ACM Transactions on Programming Languages and Systems (TOPLAS)
The type and effect discipline
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Purely functional data structures
Purely functional data structures
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LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Recursive structures for standard ML
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ACM Transactions on Programming Languages and Systems (TOPLAS)
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ACM Transactions on Computational Logic (TOCL)
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Understanding and evolving the ml module system
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A type system for recursive modules
ICFP '07 Proceedings of the 12th ACM SIGPLAN international conference on Functional programming
Journal of Functional Programming
A module system independent of base languages
Proceedings of the 1st Workshop on Modules and Libraries for Proof Assistants
Principal type schemes for modular programs
ESOP'07 Proceedings of the 16th European conference on Programming
Generative type abstraction and type-level computation
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Existential types provide a simple and elegant foundation for understanding generative abstract data types, of the kind supported by the Standard ML module system. However, in attempting to extend ML with support for recursive modules, we have found that the traditional existential account of type generativity does not work well in the presence of mutually recursive module definitions. The key problem is that, in recursive modules, one may wish to define an abstract type in a context where a name for the type already exists, but the existential type mechanism does not allow one to do so.We propose a novel account of recursive type generativity that resolves this problem. The basic idea is to separate the act of generating a name for an abstract type from the act of defining its underlying representation. To define several abstract types recursively, one may first "forward-declare" them by generating their names, and then define each one secretly within its own defining expression. Intuitively, this can be viewed as a kind of backpatching semantics for recursion at the level of types. Care must be taken to ensure that a type name is not defined more than once, and that cycles do not arise among "transparent" type definitions.In contrast to the usual continuation-passing interpretation of existential types in terms of universal types, our account of type generativity suggests a destination-passing interpretation. Briefly, instead of viewing a value of existential type as something that creates a new abstract type every time it is unpacked, we view it as a function that takes as input a pre-existing undefined abstract type and defines it. By leaving the creation of the abstract type name up to the client of the existential, our approach makes it significantly easier to link abstract data types together recursively.