Hindley–Milner type system

<p>A Hindley–Milner (HM) type system is a classical <a href="/facts/Type_system/Tz0bAMS9">type system</a> for the <a href="/facts/Lambda_calculus/DaD3RuQ4">lambda calculus</a> with <a href="/facts/Parametric_polymorphism/ETb0G1zd">parametric polymorphism</a>. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by <a href="/facts/J._Roger_Hindley/clPxofjg">J. Roger Hindley</a> and later rediscovered by <a href="/facts/Robin_Milner/oMfdsRwK">Robin Milner</a>. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis.
</p><p>Among HM's more notable properties are its <a href="/facts/Completeness_(logic)/GzK9zLnu">completeness</a> and its ability to infer the <a href="/facts/Principal_type/wNhQ2BBv">most general type</a> of a given program without programmer-supplied <a href="/facts/Type_annotation/psEPS0UW">type annotations</a> or other hints. Algorithm W is an efficient <a href="/facts/Type_inference/vX9K8Qhf">type inference</a> method in practice and has been successfully applied on large code bases, although it has a high theoretical <a href="/facts/Computational_complexity/Qenh22Ja">complexity</a>. HM is preferably used for <a href="/facts/Functional_language/cdxqPEIM">functional languages</a>. It was first implemented as part of the type system of the programming language <a href="/facts/ML_(programming_language)/RfwxASRF">ML</a>. Since then, HM has been extended in various ways, most notably with <a href="/facts/Type_class/MBbIhF4n">type class</a> constraints like those in <a href="/facts/Haskell_(programming_language)/4Htv9WLu">Haskell</a>.
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Hindley–Milner type system open-in-new

Hindley–Milner type system