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Volumn 33, Issue 2, 1998, Pages 149-200

Lambda Abstraction Algebras: Coordinatizing Models of Lambda Calculus

Author keywords

Abstract substitution; Combinatory algebras; Cylindric algebras; Lambda algebras; Lambda calculus; Lambda models; Polyadic algebras; Representation theorems

Indexed keywords


EID: 0004121529     PISSN: 01692968     EISSN: None     Source Type: Journal    
DOI: 10.3233/fi-1998-33203     Document Type: Article
Times cited : (18)

References (46)
  • 2
    • 0348145471 scopus 로고
    • Research Report No. C-49, Dept. of Information Sciences, Tokio Institute of Technology
    • Adachi, T.: "A categorical characterization of lambda calculus models", Research Report No. C-49, Dept. of Information Sciences, Tokio Institute of Technology, 1983.
    • (1983) A Categorical Characterization of Lambda Calculus Models
    • Adachi, T.1
  • 5
    • 0000259875 scopus 로고
    • A set of postulates for the foundation of logic
    • Church, A.: "A set of postulates for the foundation of logic", Annals of Math., 2, 1933, 346-366.
    • (1933) Annals of Math. , vol.2 , pp. 346-366
    • Church, A.1
  • 8
    • 0347931169 scopus 로고
    • Amsterdam: North-Holland Publishing Co.
    • Curry, H. B. and Feys, R.: Combinatory Logic, Vol. I, Amsterdam: North-Holland Publishing Co., 1958.
    • (1958) Combinatory Logic , vol.1
    • Curry, H.B.1    Feys, R.2
  • 9
    • 0347301105 scopus 로고    scopus 로고
    • Frame Inform. Systems, University of Latvia, Preprint
    • Diskin, Z. B.: "Lambda term systems" Frame Inform. Systems, University of Latvia, Preprint.
    • Lambda Term Systems
    • Diskin, Z.B.1
  • 11
    • 0011848501 scopus 로고
    • Axiomatization of polynomial substitution algebras
    • Feldman, N.: "Axiomatization of polynomial substitution algebras", J. Symbolic Logic, 47, 1982, 481-492.
    • (1982) J. Symbolic Logic , vol.47 , pp. 481-492
    • Feldman, N.1
  • 12
    • 0347515597 scopus 로고
    • Representation of substitution algebras
    • Feldman, N.: "Representation of substitution algebras" (abstract), J. Symbolic Logic, 49, 1984, 677-678.
    • (1984) J. Symbolic Logic , vol.49 , pp. 677-678
    • Feldman, N.1
  • 13
    • 0346039646 scopus 로고    scopus 로고
    • The functional lambda abstraction algebras form a variety
    • D. S. Bridges, C. S. Calude, J. Gibbons, S. Reeves and I. Witten (eds.), Universities of Auckland and Waikato, Springer-Verlag, Singapore
    • Goldblatt, R.: "The functional lambda abstraction algebras form a variety". D. S. Bridges, C. S. Calude, J. Gibbons, S. Reeves and I. Witten (eds.), DMTCS'96, First Conference of the Centre for Discrete Mathematics and Theoretical Computer Science, Universities of Auckland and Waikato, Springer-Verlag, Singapore, 1996.
    • (1996) DMTCS'96, First Conference of the Centre for Discrete Mathematics and Theoretical Computer Science
    • Goldblatt, R.1
  • 14
    • 0347301106 scopus 로고    scopus 로고
    • Enlargements of functional algebras for the lambda calculus
    • Research Report 96-187, Mathematics Department, Victoria University of Wellington, To appear
    • Goldblatt, R.: "Enlargements of functional algebras for the lambda calculus", Research Report 96-187, Mathematics Department, Victoria University of Wellington, 1996, Theoret. Comp. Sci., To appear.
    • (1996) Theoret. Comp. Sci.
    • Goldblatt, R.1
  • 16
    • 0346254663 scopus 로고
    • Homogeneous locally finite polyadic Boolean algebras of infinite degree
    • Halmos, P.: "Homogeneous locally finite polyadic Boolean algebras of infinite degree", Fund. Math., 43, 1956, 255-325.
    • (1956) Fund. Math. , vol.43 , pp. 255-325
    • Halmos, P.1
  • 17
    • 0004049604 scopus 로고
    • New York: Chelsea Publishing Co.
    • Halmos, P.: Algebraic Logic, New York: Chelsea Publishing Co., 1962.
    • (1962) Algebraic Logic
    • Halmos, P.1
  • 22
    • 0347515596 scopus 로고
    • Transformation algebras
    • LeBlanc, L.: "Transformation algebras", Canad. J. Math., 13, 1961, 602-613.
    • (1961) Canad. J. Math. , vol.13 , pp. 602-613
    • LeBlanc, L.1
  • 23
