T. Crolard. From bicartesian closed categories with coexponents towards subtractive logic. Submitted to Theoretical Computer Science. (ftp://sweet-smoke.ufr-infop7. jussieu.fr/crolard/tcs.ps). Home/Search Document Not in Database Summary Related Articles Check |
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A Constructive Restriction of the lambda µ-calculus - Crolard (1999) Self-citation (Crolard) (Correct)
....hand, we do not consider tag abstraction in this paper. However, our restriction is symmetrical and thus easily extends to duality. Our purpose is to type tag abstraction with the subtraction (the connector dual to implication) Note that subtractive logic is a conservative extension of DIS logic [22, 5, 4]. 1 DIS logic DIS logic is the first order (resp. second order) intuitionistic logic extended with the following axiom schemas DIS (resp. DIS and DIS 2 ) where x (resp. X) does not occur in B: 8x(A B) 8xA B 8X(A B) 8XA B Remark. Though DIS is not valid in intuitionistic logic, if a ....
....to this issue: we need a new connector (i.e. a new type constructor) called subtraction, which is dual to implication to type contexts. We will thus obtain a calculus with first class coroutines, whose type system corresponds to subtractive logic (which a conservative extension of DIS logic [22, 5, 4]) 14 We have proved that DIS logic is constructive. We conjecture that is it possible to define a set of reduction rules for the calculus in which a normal form is canonical (a normal form does not begin with a ff[ff] or in other words, the last rule of a normal proof of CND r is an ....
T. Crolard. From bicartesian closed categories with coexponents towards subtractive logic. Submitted to Theoretical Computer Science. (ftp://sweet-smoke.ufr-infop7. jussieu.fr/crolard/tcs.ps).
A Confluent Lambda-Calculus With a Catch/throw Mechanism - Crolard Self-citation (Crolard) (Correct)
....are typed by the negation :A j A ) Of course, this is not sound anymore in intuitionistic logic since this type is the excluded middle. We will consider tag abstraction in a constructive framework in a forthcoming paper, but where subtraction (the connector dual to implication, see Crolard (1996; 1999)) will be used instead of disjunction. Acknowlegments We would like to thank Serge Grigorieff for important suggestions and careful technical proofreading. The many discussions with Hugo Herbelin have been essential for this work. Comments of the anonymous referees have also been very useful. ....
Crolard, T. (1999). From bicartesian closed categories with coexponents towards subtractive logic. To appear in Theoretical Computer Science.
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