Abstract
Both (operational or denotational) semantics and type theories for λ-calculus induce in a natural way equivalence relations between terms. The aim of the present paper is to show that in some cases the semantic and functional equivalences coincide.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H. Barendregt, G. Longo, Equality of Lambda Terms and Recursion Theoretic Reducibility in the Model Tω, Preprint n. 107, University Utrecht, (1979).
C. Böhm, The CUCH as a Formal and Description Language, in Formal Language Description Languages for Computer Programming, ed. T.B. Steel, North-Holland, Amsterdam, (1966), 179–197.
C. Böhm, Alcune proprietà della forma β-η-normali del λ-ϰ-calcolo, Pubbl. IAC-CNR n. 696, Roma, (1968).
M. Coppo, M. Dezani-Ciancaglini, A New Type Assignment for λ-terms, in Archiv für Math. Logik und Grundlageforshung, 19, (1978), 1–17.
M. Coppo, M. Dezani-Ciancaglini, B. Venneri, Functional Characters of Solvable Terms, Internal Report, Turin University.
H.B. Curry, R. Feys, Combinatory Logic, Vol. 1, North-Holland, Amsterdam, (1968).
H.B. Curry, R. Hindley, J.P. Seldin, Combinatory Logic, 2, North-Holland, Amsterdam, (1972).
J.M.E. Hyland, A Survey of Some Useful Partial Order Relations on Terms of the λ-calculus in: λ-calculus and Computer Science Theory, ed. C. Böhm, Lecture Notes in Computer Science, 37, Springer-Verlag, (1975), 83–95.
J.M.E. Hyland, A Syntactic Characterization of the Equality in Some Models of the λ-calculus, J. London Math. Soc. 12 (2), (1976), 361–370.
J.H. Morris, λ-calculus Models of Programming Languages, Ph.D.thesis, MIT, Cambridge, (1968).
G. Plotkin, Tω as a Universal Domain, D.A.I. Research report N.28, University of Edinburgh, (1977).
G. Plotkin, A Set-Theoretical Definition of Application, School of A.I., Memo MIP-R-95, Edinburgh, (1972).
P. Sallé, Une Extension de la Théorie des Types en λ-calcul, in: Automata, Languages and Programming, ed. s G. Ausiello and C. Böhm, Lecture Notes in Computer Science, 62, (1978), 398–41.
P. Sallé, Une Generalisation de la Théorie des Types, to appear in R.A.I.R.O., Informatique Theorique.
D. Scott, Continous Lattices, Lecture Notes in Mathematics, in: Toposes, Algebraic Geometry and Logic, ed. F.W. Lawvere, n. 274, Springer-Verlag, (1972), 97–136.
D. Scott, Data Types as Lattices, SIAM J. Comput., Vol. 5, n. 3, (1976), 522–587.
C.P. Wadsworth, The Relation between Computational and Denotational Properties for Scott's D∞-Models of the λ-calculus, SIAM J. Comput., Vol. 5, n. 3, (1976), 488–521.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Coppo, M., Dezani-Ciancaglini, M., Salle', P. (1979). Functional characterization of some semantic equalities inside λ-calculus. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_11
Download citation
DOI: https://doi.org/10.1007/3-540-09510-1_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09510-1
Online ISBN: 978-3-540-35168-9
eBook Packages: Springer Book Archive