| Hindley, R. (1969). The principal type-scheme of an object in combinatory logic. |
....and diculties of these systems are discussed. 2.1 Hindley Milner Type Inference One of the greatest contributions to functional languages is the Hindley Milner type system. Hindley studied expressions of the lambda calculus with constants and the typing of expressions in combinatory logic [21]. He considers type expressions built from base types using the type constructor for function types. In Hindley s terminology, a type scheme is a type in which type variables can occur. Hindley de nes the type inference rules in the form A X where X is an expression, is a type scheme and A ....
R. Hindley. The principal type scheme of an object in combinatory logic. Trans. Amer. Math. Soc., 146:29-60, 1969.
....In Information and Computation c Academic Press. To appear. 1. INTRODUCTION Type inference, the process of automatically inferring type information from untyped or partially typed programs, plays an important role in the static analysis of computer programs. Originally devised by Hindley [11] and independently by Milner [13] it has found its way into the design of several recent programming languages. Type inference may or may not be possible, depending on the language and the typing rules. If it can be carried out, type inference turns untyped programs into strongly typed ones. ....
J. R. Hindley. The principal type-scheme of an object in combinatory logic. Transactions American Math. Society, 146:29--60, 1969.
....therefore chosen a well understood property, i.e. types in functional languages a la ML. This property was extensively studied from the type systems viewpoint. There exist notions of type, where types are represented by (possibly quanti ed) terms. These include, for example, principal monotypes [15], polytypes with monomorphic recursion [17,13] and polytypes with polymorphic recursion [20] Each of these notions has a corresponding correct (often noncomplete) type inference algorithm. Some of these algorithms have been reconstructed [18,19] as computations of an abstract semantics, according ....
J.R. Hindley. The principal type-scheme of an object in combinatory logic. Transaction American mathematical Society, 146:29-60, 1969.
....[Bar92] when they are considered in Curry style, there are only three distinct sets of typable, pure, closed terms corresponding to the simply typed calculus, F, and F [GHRDR93] This is depicted in gure 2. Because it has been known that Typ is decidable for the simply typed calculus [Hin69] and (recently) undecidable for F [Urz93b, Urz97] it is once again only for F that the answer has been unknown. Thus, determining the decidability of Typ and TC for F completes our knowledge of these problems for a wide variety of calculus type systems. While the question of decidability of ....
R. Hindley. The principal type scheme of an object in combinatory logic. Trans. AMS, 146:29-60, 1969.
.... and Church Rosser (reduction strategies converge) properties whilst avoiding the complexities (such as dependent types, computationally irrelevant proof objects) of Martin Lof s type theory [11,20] We would like our language to have a type system straightforwardly based on that of Hindley Milner [6,14] and to be similar in usage to a language such as Miranda [22] The case for such a language is set out in [25] briefly, we believe that such a language will allow direct equational reasoning whilst being sufficiently elementary to be used for programming at the undergraduate level. For ....
J.R. Hindley. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society, 146:29--60, 1969.
....expect typing issues to be treated automatically behind the scenes. Any failures encountered here are apt to cause considerable confusion, until the actual problem is figured out by hand eventually. The refined type inference scheme according to Hindley Milner (also known as let polymorphism ) [Hindley, 1969] [Milner, 1978] is slightly more flexible. This improved typing discipline needs to extend pure # calculus by a separate let binder: in the term let x = t in u the variable x is bound locally to t within the body u; the canonical conversion rule is (let x = t in u) u[t x ] This operational ....
J. R. Hindley. The principal type-scheme of an object in combinatory logic. Trans. Amer. Math. Soc., 146, 1969.
....of Unity [Gir93] However, it turns out to be convenient to present this work without reference to linear logic. Some of the connections are traced in a companion paper [MOTW95] which relates linear logic to the call by need calculus of Ariola et al. We modify the Hindley Milner type system [Hin69, DM82] by attaching uses to types. Type judgements include a constraint set relating uses, similar to the constraint sets relating subtypes in the work of Mitchell [Mit84, Mit91] As with the Hindley Milner system, there is an algorithm that determines a principal type for an expression. Annotating ....
R. Hindley, The principal type scheme of an object in combinatory logic. Trans. Am. Math. Soc., 146:29--60, December 1969.
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Hindley, R. (1969). The principal type-scheme of an object in combinatory logic.
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R. Hindley. The principal type-scheme of an object in combinatory logic. Trans. AMS, 146:29-- 60, 1969.
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R. Hindley. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society, 146:29--60, December 1969.
No context found.
J.R. Hindley. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society, 146:29--60, 1969.
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Hindley, J., The principal type scheme of an object in combinatory logic, Transactions of the American Mathematical Society 146 (1969), pp. 29--60.
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J. R. Hindley. The principal type scheme of an object in combinatory logic. Trans. American Mathematical Society, 146:29--60, Dec. 1969.
No context found.
R. Hindley. The Principal Type-Scheme of an Object in Combinatory Logic. Trans. Amer. Math. Soc., 146:29-60, 1969.
No context found.
J. R. Hindley. The principal type-scheme of an object in combinatory logic. Transactions American Math. Society, 146:29--60, 1969.
No context found.
R. Hindley. The Principal Type-Scheme of an Object in Combinatory Logic. Trans. Amer. Math. Soc., 146:29--60, 1969.
No context found.
J. Roger Hindley. The principal type-scheme of an object in combinatory logic. Transactions American Math. Society, 146:29--60, 1969.
No context found.
R. Hindley, The principal type scheme of an object in combinatory logic. Trans. Am. Math. Soc., 146:29--60, December 1969.
No context found.
R. Hindley, The principal type scheme of an object in combinatory logic. Trans. Am. Math. Soc., 146:29--60, December 1969.
No context found.
J. R. Hindley. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society, 146:29--60, 1969.
No context found.
R. Hindley. The principal type scheme for an object in combinatory logic. Transactions of American Mathematical Society, 146:29--60, 1969.
No context found.
J. R. Hindley. The principal type-scheme of an object in combinatory logic. Trans. AMS, 146:29--60, 1969.
No context found.
J. R. Hindley. The principal type-scheme of an object in combinatory logic. Trans. Amer. Math. Soc., 1969.
No context found.
J. R. Hindley. The principal type-scheme of an object in combinatory logic. Transactions American Mathematical Society, 146:29-60, 1969.
No context found.
Hindley, R. The principal type scheme of an object in combinatory logic. In Transaction of the American Mathematical Society, volume 146, pages 26-60, 1969.
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