FreezeML: Complete and easy type inference for first-class polymorphism

Frank Emrich, Sam Lindley, Jan Stolarek, James Cheney, Jonathan Coates

Research output: Chapter in Book/Report/Conference proceedingConference contribution


ML is remarkable in providing statically typed polymorphism without the programmer ever having to write any type annotations. The cost of this parsimony is that the programmer is limited to a form of polymorphism in which quantifiers can occur only at the outermost level of a type and type variables can be instantiated only with monomorphic types.

Type inference for unrestricted System F-style polymorphism is undecidable in general. Nevertheless, the literature abounds with a range of proposals to bridge the gap between ML and System F.

We put forth a new proposal, FreezeML, a conservative extension of ML with two new features. First, let- and lambda-binders may be annotated with arbitrary System F types. Second, variable occurrences may be frozen, explicitly disabling instantiation. FreezeML is equipped with type-preserving translations back and forth between System F and admits a type inference algorithm, an extension of algorithm W, that is sound and complete and which yields principal types.
Original languageEnglish
Title of host publicationPLDI 2020: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation
PublisherAssociation for Computing Machinery
Number of pages15
ISBN (Print)9781450376136
Publication statusPublished - 11 Jun 2020


  • first-class polymorphism
  • type inference
  • impredicative types


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