    • 0019342627 scopus 로고
    • What is a model of the lambda calculus?
    • Meyer, A. R.: "What is a model of the lambda calculus?", Inform. Control, 52, 1982, 87-122.
    • (1982) Inform. Control , vol.52 , pp. 87-122
    • Meyer, A.R.1
  • 24
    • 0001438888 scopus 로고
    • Algebraizations of quantifier logics. An introductory overview
    • Extended version available as Math. Inst. Budapest, Preprint 1996, 86pp
    • Németi, I.: "Algebraizations of quantifier logics. An introductory overview", Studia Logica, 50, 1991, 485-569. (Extended version available as Math. Inst. Budapest, Preprint 1996, 86pp.)
    • (1991) Studia Logica , vol.50 , pp. 485-569
    • Németi, I.1
  • 25
    • 0038907120 scopus 로고    scopus 로고
    • Strong representability of fork algebras, a set theoretic foundation
    • To appear. Math. Inst. Hungar. Acad. Sci., Preprint
    • Németi, I.: "Strong representability of fork algebras, a set theoretic foundation", J. IGPL. To appear. (Math. Inst. Hungar. Acad. Sci., 1996. Preprint.)
    • (1996) J. IGPL.
    • Németi, I.1
  • 26
    • 84896541191 scopus 로고    scopus 로고
    • Ontology can turn negative results to positive
    • Németi, I.: "Ontology can turn negative results to positive", Bull. Sect. Logic, 25, 1996, 29-40.
    • (1996) Bull. Sect. Logic , vol.25 , pp. 29-40
    • Németi, I.1
  • 28
    • 0346884950 scopus 로고
    • Categorical, functorial, and algebraic aspects of the type-free lambda calculus
    • T. Traczyk (ed.), Banach Center Publications, PWD-Polish Scientific Pub., Warsaw
    • Obtulowicz, A. and Wiweger, A.: "Categorical, functorial, and algebraic aspects of the type-free lambda calculus". T. Traczyk (ed.), Universal algebra and applications, Banach Center Publications, vol. 9, PWD-Polish Scientific Pub., Warsaw, 1982.
    • (1982) Universal Algebra and Applications , vol.9
    • Obtulowicz, A.1    Wiweger, A.2
  • 29
    • 0041903326 scopus 로고
    • An introduction to lambda abstraction algebras
    • M. Abad (ed.), UNMABB-CONICET, Bahia Blanca, Argentina
    • Pigozzi, D. and Salibra, A.: "An introduction to lambda abstraction algebras". M. Abad (ed.), Proc. IX Latin American Symposium on Mathematica Logic (Part 1), UNMABB-CONICET, Bahia Blanca, Argentina, 1993, 93-113. (Notas de Logica Matematica, No. 38, Universidad Nacional del Sur, Bahia Blanca, Argentina.)
    • (1993) Proc. IX Latin American Symposium on Mathematica Logic (Part 1) , pp. 93-113
    • Pigozzi, D.1    Salibra, A.2
  • 30
    • 0346039651 scopus 로고    scopus 로고
    • Universidad Nacional del Sur, Bahia Blanca, Argentina
    • Pigozzi, D. and Salibra, A.: "An introduction to lambda abstraction algebras". M. Abad (ed.), Proc. IX Latin American Symposium on Mathematica Logic (Part 1), UNMABB- CONICET, Bahia Blanca, Argentina, 1993, 93-113. (Notas de Logica Matematica, No. 38, Universidad Nacional del Sur, Bahia Blanca, Argentina.)
    • Notas de Logica Matematica , vol.38
  • 32
    • 0346039652 scopus 로고
    • Springer-Verlag, London
    • Pigozzi, D. and Salibra, A.: "Dimension-complemented lambda abstraction algebras". M. Nivat, C. Rattray, T. Rus and G. Scollo (eds.), Algebraic Methodology and Software Technology (AMAST'93) (Proc. 3rd International Conference on Algebraic Methodology and Software Technology), University of Twente, The Netherlands, 21-25 June, 1993, 131- 138. (Workshops in Computing, Springer-Verlag, London, 1993.)
    • (1993) Workshops in Computing
  • 33
    • 0348094590 scopus 로고
    • A representation theorem for lambda abstraction algebras
    • A. M. Borzyszkowski and S. Sokolowski (eds.)
    • Pigozzi, D. and Salibra, A.: "A representation theorem for lambda abstraction algebras". A. M. Borzyszkowski and S. Sokolowski (eds.), Proc. 18th International Symposium on Mathematical Foundations of Computer Science, 1993, 629-639. (Lecture Notes in Computer Science, No. 711, Springer-Verlag, Berlin.)
    • (1993) Proc. 18th International Symposium on Mathematical Foundations of Computer Science , pp. 629-639
    • Pigozzi, D.1    Salibra, A.2
  • 34
    • 84864840163 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin
