C.B. Jay, "The structure of free closed categories", J. Pure Appl. Alg., 66 (1990) 271--285.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... , I) Gamma , I) Gamma , I (a Gamma , I) I I This pair represents also an example of twisted applications of Gamma , These facts are based mostly on the definition of j for sequent derivations and known facts about F(A) For other methods that can be used to check j see, e.g. [6], 13] Proposition 5.2 (Cut elimination theorem, cf. 9] 8] Every derivation in L is equivalent to a cut free derivation of the same sequent. Proposition 5.3 (Kelly Mac Lane coherence theorem for L) Let S be balanced sequent which does not contain occurrences of formulas of the form C Gamma ....

C.B. Jay. The structure of free closed categories. Journal of Pure and Applied Algebra, 66(3):271--287, 1990.

....iff they do not belong to W 0 . The deciding algorithm may then deal with equivalence relation in recursive way. Using the category of finite pointed sets another, non recursive algorithm may be obtained. There were works by other authors suggesting various deciding algorithms, say [13] [6]. Lemma 7.9 Let ( be cut free derivations of a balanced pure 2 sequent. Assume that they have the same last rule. If ( is not in W 0 , then the subderivations ( 0 ; 0 ) of each premise of this rule in ( also do not belong to W 0 . Remark 7.10 Now one can easily derive, ....

C.B. Jay. The structure of free closed categories. Journal of Pure and Applied Algebra, 66(3):271--287, 1990.

....with normalization in the corresponding natural deduction system. We shall follow Mints [8] and connect with the deductions in our calculus lambda terms. Two deductions are equivalent iff the corresponding lambda terms have the same normal forms. Another decision procedure was suggested by Jay [11], but for our purposes it is sufficient here to use Mints approach. We shall denote the calculus above by L. Let us call a formula A reduced, if it does not contain subformulas of the form B Omega C with B or C constant, B)C with B constant, and in A all the subformulas of the form A) B)C) are ....

C.B.Jay. The structure of free closed categories.Journal of Pure and Applied Algebra, 66(3):271-287, 1990.

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C.B. Jay, "The structure of free closed categories", J. Pure Appl. Alg., 66 (1990) 271--285.

....lists (perhaps with duplications) of the canonical natural transformations between given functors. For symmetric, monoidal closed categories it was shown in [12] how to decide in principle whether two such transformations are equal, while an effective, linear time decision procedure was given in [1]. Derivation systems (reduction rules) can be used to eliminate some duplicates in the list of cut free proofs (e.g. 8] However, in Algebra of Proofs [11] and its To appear in Notre Dame Journal of Formal Logic y Research supported by The Royal Society of Edinburgh BP, and NSERC operating ....

C.B. Jay, "The structure of free closed categories", J. Pure Appl. Alg., 66 (1990) 271--285.

No context found.

Jay, C.B. "The structure of free closed categories", Journal of Pure and Applied Algebra 66 (1990) 271--285.

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