| D.B. Mac Queen. Using dependent types to express modular structure: experience with Pebble and ML. In Proc. 13th Annual ACM Symp. on Principles of Programming Languages, 1986. |
....components of a module and, thus, the type of the module itself may depend on the value of the type components of the module. Since we are in presence of types that depend on values, then a classical approach to characterize the SML module system is to use first order dependent types [MQ86, MH88, Ler94, HL94] Modules are handled by functors. Functors are functions that transform modules into other modules and that are subtype polymorphic (intuitively, a functor defined for modules that export some given components works also on modules that export more components) Functors can be ....
D.B. Mac Queen. Using dependent types to express modular structure: experience with Pebble and ML. In Proc. 13th Annual ACM Symp. on Principles of Programming Languages, 1986.
....lead. For instance, Girard s [13] and Martin Lof s [36] type theories depict the quantification quite differently and suggest, in particular, different term decorations of rule (9) Some computer scientists argue that Martin Lof s way correctly describes the actual structure of programs [35], while others prefer Girard s way [37] The categorical proposal is that the derivation rules like (9) and (8) should be enriched to adjunctions. This means that, say, correspondence (9) should be realized by composing with some proofs jR : R(x; y) 9y 0 :R(x; y 0 ; 6 y) and P : 9y:P (x; ....
D. Mac Queen, Using dependent types to express modular structure, Proceedings of the 13th Symposium on Principles of Programming Languages (ACM, 1986) 277--286
....lead. For instance, Girard s [13] and Martin Lof s [36] type theories depict the quantification quite differently and suggest, in particular, different term decorations of rule (9) Some computer scientists argue that Martin Lof s way correctly describes the actual structure of programs [35], while others prefer Girard s way [37] The categorical proposal is that the derivation rules like (9) and (8) should be enriched to adjunctions. This means that, say, correspondence (9) should be realized by composing with some proofs jR : R(x; y) 9y 0 :R(x; y 0 ; 6 y) and P : 9y:P (x; ....
D. Mac Queen, Using dependent types to express modular structure, Proceedings of the 13th Symposium on Principles of Programming Languages (ACM, 1986) 277--286
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