    • Pigozzi, D. and Salibra, A.: "A representation theorem for lambda abstraction algebras". A. M. Borzyszkowski and S. Sokolowski (eds.), Proc. 18th International Symposium on Mathematical Foundations of Computer Science, 1993, 629-639. (Lecture Notes in Computer Science, No. 711, Springer-Verlag, Berlin.)
    • Lecture Notes in Computer Science , vol.711
  • 35
    • 0029267648 scopus 로고
    • Lambda abstraction algebras: Representation theorems
    • Pigozzi, D. and Salibra, A.: "Lambda abstraction algebras: representation theorems", Theoret. Comp. Sci., 140, 1995, 5-52.
    • (1995) Theoret. Comp. Sci. , vol.140 , pp. 5-52
    • Pigozzi, D.1    Salibra, A.2
  • 36
    • 0004150345 scopus 로고
    • The abstract variable-binding calculus
    • Pigozzi, D. and Salibra, A.: "The abstract variable-binding calculus", Studia Logica, 55, 1995, 129-179.
    • (1995) Studia Logica , vol.55 , pp. 129-179
    • Pigozzi, D.1    Salibra, A.2
  • 37
    • 84968496705 scopus 로고
    • Cylindric algebras and algebras of substitution
    • Pinter, C.: "Cylindric algebras and algebras of substitution", Trans. Amer. Math. Soc., 175, 1973, 167-179.
    • (1973) Trans. Amer. Math. Soc. , vol.175 , pp. 167-179
    • Pinter, C.1
  • 38
    • 0040472969 scopus 로고
    • On the problem of finitizing first order logic and its algebraic counterpart. (A survey of results and methods.)
    • L. Csirmaz, D. M. Gabbay and M. de Rijke (eds.), CSLI Publishing, Stanford
    • Sain, I.: "On the problem of finitizing first order logic and its algebraic counterpart. (A survey of results and methods.)". L. Csirmaz, D. M. Gabbay and M. de Rijke (eds.), Logic Colloqium 1992, CSLI Publishing, Stanford, 1995.
    • (1995) Logic Colloqium 1992
    • Sain, I.1
  • 39
    • 0346039650 scopus 로고
    • On the search for a finitizable algebraization of first order logic (Shortened version A)
    • Preprint
    • Sain, I.: "On the search for a finitizable algebraization of first order logic (Shortened version A)", Math. Inst. Hungar. Acad. Sci., 1988. (Preprint.)
    • (1988) Math. Inst. Hungar. Acad. Sci.
    • Sain, I.1
  • 40
    • 0347931160 scopus 로고
    • Finite schematazible algebraic logic
    • (Preprint.) (To appear in J. IGPL.)
    • Sain, I. and Gyuris, V.: "Finite schematazible algebraic logic", Math. Inst. Hungar. Acad. Sci., 1995. (Preprint.) (To appear in J. IGPL.)
    • (1995) Math. Inst. Hungar. Acad. Sci.
    • Sain, I.1    Gyuris, V.2
  • 41
    • 0342603327 scopus 로고
    • A general theory of algebras with quantifiers
    • H. Andréka, J. D. Monk and I. Németi (eds.), Colloq. Math. Soc. J. Bolyai, North-Holland Publishing Co., Amsterdam
    • Salibra, A.: "A general theory of algebras with quantifiers". H. Andréka, J. D. Monk and I. Németi (eds.), Algebraic Logic (Proc. Conf. Budapest 1988), Colloq. Math. Soc. J. Bolyai, Vol. 54, North-Holland Publishing Co., Amsterdam, 1991, 573-620.
    • (1991) Algebraic Logic (Proc. Conf. Budapest 1988) , vol.54 , pp. 573-620
    • Salibra, A.1
  • 42
    • 0346884948 scopus 로고    scopus 로고
    • Research Report 97-210, Mathematics Department, Victoria University of Wellington
    • Salibra, A.: "On the algebraic models of lambda calculus", Research Report 97-210, Mathematics Department, Victoria University of Wellington, 1997.
    • (1997) On the Algebraic Models of Lambda Calculus
    • Salibra, A.1
  • 45
    • 0000889413 scopus 로고
    • Data types as lattices
    • Scott, D. S.: "Data types as lattices", SIAM J. Computing, 5, 1976, 522-587.
    • (1976) SIAM J. Computing , vol.5 , pp. 522-587
    • Scott, D.S.1
  • 46
    • 33750710624 scopus 로고
    • Lambda calculus: Some models, some philosophy
    • J. Barwise, H. J. Keisler and K. Kunen (eds.), North-Holland Publishing Co., Amsterdam
    • Scott, D. S.: "Lambda calculus: some models, some philosophy". J. Barwise, H. J. Keisler and K. Kunen (eds.), The Kleene Symposium, Studies in Logic, No. 101, North-Holland Publishing Co., Amsterdam, 1980.
    • (1980) The Kleene Symposium, Studies in Logic , vol.101
    • Scott, D.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.