Geodesic
On the type correctness of polymorphic $\lambda$-terms. 1
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2009), pp. 42-51.

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In this paper polymorphic lambda terms are considered, where no type information is provided for the variables. The aim of this work is to extend the algorithm of typification [1] of such terms introducing type constants and term constants.
Keywords: type, skeleton, expansion, typing.
Mots-clés : term, constraint 
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A. H. Arakelyan. On the type correctness of polymorphic  $\lambda$-terms. 1. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2009), pp. 42-51. http://geodesic.mathdoc.fr/item/UZERU_2009_3_a6/

[1] S. Carlier, J.B. Wells, “Type Inference with Expansion Variables and Intersection Types in System E and an Exact Correspondence with $\beta$-reduction”, Proc. 6th Intl Conf. Principles $\$ Practice Declarative Programming, 2004

[2] R. Milner, “A theory of type polymorphism in programming”, Journal of Computer and System Sciences, 17 (1978), 348–375 | DOI | MR | Zbl

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[4] T. Jim, “What are Principal Typings and What are They Good for?”, Conf. Rec. POPL '96: 23rd ACM Symp. Princ. of Prog. Langs, 1996

[5] S. Carlier, J. Polakow, J.B. Wells, A.J. Kfoury, “System $E$: Expansion Variables for Flexible Typing with Linear and Non-linear Types and Intersection Types”, In Programming Languages $\$ Systems (13th European Symp. Programming), LNCS, 2986, Springer-Verlag, 2004 | Zbl

[6] H.P. Barendregt, The Lambda Calculus: Its Syntax and Semantics, North Holand, Amsterdam, 1981 | MR | Zbl