Datatypes in L2

  • Nick Chapman
  • Simon Finn
  • Michael P. Fourman
Invited Paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 859)


We describe the axiomatisation of a subset of Standard ML's datatypes in L2 (the LAMBDA Logic). The subset includes parameterisation and mutual recursion but has restrictions on the use of function type construction. We sketch a set-theoretic model for these datatypes. Finally, we briefly discuss the relationship between L2's datatypes and datatypes in HOL.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Matt Fairtlough, Research into ML Datatypes, in Formal System Design (IED Project 1292) Deliverable D13, Edinburgh University, February 1992.Google Scholar
  2. 2.
    Simon Finn, Michael P. Fourman, L2 — The LAMBDA Logic, in LAMBDA 4.3 Reference Manuals, Abstract Hardware Limited, September 1993.Google Scholar
  3. 3.
    Simon Finn, Michael Fourman, John Longley, Partial Functions in a Total Setting, in preparation.Google Scholar
  4. 4.
    M.P. Fourman and W.K. Phoa, A Proposed Categorical Semantics for Pure ML, in ICALP '92 International Colloquium on Automata, Languages, and Programming, Wien Austria, Springer-Verlag LNCS, 1993.Google Scholar
  5. 5.
    Elsa L. Gunter, Why We Can't have SML Style datatype Declarations in HOL, in Higher Order Logic Theorem Proving and its Applications (HOL'92), ed. L.J.M. Claessen, M.J.C. Gordon, North-Holland 1993.Google Scholar
  6. 6.
    Elsa L. Gunter, A Broader Class of Trees for Recursive Type definitions in HOL, in Higher Order Logic Theorem Proving and its Applications (HUG'93), ed. Jeffrey J. Joyce, Carl-Johan H. Seger, Lecture Notes in Computer Science 780, Springer-Verlag 1994.Google Scholar
  7. 7.
    Thomas F. Melham, Formalizing Abstraction Mechanisms for Hardware Verification in Higher Order Logic, PhD Thesis and Technical Report 201, University of Cambridge, August 1990.Google Scholar
  8. 8.
    Robin Milner, Mads Tofte and Robert Harper, The Definition of Standard ML, MIT Press, 1990.Google Scholar
  9. 9.
    Andy Pitts, Set-Theoretic Semantics, in The HOL System DESCRIPTION, HOL88 Documentation, 1991.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Nick Chapman
    • 1
  • Simon Finn
    • 1
  • Michael P. Fourman
    • 2
  1. 1.Abstract Hardware Ltd.UK
  2. 2.Abstract Hardware Ltd. and Edinburgh UniversityUK

Personalised recommendations