Part 1 Syntax of the core: reserved words special constants comments identifiers lexical analysis infixed operators derived forms grammar syntactic restrictions. Part 2 Syntax of modules: reserved words identifiers infixed operators grammar for modules syntactic restrictions. Part 3 Static semantics for the core: simple objects compound objects projection, injection and modification types and type functions type schemes scope of explicit type variables non-expansive expressions closure type structures and type environments inference rules further restrictions. Part 4 Static semantics for modules: semantic objects type realization signature instantiation functor signature instantiation enrichment signature matching inference rules. Part 5 Dynamic semantics for the core: reduced syntax simple objects compound objects basic values basic exceptions function closures inference rules. Part 6 Dynamic semantics for modules: reduced syntax compound objects inference rules. Part 7 Programmes. Part 8 Appendices.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTIntramolecular energy transfer in the inverted regionD. Brent MacQueen, John R. Eyler, and Kirk S. SchanzeCite this: J. Am. Chem. Soc. 1992, 114, 5, 1897–1898Publication Date (Print):February 1, 1992Publication History Published online1 May 2002Published inissue 1 February 1992https://pubs.acs.org/doi/10.1021/ja00031a063https://doi.org/10.1021/ja00031a063research-articleACS PublicationsRequest reuse permissionsArticle Views227Altmetric-Citations96LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-AlertscloseSupporting Info (1)»Supporting Information Supporting Information Get e-Alerts
The ML module system is a powerful and expressive language for modular programming and enforcing data abstraction. Several dialects of ML have extended the module system with support for higher-order modules, which improves support for modular programming and elevates the module system to a full functional language. With the exception of Standard ML of New Jersey and MLton, higher-order modules in all these dialects do not obey natural β-reduction semantics for higher-order functor application (true higher-order semantics ). The design space and semantics of a true higher-order module system have not been thoroughly explored. Most of the existing formal accounts of module system semantics neglect true higher-order semantics by separating higher-order functors from type generativity, which limits the flexibility of higher-order functors. The accounts which consider higher-order module semantics neglect to account for interactions between higher-order modules and key core language features such as generative datatype declarations. True higher-order semantics also paradoxically complicates true separate compilation.
In this dissertation, I contribute (1) a novel formal account of a module system with true higher-order semantics, (2) a static entity calculus that cleanly isolates and expresses the higher-order semantics, (3) an exploration of the design space of higher-order module semantics including true separate compilation and the signature calculus, and (4) a translation semantics for compiling the module system to a variant of System Fω.
In [1] Gandy established the following selection theorem for recursion in type-2 objects. Theorem. Let F be a normal type-2 object. Then it is possible to select (uniformly and effectively in F ) an integer from each nonempty set of integers semirecursive in F . Notice that this really asserts that the predicates semirecursive in F are closed under existential quantification over type-0. Moschovakis [6] has essentially proven this theorem for F of arbitrary type. In [2] Grilliot stated a powerful generalization of Gandy's result, namely: Grilliot's Selection Theorem. Let F be a normal type-(n + 2) object (n an arbitrary integer). Then it is possible to select (uniformly and effectively in F ) a nonempty recursive in F subset of each nonempty semirecursive in F set oftype-(n − 1) objects . Notice again that this actually says that predicates semirecursive in F are closed under quantification over type-( n − 1) objects. Despite the similarity of these two results, Gandy and Grilliot proposed rather different methods of proof. Furthermore, the proof that Grilliot presented in [2] contains an error which cannot easily be corrected. (We will comment on the nature of this error at the end of §1.) Fortunately, however, Grilliot's theorem is valid. We will present a proof of Grilliot's selection theorem which is a direct generalization of the proof of Gandy's theorem given in [6]. In fact, we will prove a general result (the theorem stated in §2) which subsumes both Gandy's and Grilliot's results.
The functional programming language ML has been undergoing a thorough redesign during the past year, and the module facility described here has been proposed as part of the revised language, now called Standard ML. The design has three main goals: (1) to facilitate the structuring of large ML programs; (2) to support separate compilation and generic library units; and (3) to employ new ideas in the semantics of data types to extend the power of ML's polymorphic type system. It is based on concepts inherent in the structure of ML, primarily the notions of a declaration, its type signature, and the environment that it denotes.
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