A. Moran. Natural Semantics for Non-Determinism. Licentiate Thesis, Chalmers University of Technology and University of Goteborg, Sweden, May 1994. Home/Search Document Details and Download
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A Tutorial on Co-induction and Functional Programming - Gordon (1994) (10 citations) (Correct)
....divergence co inductively in terms of unbounded reduction. Let D : Prog) Prog) and Prog be D(X) def = fa j 9b(a b b 2 X)g def = X: D(X) We can easily see that D is monotone. Hence by its co inductive definition we have: is the greatest D dense set and = D( Hughes and Moran (1993) give an alternative, big step , co inductive formulation of divergence. As a simple example we can show that Omega . Let X Omega def = f Omega g. X Omega is D dense, that is, X Omega D(X Omega ) because Omega Omega and Omega 2 X Omega . So X Omega by co induction, and ....
Hughes, J. and A. Moran (1993, June). Natural semantics for nondeterminism.
Making Choices Lazily - Hughes, Moran (1995) (3 citations) Self-citation (Moran) (Correct)
....example. Plural choice results if choice expressions are copied when substituted; it arises immediately in a call by name context. Considering again the example from the introduction: if 8 was plural amb, the left hand side could evaluate to 2, 3, or 4. This section summarizes parts of [16]. The central idea is to produce two operational semantics: one intensional and low level semantics that has a clear correspondence to our operational intuitions, and a more abstract natural semantics that is easier to use for equational reasoning. To justify using the latter so, the two semantics ....
....by the following theorem) Theorem 2.2 (Bottom Avoidance) For all closed small step terms e1 and e2 , e1 e2 ( e1 m 8 n e2 : Together, these two theorems imply that 8, as implemented by the rules in gure 1, is McCarthy s amb. The proofs of these theorems appear in [16], and are simpler versions of the proofs of the analogous theorems that appear in section 4. 2.2 Natural Semantics To model the operational behaviour of the language more abstractly, we give natural semantics for convergence (de ned inductively) and for divergence (de ned co inductively) We ....
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A. Moran. Natural Semantics for Non-Determinism. Licentiate Thesis, Chalmers University of Technology and University of Goteborg, Sweden, May 1994.
Making Choices Lazily - John Hughes Andrew (1995) (3 citations) Self-citation (Moran) (Correct)
....example. Plural choice results if choice expressions are copied when substituted; it arises immediately in a call by name context. Considering again the example from the introduction: if 8 was plural amb, the left hand side could evaluate to 2, 3, or 4. This section summarizes parts of [16]. The central idea is to produce two operational semantics: one intensional and low level semantics that has a clear correspondence to our operational intuitions, and a more abstract natural semantics that is easier to use for equational reasoning. To justify using the latter so, the two semantics ....
....by the following theorem) Theorem 2.2 (Bottom Avoidance) For all closed small step terms e1 and e2 , e1 e2 ( e1 m 8 n e2 : Together, these two theorems imply that 8, as implemented by the rules in figure 1, is McCarthy s amb. The proofs of these theorems appear in [16], and are simpler versions of the proofs of the analogous theorems that appear in section 4. 2.2 Natural Semantics To model the operational behaviour of the language more abstractly, we give natural semantics for convergence (defined inductively) and for divergence (defined co inductively) We ....
[Article contains additional citation context not shown here]
A. Moran. Natural Semantics for Non-Determinism. Licentiate Thesis, Chalmers University of Technology and University of Goteborg, Sweden, May 1994.
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