[Bar84]

H. P. Barendregt. *The Lambda Calculus: Its Syntax and Semantics*, volume 103 of *Studies in Logic and the Foundations of Mathematics*. North-Holland, Amsterdam, revised edition, 1984.

[BL84]

R. Burstall and Butler Lampson. A kernel language for abstract data types and modules. In G. Kahn, D. MacQueen, and G. Plotkin, editors, *Semantics of Data Types*, volume 173 of *Lecture Notes in Computer Science*, pages 1–50. Springer-Verlag, 1984.

[Car]

Luca Cardelli. Phase distinctions in type theory. unpublished manuscript.

[Car86]

Luca Cardelli. A polymorphic λ-calculus with Type:Type. Technical report, DEC SRC, 1986.

[CDD+85]

D. Clément, J. Despeyroux, T. Despeyroux, L. Hascoet, and G. Kahn. Natural semantics on the computer. Technical Report RR 416, INRIA, Sophia-Antipolis, France, June 1985.

Google Scholar[CDDK86]

D. Clément, J. Despeyroux, T. Despeyroux, and G. Kahn. A simple applicative language: Mini-ML. In *Proceedings of the Conference on Lisp and Functional Programming*, 1986.

[CH85]

Thierry Coquand and Gérard Huet. Constructions: a higher-order proof system for mechanizing mathematics. In B. Buchberger, editor, *EUROCAL '85: European Conference on Computer Algebra*, volume 203 of *Lecture Notes in Computer Science*, pages 151–184. Springer-Verlag, 1985.

[Cha77]

Tat-Hung Chan. An algorithm for checking PL/CV arithmetical inferences. Technical Report 77-236, Computer Science Department, University, Ithaca, New York, 1977.

Google Scholar[Chu40]

Alonzo Church. A formulation of the simple theory of types.

*Journal of Symbolic Logic*, 5:56–68, 1940.

Google Scholar[Con86]

Robert L. Constable,

*et al. Implementing Mathematics with the NuPRL Proof Development System*. Prentice-Hall, Englewood Cliffs, NJ, 1986.

Google Scholar[Coq85]

Thierry Coquand. *Une théorie des constructions*. PhD thesis, Université Paris VII, January 1985.

[Coq86]

Thierry Coquand. An analysis of Girard's paradox. In *Proc. of the Symposium on Logic in Computer Science*, pages 227–236, Boston, June 1986.

[Coq88]

Thierry Coquand. Private communication.

[CZ82]

Robert L. Constable and Daniel R. Zlatin. Report on the type theory (V3) of the programming logic PL/CV3. In *Logics of Programs*, volume 131 of *Lecture Notes in Computer Science*. Springer-Verlag, 1982.

[CZ84]

Robert L. Constable and Daniel R. Zlatin. The type theory of PL/CV3.

*ACM Transactions on Programming Languages and Systems*, 7(1):72–93, January 1984.

Google Scholar[Des84]

T. Despeyroux. Executable specifications of static semantics. In G. Kahn, D. MacQueen, and G. Plotkin, editors, *Semantics of Data Types*, volume 173 of *Lecture Notes in Computer Science*. Springer-Verlag, June 1984.

[DM82]

Luis Damas and Robin Milner. Principal type schemes for functional programs. In *Proceedings of the 9th ACM Symposium on the Principles of Programming Languages*, pages 207–212, 1982.

[Erh88]

Thomas Erhard. A categorical semantics of Constructions. In *Proceedings of the Third Annual Symposium on Logic in Computer Science*, pages 264–273, Edinburgh, July 1988.

[GdR88]

Paola Giannini and Simona Ronchi della Rocca. Characterization of typings in polymorphic type discipline. In *Proceedings of the Third Annual Symposium on Logic in Computer Science*, pages 61–71, July 1988.

[HH86]

James G. Hook and Douglas Howe. Impredicative strong existential equivalent to Type:Type. Technical Report TR 86–760, Cornell University, Ithaca, New York, 1986.

