References
Abramsky, S., 'Computational interpretations of linear logic', Theoretical Computer Science 111, 1993, 3-57.
Babaev, A., 'Equality of canonical maps in closed categories' (Russian), Izvestija Azerb. Akad. Nauk, Ser. matern., 1996, N6.
Benton, N., G. Bierman, V. de Paiva and M. Hyland, 'Linear lambda-calculus and categorical models revisited', Springer LNCS 702, 61-84, 1993.
Barendregt, H., The Lambda Calculus, Amsterdam, North-Holland, 1981.
Cervesato, I., and F. Pfenning, 'A linear logical framework', LICS 96, 264-275.
Curry, H., R. Feys and W. Craig, Combinatory Logic, Amsterdam, North-Holland, 1958.
Gentzen, G., 'Untersuchungen über das logische Schliessen', Mathematische Zeitschrift 39, 1934, 176-210, 405–431.
Girard, J.-Y., 'Linear logic', Theoretical Computer Science 50, 1987, 1-102.
Herbelin, H., 'A λ-calculus structure isomorphic to Gentzen-style sequent structure', CSL 94, 61-75.
Howard, W., 'The Formulae-as-types notion of construction', in H. B. Curry, Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, 1980, 479-490.
Kleene, S. C., 'Permutability of inferences in Gentzen's calculi LK and LJ', Memoirs of the AMS, no 10, 1952, 1-26.
Kelly, G. M., and S. MacLane, 'Coherence in closed categories', Journal of Pure and Applied Algebra 1, 1971, 97-140.
Lincoln, P., and J. Mitchell, 'Operational aspects of linear lambda calculus', Proc. IEEE Symp. on Logic in Computer Science, 1992, 235-247.
Lamarche, F., 'Game semantics for full propositional linear logic', Proc. IEEE Symp. on Logic in Computer Science, 1995, 464-473.
Mints, G., 'Closed categories and the theory of proofs', J. Soviet Mathematics 15, 1981, 45-62, [21] 183–212 (Russian original 1977).
Mints, G., Normal Forms of Sequent Derivations, CSLI Technical Report No. CSLI-94-193, 1994.
Mints, G., 'Normal forms for sequent derivations', Kreiseliana, A. K. Peters, 1996, 469-492.
Mints, G., Normal Deduction in the Intuitionistic Linear Logic, CSLI report CSLI-95-50, 1995, to be published in Archive for Mathematical Logic.
Mints, G., 'On E-theorems', in [21], 1992, 105-116 (Russian original 1974).
Mints, G., 'Finite investigations of transfinite derivations', J. Soviet Mathematics 10, 1978, 548-596, [21], 17–72 (Russian original 1975)
Mints, G., Selected Papers in Proof Theory, North-Holland-Bibliopolis, 1992.
Mints, G., Review of [23], Referativnyi Zhurnal Matematika 10, 1978, 10A26 (Russian).
Pottinger, H., 'Normalization as a homomorphic image of cutelimination', Annals of Pure and Applied Logic 12, 1977, 323-357.
Prawitz, D., Natural Deduction, Almquist and Wiksell, 1965.
Ronchi della Rocca, S., and L. Roversi, 'Lambda calculus and intuitionistic linear logic' (manuscript).
Troelstra, A., and D. van Dalen, Constructivism in Mathematics, An Introduction, vol. 2, 1988, North-Holland.
Troelstra, A., 'Natural deductions for intuitionistic linear logic', APAL 73,no. 1, 1995, 79-108.
Troelstra, A., Mathematical Investigation of Intuitionistic Arithmetic and Analysis, Springer Lecture Notes in Mathematics, vol. 344, 1973.
Valentini, S., 'The judgement calculus for intuitionistic linear logic: proof theory and semantics', Zeitschrift f. math. Log. 38,no. 1, 1992, 38-58.
Zucker, J., 'The correspondence between cut elimination and normalization', Annals of Pure and Applied Logic 7, 1974, 1-156.
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Mints, G. Linear Lambda-Terms and Natural Deduction. Studia Logica 60, 209–231 (1998). https://doi.org/10.1023/A:1005016206457
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DOI: https://doi.org/10.1023/A:1005016206457