On the Undecidability of Partial Polymorphic Type Reconstruction

We prove that partial type reconstruction for the pure polymorphic lambda-calculus is undecidable by a reduction from the second-order unification problem, extending a previous result by H.-J. Boehm. We show further that partial type reconstruction remains undecidable even in a very small predicative fragment of the polymorphic lambda-calculus, which implies undecidability of partial type reconstruction for lambda^ML as introduced by Harper, Mitchell, and Moggi.

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