A Proposed Categorical Semantics for ML Modules
نویسندگان
چکیده
We present a simple categorical semantics for ML signatures, structures and functors. Our approach relies on realizablity semantics in the category of assemblies. Signatures and structures are modelled as objects in slices of the category of assemblies. Instantiation of signatures to structures and hence functor application is modelled by pullback.
منابع مشابه
A Category-theoretic Account of Program Modules
The type-theoretic explanation of modules proposed to date (for programming languages like ML) is unsatisfactory, because it does not capture that evaluation of type-expressions is independent from evaluation of programexpressions. We propose a new explanation based on “programming languages as indexed categories” and illustrates how ML can be extended to support higher order modules, by develo...
متن کاملFunctorial semantics of topological theories
Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...
متن کاملA Theory of Mixin Modules: Algebraic Laws and Reduction Semantics
Received Mixins are modules which may contain deferred components, i.e. components not deened in the module itself; moreover, in contrast to parameterized modules (like ML functors), they can be mutually dependent and allow their deenitions to be overridden. In a preceding paper we have deened syntax and a categorical semantics of a kernel language of mixin modules. Here, we take instead an axi...
متن کاملMechanizing the Metatheory of Standard ML
We present an internal language with equivalent expressive power to Standard ML, and discuss its formalization in LF and the machine-checked verification of its type safety in Twelf. The internal language is intended to serve as the target of elaboration in an elaborative semantics for Standard ML in the style of Harper and Stone. Therefore, it includes all the programming mechanisms necessary ...
متن کاملTypes for modules
The programming language Standard ML is an amalgam of two, largely orthogonal, languages. The Core language expresses details of algorithms and data structures. The Modules language expresses the modular architecture of a software system. Both languages are statically typed, with their static and dynamic semantics specified by a formal definition. Over the past decade, Standard ML Modules has b...
متن کامل