A Parigot-style linear λ-calculus for Full Intuitionistic Linear Logic

Theory and Applications of Categories

Volumn 17, Issue , 2006, Pages 30-48

  De Paiva, Valeria ^a   Ritter, Eike ^b  

^a PALO ALTO RESEARCH CENTER   (United States)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

calculus; Curry howard isomorphism; Linear logic

Indexed keywords

EID: 33846524198     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. M. Barr. The Chu construction. Theory and Applications of Categories, 2:17-35, 1996.
2. Torben Braüner and Valeria de Paiva. A formulation of linear logic based on dependency-relations. In Proc. of Computer Science Logic '97, Lecture Notes in Computer Science. Springer Verlag, 1998.
3. G. Bierman. A classical linear lambda calculus. Theoretical Computer Science, 227(1-2):43-78, 1999.
4. T. Crolard. A formulae-as-types interpretation of subtractive logic. Journal of Logic and Computation, 14(4):529-570, 2004.
5. J.R.B. Cockett and R.A.G. Seely. Weakly distributive categories. Journal of Pure and Applied Algebra, 114(2):133-173, 1997.
6. V.C.V de Paiva. A dialectica-like model of linear logic. In David H. Pitt, David E. Rydeheard, Peter Dybjer, Andrew M. Pitts, and Axel Poigné, editors, Category Theory and Computer Science, volume 389 of Lecture Notes in Computer Science. Springer, 1989.
7. M. Dummett. Elements of Intuitionism. OUP, Oxford, 1980.
8. G. Gentzen. Untersuchungen über das logische Schließen. Mathematische Zeitschrift, pages 176-210, 405-431., 1935.
9. J.-Y. Girard. Linear logic: its syntax and semantics. In J.-Y. Girard, Y. Lafont, and L. Regnier, editors, Advances in Linear Logic, pages 1-42. Cambridge University Press, 1995. London Mathematical Society Lecture Note Series 222, Proceedings of the 1993 Workshop on Linear Logic, Cornell Univesity, Ithaca.
10. M. Hyland and V. de Paiva. Full intuitionistic linear logic (extended abstract). Annals of Pure and Applied Logic, 64(3):273-291, 1993.
11. M. Parigot. λμ-calculus: an algorithmic interpretation of classical natural deduction. In Proc. Logic Progr. and Automatic Reasoning, St. Petersburg, pages 190-201. Lecture Notes in Computer Science No. 624, Berlin, Heidelberg, New York, 1992.
12. V. Pratt. Chu spaces as a semantic bridge between linear logic and mathematics,. Theoretical Computer Science, 294:439-471, 2003.
13. E. Ritter and D. Pym. On the semantics of classical disjunction. Journal of Pure and Applied Algebra, 159:315-338, 2001.
14. E. Ritter, D. Pym, and L. A. Wallen. On the intuitionistic force of classical search. Journal of Logic and Computation, 10(2):173-207, 2000.
15. E. Ritter, D. Pym, and L.A. Wallen. Proof-terms for classical and intuitionistic logic. Theoretical Computer Science, 232(1-2):299-333, 2000.