Advertisement

A survey of some syntactic results in the λ-calculus

  • Gérard Berry
  • Jean-Jacques Lévy
Appendix
Part of the Lecture Notes in Computer Science book series (LNCS, volume 74)

Keywords

Normal Form Final Expression Combinatory Logic Parallel Reduction Standard Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [Ba1]
    Barendregt H.,Some extensional terms models for combinatory logics and lambdacalculi,PhD Thesis,Utrecht,1971.Google Scholar
  2. [Ba2]
    Barendregt H.,The lambda-calculus,Its syntax and semantics,North-Holland,Amsterdam,to appear.Google Scholar
  3. [Ba3]
    Barendregt H.,Longo G.,Equality of lambda terms and recursion theoretic reducibility in the model Tω,University of Utrecht,Math.report no107,1979.Google Scholar
  4. [Be1]
    Berry G.,Séquentialité de l'évaluation formelle des lambda-expressions,3ème Colloque international sur la programmation,Paris,1978,Dunod éditeur.Rapport IRIA-LABORIA no304.Google Scholar
  5. [Be2]
    Berry G.,Stable models of typed lambda-calculi,5thICALP Conf.,Udine,1978.Springer Verlag LNCS no62,p.72–90.Google Scholar
  6. [Be3]
    Berry G.,Modèles complètement adéquats et stables des lambda-calculs typés, University of Paris 7,Thèse d'état,1979.Google Scholar
  7. [Be4]
    Berry G.,Lévy J-J.,Minimal and optimal computations of recursive programs,JACM,vol 26,no1,Jan 1979,p.148–175.CrossRefGoogle Scholar
  8. [Bo1]
    Bohm C., Alcune proprieta della forme βη-normali del λβ κ-calcolo,Publicazioni dell' istituto per le applicazioni del calcolo,no696,Rome,1968.Google Scholar
  9. [Bo]
    Boudol G.,Sur la sémantique des shémas de programmes récursifs non-déterministes,1stcolloque AFCET-SMF de mathématiques appliquées,Ecole polytechnique,Palaiseau,1978.Google Scholar
  10. [Ch1]
    Church A.,The calculi of lambda-conversions,Annals of Math.Studies no6,Princeton University Press,1941.Google Scholar
  11. [Cu1]
    Curry H.B.,Feys R.,Combinatory logic,Vol 1,North-Holland,1958.Google Scholar
  12. [Cu2]
    Curien P-L.,Algorithmes séquentiels sur structures de données concrètes,Thèse de 3ème cycle,University of Paris 7,1979.Google Scholar
  13. [Hi1]
    Hindley R.,Reductions of residuals are finite,Transactions of american math.soc.,vol 240,Jun 1978.Google Scholar
  14. [Hu1]
    Huet G.,Confluent reductions:Abstract properties and applications to term rewriting systems,18th FOCS Conf.,1977.Google Scholar
  15. [Hu2]
    Huet G.,Lévy J-J.,Computations in non-ambiguous linear term rewriting systems,to appear as IRIA-LABORIA report,1979.Google Scholar
  16. [Hy1]
    Hyland M.,A syntactic characterisation of equality in some models of the lambda calculus,Journal of London math.soc. 12,2,1976,p.361–370.Google Scholar
  17. [KP]
    Kahn G.,Plotkin G.,Structures de données concrètes,IRIA-LABORIA report no336, 1978.Google Scholar
  18. [Le1]
    Lévy J-J.,Réductions correctes et optimales dans le lambda-calcul,Thèse d'état, University of Paris 7,1978.Google Scholar
  19. [Le2]
    Lévy J-J.,Le problème du partage dans l'évaluation des lambda-expressions, 1st Colloque AFCET-SMF de math.appliquées,Ecole polytechnique,Palaiseau,1978.IRIA-LABORIA report no325.Google Scholar
  20. [Le3]
    Lévy J-J.,An algebraic interpretation of the lambda calculus and an application of a labelled lambda calculus,TCS,vol 2,no1,1976.IRIA-LABORIA report no103.Google Scholar
  21. [Mi1]
    Milner R.,Implementation and applications of Scott's logic for computable functions,ACM-SIGACT Conf.on proving assertions about programs,Las Cruces,1972.Google Scholar
  22. [Mi2]
    Milner R.,Fully abstract models of typed lambda-calculi,TCS,vol 4,no1,1977.Google Scholar
  23. [Na]
    Nakajima R.,Infinite normal forms in the lambda-calculus,Lambda calculus and Computer science theory,Springer Verlag, LNCS no37,1975.Google Scholar
  24. [Ni]
    Nivat M.,On the interpretation of recursive program schemes,Symposia mathematica,vol 15,Istituto nazionale di alta matematica,1975,p.225–281.Google Scholar
  25. [Pl1]
    Plotkin G.,A set theoritical definition of application,University of Edinburgh,AI memo. MIP-R-95,1972.Google Scholar
  26. [P12]
    Plotkin G.,LCF considered as a programming language,TCS,vol 5,no3,1977,p.223–256.Google Scholar
  27. [P13]
    Plotkin G.,Tω as a universal domain,JCSS,vol 17,no2,Oct 1978.Google Scholar
  28. [Sc1]
    Scott D.S.,Continuous lattices,Oxford PRG 7,1971.Springer Verlag, LNM,no274, 1971.Google Scholar
  29. [Sc2]
    Scott D.S.,Data types as lattices,SIAM Journal on computing,vol 5,no3,Sept 1976.Google Scholar
  30. [Vu]
    Vuillemin J.,Proof techniques for recursive programs,PhD thesis,Stanford,1973.Google Scholar
  31. [Wa1]
    Wadsworth C.,Semantics and pragmatics of the lambda-calculus,PhD thesis,Oxford,1971.Google Scholar
  32. [Wa2]
    Wadsworth C.,The relation between computational and denotational properties for Scott's D model of the lambda-calculus,SIAM Journal on computing,vol 5,no3,Sept 1976.Google Scholar
  33. [We]
    Welch P.,Continuous semantics and inside-out reductions,Lambda-calculus and computer science theory,Springer Verlag, LNCS no37,1975.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Gérard Berry
    • 1
  • Jean-Jacques Lévy
    • 2
  1. 1.Ecole des Mines Sophia-AntipolisValbonne
  2. 2.IRIA-LABORIA Domaine de VoluceauRocquencourt

Personalised recommendations