Transparent and Opaque Interpretations of Datatypes

Crary, Karl; Harper, Robert; Cheng, Perry; Petersen, Leaf; Stone, Chris

doi:10.21236/ada358589

Cited by 1 publication

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“…While this solves the efficiency problem with the opaque interpretation, Crary et al have pointed out that it introduces a separate problem, namely that certain kinds of valid Standard ML programs fail to typecheck [4]. For example, suppose that the argument signature of a functor F includes the specification of a type t1 and a datatype t2 that refers to it: functor F (X: sig type t1 datatype t2 = C | D of int * t1 ... end) = ... Then, suppose F is applied to a pair of mutually recursive datatypes t1 and t2 defined as follows: datatype t1 = A | B of string * t2 and t2 = C | D of int * t1…”

Section: Transparent and Opaque Interpretations Of Datatypesmentioning

confidence: 99%

“…Under the simple equivalence rule for iso-recursive constructors that was given in Section 4.2.1, there is no way to equate the actual and required definitions for t2, so the functor application is not valid under the transparent interpretation of datatypes. One way to remedy this problem, as detailed by Crary et al [4], is to use what they refer to as Shao's equation (after its original implementation by Shao in the FLINT compiler). For iso-recursive types, the equation can be written as follows:…”

Section: Transparent and Opaque Interpretations Of Datatypesmentioning

confidence: 99%

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Toward a Practical Type Theory for Recursive Modules

Dreyer¹,

Harper

Crary³

2001

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Module systems for languages with complex type systems, such as Standard ML, often lack the ability to express mutually recursive type and function dependencies across module boundaries. Previous work by Crary, Harper and Puri [5] set out a type-theoretic foundation for recursive modules in the context of a phase-distinction calculus for higher-order modules. Two constructs were introduced for encoding recursive modules: a fixed-point module and a recursively dependent signature. Unfortunately, the implementations of both constructs involve the use of equi-recursive type constructors at higher-order kinds, the equivalence of which is not known to be decidable.In this paper, we show that the practicality of recursive modules is not contingent upon that of equi-recursive constructors. We begin with the theoretical infrastructure described above and study precisely how equi-recursiveness is used in the recursive module constructs, resulting in a clarification and generalization of the underlying ideas. We then examine in depth how the recursive module constructs in the revised type system can serve as the target of elaboration for a recursive module extension to Standard ML. Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Section: Transparent and Opaque Interpretations Of Datatypesmentioning

confidence: 99%

Section: Transparent and Opaque Interpretations Of Datatypesmentioning

confidence: 99%