Abstract
This paper discusses the problem of finding common instances to terms in typed λ-calculus. It is shown that here the notion of most general unifier must be extended. Complete sets of unifiers are defined, and their structure with respect to substitution composition is studied.
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Bibliography
Andrews P.B., (1971): “ Resolution in type theory”. Journal of Symbolic Logic 36, 3 pp. 414–432.
Church A. (1940): “A formulation of the simple theory of types” Journal of Symbolic Logic 5,1 pp. 56–68.
Church A. (1941): “The calculi of lambda-conversion”. Annals of Mathematical Studies n∘6. Princeton University Press.
Curry H.B., Feys R., Craig W. (1958): Combinatory Logic, vol 1, North Holland.
Darlington J.L., (1971): “A partial mechanization of second-order logic”. Machine Intelligence 6, pp. 91–100. American Elsevier, New York.
Darlington J.L. (1973): “Automatic program synthesis in second-order logic”. Proceedings 3rd IJCAI, Stanford August 73.
Ernst G.W. (1971): “A matching procedure for type theory”. Personal communication.
Gould W.E. (1966): “A matching procedure for ω-order logic”. Scientific report n∘4, AFCRL 666-781. Contrat AF 19(628)-3250.AD 646-560.
Guard J.R. (1964): “Automated logic for semi-automated mathematics”. Scientific report n∘1, AFCRL-64-411. Contrat AF 19(628)-3250. AD 602 710.
Huet G.P. (1973): “The undecidability of unification in third order logic”. Information and Control 22,3 pp. 257–267.
Huet G.P. (1973): “A mechanization of type theory”. Proceedings of 3rd IJCAI, Stanford August 73.
Huet G.P. (1975): “A unification algorithm for typed λ-calculus”. Theoretical Computer Science 1,1.
Lucchesi C.L. (1972): “The undecidability of the unification problem for third order languages”. Report CSRR 2059, Dept. of Applied Analysis and Computer Science. University of Waterloo.
Pietrzykowski T. (1971): “A complete mechanization of second order logic”. Journal of Assoc. for Comp. Mach. 20,2 pp. 333–364.
Pietrzykowski T. and Jensen D. (1972): “ A complete mechanization of ω-order type theory”. Association for computing Machinery National Conference 1972, vol.1, pp. 82–92.
Plotkin G.D. (1972): “Building-in equational theories”. Machine Intelligence 7, pp. 73–90. American Elsevier. New York.
Robinson J.A. (1965): “A machine-oriented logic based on the resolution principle”. Journal of Assoc. for Comp. Mach. 12,1, pp.23–41.
Sanchis L.E. (1967): “Functionals defined by recursion”. Notre Dame Journal of Formal Logic VIII, 3 pp. 161–174.
Jensen D. & Pietrzykowski T. (1973): “Mechanizing ω-order type theory through unification”. Report CS-73-16, Dept. of Applied Analysis and Computer Science, University of Waterloo.
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© 1975 Springer-Verlag Berlin Heidelberg
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Huet, G. (1975). Unification in typed lambda calculus. In: Böhm, C. (eds) λ-Calculus and Computer Science Theory. LCCST 1975. Lecture Notes in Computer Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029526
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DOI: https://doi.org/10.1007/BFb0029526
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