Skip to main content
SpringerLink
Log in

Limits, higher type computability and type-free languages

  • Invited Lectures
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1984 (MFCS 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 176))

  • 147 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Albano A., Cardelli L., Orsini R. (1983) "Galileo: a strongly typed, Interactive Conceptual Language" Tech. Note 30 C.S. Dept. Toronto (revised: Tech. rep. 83-11271-2, Bell Lab.).

    Google Scholar 

  • Barendregt H. (1978) "The type-free lambda-calculus" in Handbook of Math. Logic (Barwise ed.), North-Holland.

    Google Scholar 

  • Barendregt H. (1984) The lambda-calculus: its syntax and semantics (revised and expanded edition), North-Holland.

    Google Scholar 

  • Barendregt H., Coppo M., Dezani M. (1983) "A filter lambda model and the completeness of type assignement" J. Symb. Lcgic 48, 4, 931–940.

    Google Scholar 

  • Barendregt H., Longo G. (1980) "Equality of λ-terms in the model Tω" in To H.B. Curry: essays in Combinatory Logic, λ-calculus and formalism (Hindley, Seldin eds) Academic Press.

    Google Scholar 

  • Barendregt H., Longo G. (1982) "Recursion theoretic operators and morphisms of numbered sets" Fund. Math., CXIX, 49–62.

    Google Scholar 

  • Coppo M. (1983) "Completeness of Type Assignment in continuous lambdamodels" Teor. Comp. Sci. (to appear).

    Google Scholar 

  • Coppo M., Dezani M., Venneri B. (1981) "Functional character of solvable terms" ZML, 27, 45–58.

    Google Scholar 

  • Egli H., Constable R. (1976) "Computability concepts for programming languages semantics" Theor. Comp. Sci. 2, 133–145.

    Google Scholar 

  • Ershov Yu.L. (1972) "Computable functionals of finite type" Algebra and Logic 11, 4, 367–437.

    Google Scholar 

  • Ershov Yu.L. (1974) "Maximal and everywhere defined functionals" Algebra and Logic 13, 4, 374–397.

    Google Scholar 

  • Ershov Yu.L. (1976) "Model C of the continuous functionals" Logic Coll. 76 (Gandy, Hyland eds.), North-Holland.

    Google Scholar 

  • Gandy R., Hyland M. (1976) "Computable and recursively countable functions of higher type" Logic Coll. '76 (Gandy, Hyland eds), North-Holland.

    Google Scholar 

  • Gordon M. (1973) "Evaluation and denotation of pure LISP programs" Ph. D. Thesis, Edinburgh.

    Google Scholar 

  • Gordon M., Milner R., Wadsworth C. (1979) Edinburgh LCF LNCS-78, Springer-Verlag.

    Google Scholar 

  • Heller A. (1983) "Dominical Categories and Recursion Theory" Underground, New York.

    Google Scholar 

  • Hyland M. (1976) "The countable functionals" Underground, Oxford.

    Google Scholar 

  • Hyland M. (1979) "Filter spaces and the continuous functionals" Ann. Math. Logic 16, 101–143.

    Google Scholar 

  • Kanda A. (1980) "Fully effective solution of recursive domain equations" Ph. D. Thesis, Warwick.

    Google Scholar 

  • Kelley J. (1955) General topology Springer-Verlag.

    Google Scholar 

  • Kleene S.C. (1959) "Recursive functionals and quantifiers of finite type I" Trans. A.M.S. 91, 1–52.

    Google Scholar 

  • Kleene S.C. (1959a) "Countable functionals" in Constructivity in Mathematics (Heyting ed.), North-Holland.

    Google Scholar 

  • Kreisel G. (1959) "Interpretation of Analysis by means of functionals of finite type" in Constructivity in Mathematics (Heyting ed.), North-Holland.

    Google Scholar 

  • Kuratowski C. (1952) Topologie, vol. 1, Warsaw.

    Google Scholar 

  • Longo G. (1983) "Set-theoretical models of lambda-calculus: theories, expansions, isomorphisms" Ann. Pure Applied Logic (formerly: Ann. Math. Logic), 24, 153–188.

    Google Scholar 

  • Longo G. (1984) "Continuous structures and analytic methods in Computer Science" Proceedings CAAP (Courcelle ed.), Cambridge University Press.

