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Type Inference Verified: Algorithm W in Isabelle/HOL

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Abstract

This paper presents the first machine-checked verification of Milner's type inference algorithm W for computing the most general type of an untyped λ-term enriched with let-expressions. This term language is the core of most typed functional programming languages and is also known as Mini-ML. We show how to model all the concepts involved, in particular types and type schemes, substitutions, and the thorny issue of “new” variables. Only a few key proofs are discussed in detail. The theories and proofs are developed in Isabelle/HOL, the HOL instantiation of the generic theorem prover Isabelle.

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Authors and Affiliations

  1. Technische Universität München, Institut für Informatik, 80290, München, Germany

    Wolfgang Naraschewski

  2. Technische Universität München, Institut für Informatik, 80290, München, Germany

    Tobias Nipkow

Authors
  1. Wolfgang Naraschewski
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  2. Tobias Nipkow
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Naraschewski, W., Nipkow, T. Type Inference Verified: Algorithm W in Isabelle/HOL. Journal of Automated Reasoning 23, 299–318 (1999). https://doi.org/10.1023/A:1006277616879

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