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Berry, G. “Stable models of the typed λ-calculi” ICALP, Springer-Verlag, LNCS 62, 1978 pp. 72–89
V. Breazu-Tannen and A. Meyer. “Lambda Calculus with Constrained Types” Abstract (1985)
A. Burroni. “Algèbres graphiques” Cahiers de Topologie et Geometrie Differentielle Volume XXII-3 1981
G. Cousineau, P.L. Curien and M. Mauny. “The Categorical Abstract Machine.” In Functional Programming Languages and Computer Architecture, Ed. J. P. Jouannaud, Springer-Verlag LNCS 201 (1985) 50–64.
T. Coquand, C. Gunter, G. Winskel. “Polymorphism and domain equations” Technical report Cambridge no 107.
P. L. Curien. “Categorical Combinators, Sequential Algorithms and Functional Programming.” Research Notes in Theoretical computer Science, Pitman (1986).
P. L. Curien “Categorical combinators for (existential) quantification” unpublished notes.
N.G. de Bruijn. “Lambda-Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem.” Indag. Math. 34,5 (1972), 381–392.
A. Church. “A formulation of the simple theory of types.” Journal of Symbolic Logic 5,1 (1940) 56–68.
P. Gabriel and F. Ulmer. “Lokal Präsentierbare Kategorien” Lecture Notes in Mathematics, Vol. 221 (Springer, Berlin).
R.O. Gandy. “On the axiom of extensionality-Part I.” J.S.L. 21 (1956).
J.Y. Girard. “Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieure.” Thèse d'Etat, Université Paris VII (1972).
J.Y. Girard. “The system F of variable types, fifteen years later” in TCS 86.
C. Gunter. “Profinite Solutions for Recursive Domain Equations” PhD thesis, CMU, (1985).
W. A. Howard. “The formulæ-as-types notion of construction.” Unpublished manuscript (1969). Reprinted in to H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Eds J. P. Seldin and J. R. Hindley, Academic Press (1980).
G. Huet. “Cartesian closed categories and Lambda-Calculus” in Combinators and functional programming languages Eds P.L. Curien, G. Cousineau et B. Robinet. LNCS 242
J.M.E. Hyland, P.T. Johnstone, A.M. Pitts. “Tripos theory.” Math. Proc. Camb. Phil. Soc. 88 (1980).
J. Lambek and P. J. Scott. “Introduction to higher order categorical logic” Cambridge studies in advanced mathematics, Cambridge University Press, 1986.
Lawvere. “Adjointness in foundations” Dialectica 23 (1969) 281–296.
P. Martin-Löf. “Intuitionistic Type Theory.” Bibliopolis (1982).
N. McCracken. “An investigation of a programming language with a polymorphic type structure.” Ph.D. Dissertation, Syracuse University (1979).
R. Paré, D. Schumacher. “Indexed Categories and Their Applications.” Springer-Verlag, Lecture Notes in Mathematics, 661.
M.B. Plotkin and G.D. Smyth. “The category-theoretic solution of recursive domain equations” SIAM J. COMPUT. Vol. 11, No 4, November 1982
D. Scott. “Relating Theories of the Lambda-Calculus.” in To H. B. Curry: Essays on Combinatory Logic, Lambda-calculus and Formalism, Eds. J. P. Seldin and J. R. Hindley, Academic Press (1980).
R.A.G. Seely. “Hyperdoctrines, natural deduction and the Beck condition” Zeitschrift für Mat. Logik und Grundlagen d. Math. 29 505–542.
R.A.G Seely. “Locally Cartesian Closed Categories and Type Theory” Math. Proc. Camb. Phil. Soc. 95, 1984.
R.A.G. Seely. “Categorical Semantics for Higher Order Polymorphic Lambda Calculus” Draft.
J.E. Stoy. “Denotational Semantics: the Scott-Strache Approach to the Programming Language Theory” The M.I.T. Press, Cambridge, Massachussetts, and London, England.
G. Takeuti. “Proof theory.” Studies in Logic 81 Amsterdam (1975).
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Coquand, T., Ehrhard, T. (1987). An equational presentation of higher order logic. In: Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds) Category Theory and Computer Science. Lecture Notes in Computer Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18508-9_19
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