    Google Scholar 

  • Longo G., Moggi E. (1983) "The Hereditary Effective Partial Functionals and Recursion Theory in Higher Types" J. Symb. Logic (to appear).

    Google Scholar 

  • Longo G., Moggi E. (1984 an) "Cartesian Closed Categories and partial morphisms for effective type structures I" Symp. Semantics Data Types LNCS, Springer-Verlag (to appear).

    Google Scholar 

  • Longo G., Moggi E. (1984 pr) "Gödel-numberings, principal morphisms, combinatory algebras" MFCS '84 (Chytil ed.) LNCS, Springer-Verlag.

    Google Scholar 

  • Mac Lane S. (1971) Categories for the Working Mathematician, Springer-Verlag.

    Google Scholar 

  • Milne R. (1974) "The formal semantics of computer languages and their implementations" Ph. D. Thesis, Cambridge.

    Google Scholar 

  • Moschavakis Y. (1963) "Recursive analysis" Ph. D. Dissertation, Madison.

    Google Scholar 

  • Normann D. (1980) Recursion on the countable functionals LNM 811, Springer-Verlag.

    Google Scholar 

  • Plotkin G. (1977) "LCF considered as a programming language" Theor. Comp. Sci. 5, 223–255.

    Google Scholar 

  • Plotkin G. (1980) "Lambda-definability in the full type hierarchy" in To H.B. Curry: essays... (Hindley, Seldin eds), Academic Press.

    Google Scholar 

  • Plotkin G., Smyth M. (1982) "The category-theoretic solution of recursive domain equations" C.S. Dept., Edinburgh.

    Google Scholar 

  • Rogers H. (1967) Theory of recursive functions and effective computability, McGraw-Hill.

    Google Scholar 

  • Ruggeri F. (1984) "Spazi di filtri ed operatori di Turing" Tesi di Laurea in Matematica, Pisa.

    Google Scholar 

  • Scarpellini B. (1971) "A model for bar recursion of higher types" Comp. Math. 23, 113–153.

    Google Scholar 

  • Scott D.S. (1969) "A theory of computable functions in higher types" Seminar Notes, University of Oxford.

    Google Scholar 

  • Scott D.S. (1970) "Outline of a mathematical theory of computation" IV Annual Princeton Conf. on Info. Syst. and Sci., 169–176.

    Google Scholar 

  • Scott D.S. (1976) "Data types as lattices" SIAM J. Comp., 5, 522–587.

    Google Scholar 

  • Scott D.S. (1982) "Some ordered sets in Computer Science" in Ordered sets (Rival ed.), Reidel.

    Google Scholar 

  • Spreen D. (1983) "Effective operators in a topological setting" Logic Coll. 83, LNM, Springer-Verlag (to appear).

    Google Scholar 

  • Statman R. (1980) "Completeness, invariance and lambda-definability" J. Symb. Logic (to appear).

    Google Scholar 

  • Steicher T. (1984) "A solution for the definability problem for deterministic domains" Inst. Math. J. Kepler Univ., Linz.

    Google Scholar 

  • Wand M. (1983) "Loops in Combinator-Based Compilers" Info. Contr. (to appear).

    Google Scholar 

  • Wand M. (1984) "A Types-as-Sets Semantics for Milner-Style Polymorphism" 11th ACM Symp. Principle of Progr. Lang..

    Google Scholar 

  • Weihrauch K., Schäfer G. (1983) "Admissible representation of effective cpo's" Theor. Comp. Sci. (to appear).

    Google Scholar 

  • Giannini P., Longo G. (1982) "Effectively given domains and lambda-calculus semantics" Info. Contr. (to appear).

    Google Scholar 

  • Longo G., Martini S. (1984) "Higher type computability, Pω and the completeness of type assignement" (Prelim. incomplete version: Proc. STACS, LNCS, Springer-Verlag).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. Informatica, Università di Pisa, Corso Italia 40, I-56100, Pisa

    G. Longo

Authors
  1. G. Longo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. P. Chytil V. Koubek

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Longo, G. (1984). Limits, higher type computability and type-free languages. In: Chytil, M.P., Koubek, V. (eds) Mathematical Foundations of Computer Science 1984. MFCS 1984. Lecture Notes in Computer Science, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030292

Download citation

  • DOI: https://doi.org/10.1007/BFb0030292

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13372-8

  • Online ISBN: 978-3-540-38929-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation