi v ....

....Also one can deduce A A for y:y, but this type cannot be deduced for (xy:y) z:zz) z:zz) which has no type at all. Thus this type assignment system does not induce a model. Instead it gives a model of the call byvalue calculus. The call by value calculus, as introduced by Plotkin [9], is obtained by restricting the fi rule to redexes whose argument is a value (i.e. a variable or an abstraction) Definition 4.1 (Call by value calculus) The set of values Val ae is defined by Val = Var [ fx:M jM 2 g where Var is the set of term variables. The call by value fi reduction rule ....

G. D. Plotkin, "Call-by-name, call-by-value and the -calculus", Theoretical computer science 1 (1975), pp. 125-159.

....Observe that the cone (e i : M Gamma V i ) i2I is empty or singleton because the calculus admits no conflict (orthogonality) This path is precisely the head reduction described syntactically by Wadsworth. Example 2. Another instance of the theorem was described by Plotkin in the v calculus [Pl]. Recall that a value is a variable or a term of the form x:M and that the fi v reduction (x:M )V M [V=x] is the fi rule restricted to value arguments V . Since the v calculus verifies the axioms in [1] and the set of values is open stable (w.r.t. the v calculus) the fundamental theorem ....

....restricted to value arguments V . Since the v calculus verifies the axioms in [1] and the set of values is open stable (w.r.t. the v calculus) the fundamental theorem implies that there is a head reduction in the v calculus. In fact, this non trivial reduction was described by Plotkin in [Pl] as the strategy which implements Landin s SECD machine. See also [FH] Example 3. The fundamental theorem has been used by the author to prove that the weak evaluation strategy defined by Abadi and Cardelli on their object calculus is complete, see [AC] pages 60 65. More generally, the ....

G. Plotkin, "Call-by-name, call-by-value, and the - calculus", Theoretical Computer Science 1, 1975.

....studied using the intersection types. All the above mentioned models are models of the classical calculus, but intersection type disciplines are also suitable for describing models of the I calculus [9, 55] of the lazy calculus [2, 18] of the call by value calculus (introduced by Plotkin in [74]) 49, 78, 79] and of some extensions of the calculus which include parallel features [21, 42, 43, 6] The finitary descriptions of domains have been a major point of interest. Scott pioneered this topic with his Information Systems in [87] Abramsky extended the intersection types, models, ....

G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", Theoretical Computer Science 1, 1975, 125--159. 94 m. dezani-ciancaglini, e. giovannetti, u. de'liguoro

....about M is that it is tail recursive: no operand is a combination. This property, furthermore, is preserved under beta reduction) Thus there is at most one redex which is not inside the scope of a lambda, and thus call by value reduction coincides with outermost or callby name reduction [Plotkin 75] This also allows simpler implementation on standard machines [Abelson Sussman 85] 6. Retractions. We say ff is a retract of fi (we write ff fi) iff there exist lambda definable maps i: ff fi and j: fi ff such that j ffi i is the identity function on ff. We can formulate retractions ....

....MN = N(n:M (m: mn) where the operand is evaluated before the operator, or even to allow the algorithm to choose nondeterministically between the two. In that case we need to ensure that both versions of S satisfy the concrete invariant. The case of the call by name transformation, as given in [Plotkin 75] can also be treated by these methods. The situation becomes more complicated if we study calculi in which strong normalization fails, such as the typed calculus with fixed point operators. We are currently studying both this and the untyped case, but it is not clear as of this writing whether ....

Plotkin, G.D. "Call-by-Name, Call-by-Value and the -Calculus," Theoret. Comp. Sci. 1 (1975) 125--159.

....: i) i = h 0 ; extRhv; hproc; closure u 0 0 iiu 0 ; hi; cont ui)i Auxiliaries: choose v 0 ) v = hint; 0i) 0 Figure 1: Actions of the abstract machine. It can also be shown that the machine is complete with respect to either call by value or call by name reduction [13], since these reduction strategies coincide on the terms manipulated by the machine, and the machine emulates these reduction strategies. So far this is just an example of the method set out in [3, 18] see also [5] for some more extended examples) We next turn to our main topic: the ....

Plotkin, G.D. "Call-by-Name, Call-by-Value and the - Calculus," Theoret. Comp. Sci. 1 (1975) 125--159.

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Plotkin, G. (1975), `Call-by-name, call-by-value and the #-calculus', Theoretical Computer Science 1, 125--159.

No context found.

G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", Theoretical Computer Science 1, 1975, 125--159.

No context found.

G. Plotkin, "Call-by-name, call-by-value, and the - calculus", Theoretical Computer Science 1, 1975.

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G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", TCS 1, 1975.

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G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", TCS 1, 1975.

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G. D. Plotkin, "Call-by-name, call-by-value and the -calculus", Theoretical computer science 1 (1975), pp. 125-159.

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G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", Theor. Comp. Sci. 1, 1975, 125-159.

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G.D. Plotkin, "Call-by-name, Call-by-value and the -calculus", TCS 1, 1975.

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Funct. Progr. 2(2), 127--202. Plotkin, G. D. (1975), `Call-by-name, call-by-value, and the -calculus', Theor. Comp. Sci. 1, 125--159.

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