Computing ML Equality Kinds Using Abstract Interpretation

The definition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to define an equality relation in ML. However, the standard definition is incomplete in the sense that there are interesting and useful types which ar...

Full description

Saved in:
Bibliographic Details
Published inInformation and computation Vol. 107; no. 2; pp. 303 - 323
Main Authors Gunter, C.A., Gunter, E.L., Macqueen, D.B.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.12.1993
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Language theory and syntactical analysis
Theoretical computing
Monotonic function
Inference
Type
Fast algorithm
Interpretation
Online AccessGet full text

Cover

More Information
Summary:The definition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to define an equality relation in ML. However, the standard definition is incomplete in the sense that there are interesting and useful types which are not inferred to be equality types but for which an equality relation can be defined in ML in a uniform manner. In this paper, a refinement of the Standard ML system of equality types is introduced and is proven sound and complete with respect to the existence of a definable equality. The technique used here is based on an abstract interpretation of ML operators as monotone functions over a three point lattice. It is shown how the equality relation can be defined (as an ML program) from the definition of a type with our equality property. Finally, a sound, efficient algorithm for inferring the equality property, which corrects the limitations of the standard definition in all cases of practical interest, is demonstrated.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.1993.1070