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Programming Language Theory: Difference between revisions
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Two mechanisms were proposed for adding types to the λ-calculus: | Two mechanisms were proposed for adding types to the λ-calculus: | ||
* Church suggested explicit type annotations on all terms (simply-typed λ-calculus (λ<sub>→</sub>), "simple" due to single type constructor →) | * Church suggested explicit type annotations on all terms (simply-typed λ-calculus (λ<sub>→</sub>), "simple" due to single type constructor →) | ||
* Curry suggested inferred types | * Curry suggested inferred types (now implemented via techniques such as <a href="http://en.wikipedia.org/wiki/Hindley-Milner_type_inference">Hindley-Milner</a>) | ||
Either way, we lose some properties of the untyped λ-calculus (there's no type for the Y-combinator, for instance!). Nonetheless, the benefits of [[Programming_Language_Theory#Typing|typing]] (especially in the presence of type inference) lead to most functional programming languages making use of a strict typing system. | Either way, we lose some properties of the untyped λ-calculus (there's no type for the Y-combinator, for instance!). Nonetheless, the benefits of [[Programming_Language_Theory#Typing|typing]] (especially in the presence of type inference) lead to most functional programming languages making use of a strict typing system. | ||
