Polymorphic Type Inference And Semi Unification

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Polymorphic Type Inference And Semi Unification
Fritz Henglein
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Typability in the Mycroft Calculus; 2. (nonuniform) semi-unifiability; 3. Typability in the Flat Mycroft Calculus.
Proof: The steps (1) => (2) and (2) => (3) are proved in theorems 8 and 12; (3) => (1) is trivial since FMM-typability instances are a subclass of MM-typability instances.
This corollary stands in contradiction to a statement by Mycroft who suggests prohibiting nested polymorphically typed fix-definitions "due to the exponential cost of analysing nested fix definitions" [85]. Indee
...d nesting does not make things any worse than they already are in a single fix definition.
Corollary 20 1. The Mtlner Calculus is polynomial-time reducible to the Flat Mycroft Cal- culus.
2. The Flat Mycroft Calculus is PSPACE-hard. Proof: 1. By theorem 8 the Milner Calculus is polynomial-time reducible to semi- unification, which in turn is polynomial-time reducible to the Flat Mycroft Calculus by theorem 12.
2. By (1) and the PSPACE-hardness result of Kanellakis and Mitchell [53] for the Milner Calculus.


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