NDLI: The essence of ML

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The essence of ML

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The essence of ML

Content Provider	ACM Digital Library
Author	Harper, R. Mitchell, J. C.
Abstract	Standard ML is a useful programming language with polymorphic expressions and a flexible module facility. One notable feature of the expression language is an algorithm which allows type information to be omitted. We study the implicitly-typed expression language by giving a “syntactically isomorphic” explicitly-typed, polymorphic function calculus. Unlike the Girard-Reynolds polymorphic calculus, for example, the types of our ML calculus may be built-up by induction on type levels (universes). For this reason, the pure ML calculus has straightforward set-theoretic, recursion-theoretic and domain-theoretic semantics, and operational properties such as the termination of all recursion-free programs may be proved relatively simply. The signatures, structures, and functors of the module language are easily incorporated into the typed ML calculus, providing a unified framework for studying the major features of the language (including the novel “sharing constraints” on functor parameters). We show that, in a precise sense, the language becomes inconsistent if restrictions imposed by type levels are relaxed. More specifically, we prove that the important programming features of ML cannot be added to any impredicative language, such as the Girard-Reynolds calculus, without implicitly assuming a type of all types.
Starting Page	28
Ending Page	46
Page Count	19
File Format	PDF
ISBN	0897912527
DOI	10.1145/73560.73563
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1988-01-13
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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