Plotkin, G.D. A set-theoretical definition of application. Research Memorandum MIP-R-95, 32 pp. Dept. of Machine Intelligence and Perception, University of Edinburgh (1972).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....collapse OE of A. There are prominent pca s which share this property. We give two examples. Example 1. The first example uses only elementary properties of sets, and is directly taken from Engeler [Eng81] It is in fact a notational variant of one of several ca s first described in Plotkin [Plo72] which in turn are nearly the same as the better known P construction of Scott [Sco76] Let A be any nonempty set, and let B be the least set containing A and all ordered pairs consisting of a finite subset fi B and an element b 2 B. Assume that elements of A are distinguishable from ordered ....

G.D. Plotkin. A set-theoretical definition of application. Technical Report Memorandum MIP-R-95, School of Artificial Intelligence, University of Edinburgh, 1972.

....a powerful proof technique called candidates of reducibility. To prove the strong normalization of System F [ Girard, 1972 ] see the lucid account in Girard s book [ Girard et al. 1989 ] Another variation of the same theme called logical relation was independently developed by Plotkin [ Plotkin, 1972 ] see also [ Statman, 1985 ] Logical relations are a very useful tool for proving properties of typed lambda calculi. Denotational semantics prescribes meanings to syntactic entities compositionally. This means that the meaning of a composite term is defined in terms of the meanings of the ....

G. D. Plotkin. A set-theoretical definition of application. Technical Report MIP-R-95, School of A.I., University of Edinburgh, 1972.

....strengthened to LT ae B (see Theorem 6.1) A very general theory of full abstraction for the Lazy Lambda Calculus based on the notion of applicative simulation has been developed; we direct the reader to [AO93] for details. Lazy Models All the well known models e.g. D1 [Sco72] P( [Plo72, Sco76], T [Plo78] and B (Bohm tree model, see e.g. Bar84, Ch. 18] are sensible; and so these concrete models are of no use to our purpose. What about the very definition of a model 6 Are the three equivalent formulations of a model viz. environmental, functional and first order, specific and ....

....3 Plotkin Scott Engeler Algebras and Models We introduce a family of combinatory algebras called Plotkin Scott Engeler (pse) algebras. First formalized by Engeler [Eng81] pse algebras may be seen as a code free variant of the well known graph model P( due independently to Plotkin [Plo72] and Scott [Sco76] Let B be a non empty set satisfying (io) fi fin B b 2 B ( fi; b) 2 B; where the meta variable fi ranges over finite sets (similarly for meta variables fi 0 ; fi 1 ; Delta Delta Delta ; fl i ; Delta Delta Delta) We call (fi; b) an io pair. Plotkin Scott Engeler ....

G. D. Plotkin. A set-theoretical definition of application. Technical Report MIP-R-95, School of A.I., Univ. of Edinburgh, 1972.

....even though this unfortunately clashes with the tradition in logic of regarding conjunctions as meets and disjunctions as joins. to explicitly test the information content of its argument, while the argument is being evaluated. How best should this be done In the graph models of the calculus [Plo72, Sco80], the denotation of an abstraction x:M is obtained by probing M with all possible pieces of partial information u for x, in a manner very reminescent of the notion of asks. So a simple way suggests itself: introduce the notion of abstractions which test their body only with pieces of information ....

Gordon Plotkin. A set-theoretical definition of application. Memorandum MIPR -95, 17th March, 1972.

....is computable as established in the previous case, Y(r)p q) t v. The rest are entirely similar. The computability argument central to the proof can be traced back to an important paper of Tait [29] A variation of the theme called logical relation was independently developed by Plotkin [20]; see also [28] Logical relations are a very useful tool for proving properties of typed lambda calculi. Plotkin s adequacy result for PCF has been extended to richer computational settings. For example, in [25] it is shown that adequacy holds for a meta language for denotational semantics which ....

G. D. Plotkin. A set-theoretical definition of application. Technical Report MIP-R-95, School of A.I., Univ. of Edinburgh, 1972.

.... has already been obtained for the simple semantics [4,17] and the Fsemantics [12] We obtain completeness for two more general classes of type interpretations, where there is a pleasing correspondence between the type expression models and the set theoretic models of Plotkin and Engeler [30, 14]. It would be interesting to have a formal definition of a notion of a static type inference system. Such a system provides the basis for static type inference (or type checking) algorithms. It is desirable that the system admits a reduction rule. That implies that the types of terms after ....

....There is nonetheless some interest in pursuing such systems. First the availability of non simple type interpretations allows completeness proofs for other, perhaps simpler, type inference systems. Secondly these systems are very closely connected to the models of the k calculus given by Plotkin [30] and Engeler [14] A natural basic system with intersection types is obtained by adding to the system k binary and empty intersections of types: and co. The rules we take are (I) F [ M: x, F [ M:3 F M:c3 (E) 1. F [ M:ct 2. F M:3 (mI) F I M:m This system has not been considered ....

[Article contains additional citation context not shown here]

Plotkin, G.D. A set-theoretical definition of application. Research Memorandum MIP-R-95, 32 pp. Dept. of Machine Intelligence and Perception, University of Edinburgh (1972).

No context found.

Plotkin, G., 1972. A set-theoretical definition of application, School of Artificial Intelligence, Memo MIP-R-95, University of Edinburgh.

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