Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1-models of the lambda-calculus. SIAM Journal of Computing, 5(3):488-- 521, September 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... trees are in one one correspondence with Nakajima trees [23] Hence, the various notions of tree represent different notions of meaning of a term (in particular they also specify different notions of undefined value [20] This apparently vague intuition is substantiated by results starting with [29], which show that there exist precise correspondences between the tree representations of terms and the local structures (or equivalently the theories) of certain models ( 4] Chapter 19) In particular, such correspondences amount to the fact that two terms have the same tree representation if ....

....19) In particular, such correspondences amount to the fact that two terms have the same tree representation if and only if they are equal in the model. For example, ffl the infinite eta trees represent the local structure of Scott s D1 model as defined in [26] this result was proved in [29]) ffl the eta trees represent the local structure of the inverse limit model defined in [12] ffl the head trees represent the local structure of Scott s P model as defined in [27] a discussion on this topic can be found in [4] Chapter 19) ffl the weak trees were introduced by Longo in ....

[Article contains additional citation context not shown here]

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1-models of the lambda-calculus. SIAM Journal of Computing, 5(3):488--521, 1976.

.... eta trees are in one one correspondence with Nakajima trees [23] Hence, the various notions of tree represent different notions of meaning of a term (in particular, they specify different notions of undefined value [20] This apparently vague intuition is substantiated by results starting with [29], which show that there exist precise correspondences between the tree representations of terms and the local structures (or, equivalently, the theories) of certain models ( 4] Chapter 19) In particular, such correspondences amount to the fact that two terms have the same tree ....

....19) In particular, such correspondences amount to the fact that two terms have the same tree representation if and only if they are equal in the model. For example, ffl the infinite eta trees represent the local structure of Scott s D1 model as defined in [26] this result was proved in [29]) ffl the eta trees represent the local structure of the inverse limit model defined in [12] ffl the head trees represent the local structure of Scott s P model as defined in [27] a discussion on this topic can be found in [4] Chapter 19) ffl the weak trees were introduced by Longo in ....

[Article contains additional citation context not shown here]

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1 -models of the lambda-calculus. SIAM Journal of Computing, 5(3):488--521, 1976.

.... trees are in one one correspondence with Nakajima trees [23] Hence, the various notions of tree represent different notions of meaning of a term (in particular they also specify different notions of undefined value [20] This apparently vague intuition is substantiated by results starting with [29], which show that there exist precise correspondences between the tree representations of terms and the local structures (or equivalently the theories) of certain models ( 4] Chapter 19) In particular, such correspondences amount to the fact that two terms have the same tree representation if ....

....19) In particular, such correspondences amount to the fact that two terms have the same tree representation if and only if they are equal in the model. For example, ffl the infinite eta trees represent the local structure of Scott s D1 model as defined in [26] this result was proved in [29]) ffl the eta trees represent the local structure of the inverse limit model defined in [12] ffl the head trees represent the local structure of Scott s P model as defined in [27] a discussion on this topic can be found in [4] Chapter 19) ffl the weak trees were introduced by Longo in ....

[Article contains additional citation context not shown here]

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1 -models of the lambda-calculus. SIAM Journal of Computing, 5(3):488--521, 1976.

....consult e.g. 7] 1. 2 Motivation In 1969, Scott provided the first mathematical model for the calculus, using an inverse limit construction (see [6] However, it was considered somewhat contrived, although the domain in question, called D1 , was shown to have many nice properties, e.g. in [10]. Later, he constructed a model in P , the set of all subsets of the natural numbers (see [7] by means of retracts and fixed points. Since natural numbers are a lot more concrete than inverse limits of lattices, one may think that it should be easier to extract properties of the latter model, ....

.... 0 (x 0 ) x 0 ( D0 ) x 0 2 D 1 OE n 1 (x) OE n ffi x ffi n ; x 2 Dn 1 n 1 (x 0 ) n ffi x 0 ffi OE n x 0 2 Dn 2 The inverse limit of the D i :s and the maps is D1 = fhxn i 1 0 jx n = xn 1 ) xn 2 Dn g: The favourable properties of D1 are independent of D 0 , as stated in [10], so we may select an arbitrary initial lattice, and then prove that our domain, D, is isomorphic to the resulting inverse limit 2 . The following construction is due to Jonsson in [3] 2 It it not necessary to use the OE maps, but with them, we can express the domain as a direct limit. ....

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Christopher P. Wadsworth. The Relation Between Computational and Denotational Properties for Scott's D1-Models of the Lambda Calculus. SIAM Journal on Computing, 5(3), 1976. 37

....of M . Recall that [x:A] P is Elf s concrete syntax for abstraction in the framework and binds a variable x of type A in the object P. x = x M N = app M N x: M = lam ( x:term] M ) For example, x: y: x = lam [x:term] lam [y:term] x: As far as we know, this representation is due to Wadsworth [Wad76] and used by Meyer [Mey82] in the construction of an environment model of the untyped calculus. The notation used there is Psi for lam and Phi for app. From the representation above we can read off the type of the constructors, leading to the following signature T . term : type. name term M ....

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1-models of the lambda-calculus. SIAM Journal of Computing, 5(3):488-- 521, September 1976.

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Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1-models of the lambda-calculus. SIAM Journal of Computing, 5(3):488-- 521, September 1976.

No context found.

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1 -models of the lambda-calculus. SIAM Journal of Computing, 5(3):488--521, 1976.

No context found.

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1-models of the lambda-calculus. SIAM Journal of Computing, 5(3):488-- 521, September 1976.

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Christopher Wadsworth, The Relation between Computational and Denotational Properties for Scott's D1-models of the -calculus, SIAM J. on Comp. , Vol. 5, No. 3, pp. 488-522, 1976.

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Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D1-models of the lambda-calculus. SIAM Journal on Computing, 5(3):488--521, September 1976.

No context found.

Christopher P. Wadsworth. The relation between computational and denotational properties for Scott's D#-models of the lambda-calculus. SIAM Journal on Computing, 5(3):488--521, September 1976. 34

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