Proofs about a folklore let-polymorphic type inference algorithm

Authors:
Oukseh Lee;Kwangkeun Yi
Affiliations:
Korea Advanced Institute of Science and Technology, Taejon, Korea;Korea Advanced Institute of Science and Technology, Taejon, Korea
Venue:
ACM Transactions on Programming Languages and Systems (TOPLAS)
Year:
1998

Citing 8
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Abstract

The Hindley/Milner let-polymorphic type inference system has two different algorithms: one is the de factostandard Algorithm W that is bottom-up (or context-insensitive), and the other is a “folklore” algorithm that is top-down (or context-sensitive). Because the latter algorithm has not been formally presented with its soundness and completeness proofs, and its relation with the W algorithm has not been rigorously investigated, its use in place of (or in combination with) W is not well founded. In this article, we formally define the context-sensitive, top-down type inference algorithm (named “ M”), prove its soundness and completeness, and show a distinguishing property that M always stops earlier than W if the input program is ill typed. Our proofs can be seen as theoretical justifications for various type-checking strategies being used in practice.