C. P. Wadsworth. Approximate reductions and -calculus models. SIAM Journal of Computing, 7(3):337 -- 356, 1978. 20  Home/Search Document Not in Database Summary Related Articles Check |
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Structures for Lazy Semantics - Bastonero, Pravato, Rocca (1997) (3 citations) (Correct)
....preorder is included in the local theory of every lazy regular model. The proof is an immediate consequence of the fact that all the lazy regular models share an approximation property w.r.t. the same notion of approximant, which is an adaptation of the one introduced by Hyland [12] and Wadsworth [17] for analyzing Scott s D1 model. The approximation property says that the interpretation of a term is the supremum of the interpretations of a set of normal forms in an extended languages (its approximants) 3.1 Approximation Theorem Let the ( Omega Gamma calculus be the following extension of ....
....of the pure calculus obtained by adjoining to set of variable the constant Omega . The rewriting rules are the fi rule and also the Omega rule defined by: Omega Gamma Omega M Omega Omega : The ( Omega Gamma calculus is Church Rosser because it is a restriction of the one defined in [17], which considers also the rule x: Omega Omega . This last rule is not sound in the lazy case. Definition 3.1 Let M 2 . 1. A 2 ( Omega Gamma is an approximation of M , and write A app M , if A is obtained from M by substituting Omega for some subterm of M , 2. let N fi Omega ....
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C. P. Wadsworth. Approximate reductions and -calculus models. SIAM Journal of Computing, 7(3):337 -- 356, 1978. 20
Strong Stability and the Incompleteness of Stable Models for - Calculus Olivier Bastonero (Correct)
.... approximation introduced by Honsell and Ronchi della Rocca [14] in the framework of continuous semantics, which can be naturally extended to a very large class of models, in particular to non sensible models (like Park s model) for which the standard approximation theorem of Wadsworth and Hyland [23, 24, 15] is not available. From now on D denotes either a continuous, stable or strongly stable model. Let us add a constant c 0 to the calculus, and consider the calculus induced by the fi reduction on (c 0 ) We call approximants the fi normal terms of (c 0 ) we denote by A the set of ....
...., for every n ; ffl W p n =D x x ; ffl ( p n 1 )a)b = p n ) a) p n )b. In order to prove that every stratified model satisfies the approximation property, we use an extended calculus, the labelled calculus. This calculus is very similar to the indexed calculus used by Hyland and Wadsworth [23, 24, 15]. Here we use the syntax introduced by Parigot in [19] Let C = fc n g n2 be a set of constants that we call labels. The set e of labelled terms is the subset of (C ) inductively defined by: ffl x 2 e , for every variable x, 25 ffl if u; v 2 e then (c n )u; c n )x u and (u)v belong to e ....
C.P. Wadsworth, Approximate Reductions and -calculus Models, SIAM J. of Computing 7(3)(1978) 337-356. 32
Structures for Lazy Semantics - Bastonero, Pravato, Rocca (1998) (3 citations) (Correct)
....local theory of every lazy regular model. The proof of this last point is an immediate consequence of the fact that all the lazy regular models share an approximation property w.r.t. the same notion of approximant, which is an adaptation of the one introduced by Hyland (Hyland 1976) and Wadsworth (Wadsworth 1978) for analyzing Scott s D1 model. The approximation property says that the interpretation of a term is the supremum of the interpretations of a set of normal forms in an extended language (its approximants) 3.1 Approximation Theorem Let the ( Omega Gamma calculus be the following extension of ....
Wadsworth, C. P. (1978), `Approximate reductions and -calculus models.' SIAM Journal of Computing 7(3), 337 -- 356.
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