A Semantics for Higher-Order Functors
نویسندگان
چکیده
Standard ML has a module system that allows one to deene para-metric modules, called functors. Functors are \\rst-order," meaning that func-tors themselves cannot be passed as parameters or returned as results of functor applications. This paper presents a semantics for a higher-order module system which generalizes the module system of Standard ML. The higher-order functors described here are implemented in the current version of Standard ML of New Jersey and have proved useful in programming practice.
منابع مشابه
Mei – A Module System for Mechanized
This thesis presents several module systems, in particular Mei and DMei, designed for mechanized mathematics systems. Mei is a λ-calculus style module system that supports higher-order functors in a natural way. The semantics of functor application is based on substitution. A novel coercion mechanism integrates a parameter passing mechanism based on theory interpretations with simple λ-calculus...
متن کاملAn Implementation of Higher-order Functors
Recently the module language of SML of New Jersey has been augmented with higher-order functors. Their semantics is described in Tof94, MT94]. This paper sketches how higher-order functors can be implemented with eecient static representations. The key idea of the SML/NJ implementation is the sharing of signature environments , and this idea has been carried over to the higher-order case.
متن کاملRobustly Parameterised Higher-Order Probabilistic Models
We present a method for constructing robustly parameterised families of higher-order probabilistic models. Parameter spaces and models are represented by certain classes of functors in the category of Polish spaces. Maps from parameter spaces to models (parameterisations) are continuous and natural transformations between such functors. Naturality ensures that parameterised models are invariant...
متن کاملStudying the ML Module System in Hol
Building on work done by Myra VanInwegen and Elsa Gunter, we encode the dynamic semantics of the Module system of SML in HOL. We extend this to a possible dynamic semantics for a Module system with higher order functors. We relate these two semantics by embeddings and projections and outline how we are using these to state and prove that the new evaluation relations conservatively extend the ol...
متن کاملFunctorial Semantics for Higher-order Logic Dissertation Abstract
This dissertation investigates what may be termed the model theory of higher-order logic using the methods of category theory. Of course, there is no such eld of logic as \higher-order model theory," and so our rst concern in chapter I will be to specify the basic objects under investigation, viz. higher-order logical theories and their models. This is a fairly straightforward generalization|in...
متن کامل