Google Scholar[HMT87]

Robert Harper, Robin Milner, and Mads Tofte. A type discipline for program modules. In *TAPSOFT '87*, volume 250 of *Lecture Notes in Computer Science*. Springer-Verlag, March 1987.

[HMT88]

Robert Harper, Robin Milner, and Mads Tofte. The definition of Standard ML (version 2). Technical Report ECS-LFCS-88-62, Laboratory for the Foundations of Computer Science, Edinburgh University, August 1988.

[How87]

Douglas Howe. The computational behavior of Girard's paradox. In *Proceedings of the Second Symposium on Logic in Computer Science*, pages 205–214, Ithaca, New York, June 1987.

[HP88]

J. Martin E. Hyland and Andrew M. Pitts. The Theory of Constructions: categorical semantics and topos-theoretic models. In *Proceedings of the Boulder Conference on Categories in Computer Science*, 1988. To appear.

[Hue87]

Gérard Huet. Extending the Calculus of Constructions with Type:Type. unpublished manuscript, April 1987.

[Luo88a]

Zhaolui Luo. A higher-order calculus and theory abstraction. Technical Report ECS-LFCS-88-57, Laboratory for the Foundations of Computer Science, Edinburgh University, July 1988.

[Luo88b]

Zhaolui Luo. _{∞}^{⊂} and its metatheory. Technical Report ECS-LFCS-88-58, Laboratory for the Foundations of Computer Science, Edinburgh University, July 1988.

[Mac86]

David MacQueen. Using dependent types to express modular structure. In *Proceedings of the 13th ACM Symposium on the Principles of Programming Languages*, 1986.

[Mar]

Per Martin-Löf. A theory of types. Unpublished manuscript.

[Mar73]

Per Martin-Löf. An intuitionistic theory of types: predicative part. In H. E. Rose and J. C. Shepherdson, editors, *Logic Colloquium, '73*, pages 73–118, Amsterdam, 1973. North-Holland.

[Mar82]

Per Martin-Löf. Constructive mathematics and computer programming. In *Sixth International Congress for Logic, Methodology, and Philosophy of Science*, pages 153–175, Amsterdam, 1982. North-Holland.

[Mar84]

Per Martin-Löf. *Intuitionistic Type Theory*, volume 1 of *Studies in Proof Theory*. Bibliopolis, Naples, 1984.

[MH88]

John Mitchell and Robert Harper. The essence of ML. In *Proceedings of the Fifteenth ACM Symposium on Principles of Programming Languages*, San Diego, California, January 1988.

[Mit84]

John C. Mitchell. Type inference and type containment. In G. Kahn, D. MacQueen, and G. Plotkin, editors, *Semantics of Data Types*, volume 173 of *Lecture Notes in Computer Science*, pages 257–278. Springer-Verlag, 1984.

[MP85]

John C. Mitchell and Gordon Plotkin. Abstract types have existential type. In *Proceedings of the 12th ACM Symposium on the Principles of Programming Languages*, 1985.

[MR86]

Albert Meyer and Mark Reinhold. ‘Type’ is not a type: preliminary report. In *Proceedings of the 13th ACM Symposium on the Principles of Programming Languages*, 1986.

[Pol88]

Robert Pollack. The theory of lego. Technical report, Laboratory for the Foundations of Computer Science, Edinburgh University, 1988. To appear.

[Rus08]

Bertrand Russell. Mathematical logic as based on a theory of types.

*American Journal of Mathematics*, 30:222–262, 1908.

Google Scholar[vD80]

Diedrik T. van Daalen.

*The Language Theory of AUTOMATH*. PhD thesis, Technical University of Eindhoven, Eindhoven, Netherlands, 1980.

Google Scholar[WR25]

Alfred North Whitehead and Bertrand Russell.

*Principia Mathematica, Volume 1*. Cambridge University Press, Cambridge, 1925.

Google Scholar