D. Pym and E. Ritter. On the semantics of classical disjunction. J. Pure Applied Algebra, 159:315--338, 2001. Home/Search Document Not in Database Summary Related Articles Check |
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An Implementation of the Call-By-Name - Calculus Peter Selinger (Correct)
....programming language with control primitives. However, its operational significance is not very well understood, particularly because it does not have a very satisfactory rewrite semantics. The calculus was proposed by Pym and Ritter as an extension of the calculus with disjunction types [4], again motivated by proof theory. Here, we hope to clarify the operational meaning of these calculi by giving a Krivine style abstract machine semantics and an implementation. The meaning of the control operators and of the disjunction types can be explained in the machine model in terms of ....
....1. The reason that we write the control context on the right comes from logic: A sequent x 1 :B 1 ; xn :Bn M : A j ff 1 :A 1 ; ff m :Am corresponds to a proof of the formula B 1 : Bn ) A A 1 : Am : 1. 2 Adding classical disjunction: The calculus Pym and Ritter [4] propose the following straightforward way of adding a disjunction type to the calculus: A : A B M : hffiM ff A :M with typing rules: ang) Gamma M : A B j ff:A; Delta Gamma hffiM : B j ff:A; Delta ( Gamma M : B j ff:A; Delta Gamma ff A :M : A B j ....
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D. Pym and E. Ritter. On the semantics of classical disjunction. Preprint, 1998.
Control Categories and Duality: on the Categorical Semantics of.. - Selinger (1999) (29 citations) (Correct)
.... some aspects of the present work to arbitrary computational effects in place of continuations (Fuhrmann 1999) A different class of models for the call by name calculus, based on fibrations, was defined by Ong and Ritter and later generalized to the disjunctive case by Pym and Ritter (Ong 1996; Pym and Ritter 1998). The focus of these models is different from ours, as they stress the fibered nature of the calculus with respect to control contexts, and thus they are, in a sense, higherorder. However, these models are rich in algebraic structure, and indeed, the calculus forms an internal language for them, ....
....to include a disjunction type constructor. Indeed, there is a standard way of adding disjoint sum types to the lambda calculus via left and right injections and a case construct. However, the proof theory of disjunction in classical logic is quite different from that in intuitionistic logic, and Pym and Ritter (1998) show how to add a different, classical, disjunction type to the calculus. They also show that these classical disjunction types are strictly different from the disjoint sum type under the call by name semantics. On the other hand, we shall see that under call by value, the two disjunction types ....
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D. Pym and E. Ritter. On the semantics of classical disjunction. Preprint, 1998.
A Parigot-style Linear lambda-Calculus for Full.. - de Paiva, Ritter (2003) Self-citation (Ritter) (Correct)
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E. Ritter and D. Pym. On the semantics of classical disjunction. Journal of Pure and Applied Algebra, 159:315--338, 2001.
Notes Towards a Semantics for Proof-search - Pym Self-citation (Pym) (Correct)
....a dependently typed calculus which provides a partial analysis, being both in the spirit of BI and yet somewhat reliant on the presence of a form of Dereliction. Nevertheless, can be interpreted in the general bred framework sketched in Figure 2; Classical logic: the and calculi [22,26,27,29,30] allow the presentation of a semantics of the proofs of propositional classical logic within the bred framework [29] In ( sequents are structured so as to have a chosen active position on the right (the left most position) t : where the term t inhabits (in the sense of the ....
.... on the right can be handled just as Weakening on the left) 12 One way to understand this point of view is provided by the presentation of classical logic as the calculus, a term calculus for the classical sequents which is analysed proof theoretically in [29,30] and semantically in [26] (recall the discussion in x 3) Recall that in this view, in which sequents are structured so as to have a chosen active position on the right (the left most position) t : where the term t inhabits (in the sense of the propositions as types correspondence) the formula, in the ....
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Pym, D. and E. Ritter, On the semantics of classical disjunction, to appear, Journal of Pure and Applied Algebra, 2000. Preprint available at URL: http://www.dcs.qmw.ac.uk/pym, September 2000.
Categorical Models Of First-Order Classical Proofs - McKinley (2006) (Correct)
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D. Pym and E. Ritter. On the semantics of classical disjunction. J. Pure Applied Algebra, 159:315--338, 2001.
Classical Categories and Deep Inference - McKinley (2005) (Correct)
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Pym, D., Ritter, E.: On the semantics of classical disjunction. JPAA 159 (2001) 315--338
An Interpretation of the Second Order Sequent Calculus in the.. - Th Mar Ch (Correct)
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Eike Ritter and David Pym. On the semantics of classical disjunction. ???Submitted for publication, 1998.
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