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A Type-Theoretic Interpretation of Standard ML [chapter]

2000 Proof, Language, and Interaction  
conn) labi exp v ( i ( con)) con 0 roll ( i ( con)) con 0 exp v Elaboration of Standard ML into the Internal Language The type-theoretic interpretation of Standard ML takes the form of a set of inference  ...  In this paper we outline an interpretation of Standard ML in a typed framework. The interpretation takes the form of a translation from Standard ML into an explicitly-typed -calculus.  ...  Standard ML prohibits the type of the body from depending on abstract types de ned locally|in particular, values created from a datatype cannot escape the scope of that datatype.  ... 
doi:10.7551/mitpress/5641.003.0019 fatcat:uyehiwet65hv5i4zfb2uv2zlxi

A Type-Theoretic Interpretation of Standard ML

Robert Harper, Christopher Stone
2018
for the language, inspired a large body of research into the type structure of programming languages.1 As a design tool type theory gives substance to informal ideas such as "orthogonality" and "safety  ...  It has been nearly twenty years since Robin Milner introduced ML as the metalanguage of the LCF interactive theorem prover [5].  ...  conn) labi exp v ( i ( con)) con 0 roll ( i ( con)) con 0 exp v Elaboration of Standard ML into the Internal Language The type-theoretic interpretation of Standard ML takes the form of a set of inference  ... 
doi:10.1184/r1/6602819.v1 fatcat:7mwpx6anvbaobm3rjlfptpk3y4

Collection Principles in Dependent Type Theory [chapter]

Peter Aczel, Nicola Gambino
2002 Lecture Notes in Computer Science  
By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF.  ...  Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation interpretation.  ...  The first author wishes to thank Christopher Nix for pointing out some inaccuracies in a preliminary version of the paper.  ... 
doi:10.1007/3-540-45842-5_1 fatcat:kvqbc2pgbjgyxf54io5hfsmxyy

The Type Theoretic Interpretation of Constructive Set Theory: Inductive Definitions [chapter]

Peter Aczel
1986 Studies in Logic and the Foundations of Mathematics  
We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory.  ...  The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation.  ...  The first author wishes to thank the Department of Computer Science, University of Manchester, where part of the research described here was carried out.  ... 
doi:10.1016/s0049-237x(09)70683-4 fatcat:skeuy4t4cbd3nf6kpenyv5vmd4

The generalised type-theoretic interpretation of constructive set theory

Nicola Gambino, Peter Aczel
2006 Journal of Symbolic Logic (JSL)  
We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory.  ...  The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation.  ...  The first author wishes to thank the Department of Computer Science, University of Manchester, where part of the research described here was carried out.  ... 
doi:10.2178/jsl/1140641163 fatcat:vtby3fvthzdbhhzwy4maxwqom4

An abstract interpretation for ML equality kinds [chapter]

Carl A. Gunter, Elsa L. Gunter, David B. MacQueen
1991 Lecture Notes in Computer Science  
The definition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to define a computable equality relation.  ...  In this paper, a refinement of the Standard ML system of equality types is introduced and is proven sound and complete with respect to the existence of a computable equality.  ...  semantics of Standard ML types.  ... 
doi:10.1007/3-540-54415-1_43 fatcat:hzushtrz4bhfxdcz3cr2gyfere

Computing ML Equality Kinds Using Abstract Interpretation

C.A. Gunter, E.L. Gunter, D.B. Macqueen
1993 Information and Computation  
The denition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to dene an equality relation in ML.  ...  In this paper, a renement of the Standard ML system of equality types is introduced and is proven sound and complete with respect to the existence of a denable equality.  ...  semantics of Standard ML types.  ... 
doi:10.1006/inco.1993.1070 fatcat:x7os75w4szbppobaul6rnfxckq

Page 5987 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Summary: “The definition of Standard ML provides a form of generic equality which is inferred for certain types, called equality types, on which it is possible to define an equality relation in ML.  ...  We interpret the language in a partial Cartesian closed category of ‘directed complete’ partial equivalence relations (pers) over a domain theoretic model of a type-free, call-by-value, lambda calculus  ... 

A Denotational Account of Untyped Normalization by Evaluation [chapter]

Andrzej Filinski, Henning Korsholm Rohde
2004 Lecture Notes in Computer Science  
We show that the standard normalization-by-evaluation construction for the simply-typed λ βη -calculus has a natural counterpart for the untyped λ β -calculus, with the central type-indexed logical relation  ...  replaced by a "recursively defined" invariant relation, in the style of Pitts.  ...  A natural set-theoretic model interprets each base type b as some set, and the function type as the set of all functions between the interpretations of the types, i.e., [ [[VAR(x)]] ρ = ρ(x) [[LAM(  ... 
doi:10.1007/978-3-540-24727-2_13 fatcat:gqer7disjzdwjknls7vmfdrwxi

Quality Control Assessment of Human Immunodeficiency Virus Type 2 (HIV-2) Viral Load Quantification Assays: Results from an International Collaboration on HIV-2 Infection in 2006

F. Damond, A. Benard, J. Ruelle, A. Alabi, B. Kupfer, P. Gomes, B. Rodes, J. Albert, J. Boni, J. Garson, B. Ferns, S. Matheron (+2 others)
2008 Journal of Clinical Microbiology  
In a blinded experimental design, laboratories quantified three series of aliquots of an HIV-2 subtype A strain, each at a different theoretical viral load.  ...  Human immunodeficiency virus type 2 (HIV-2) RNA quantification assays used in nine laboratories of the ACHI E V 2E (A Collaboration on HIV-2 Infection) study group were evaluated.  ...  The members of the ACHI E V 2E study group in Belgium are Patrick Goubau and Jean Ruelle  ... 
doi:10.1128/jcm.00126-08 pmid:18434556 pmcid:PMC2446851 fatcat:zhcdhv2lzvfazihbycmhublbu4

The essence of ML

J. C. Mitchell, R. Harper
1988 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '88  
To copy otherwise, or to republish, requires a fee and/or specfic permission.  ...  Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the  ...  Acknowledgements: Thanks to Dave MacQueen for many insightful discussions of ML over the last few years, and comments on this paper in particular.  ... 
doi:10.1145/73560.73563 dblp:conf/popl/MitchellH88 fatcat:gt75bavmljgpbh75e4hs3knadm

What is a recursive module?

Karl Crary, Robert Harper, Sidd Puri
1999 SIGPLAN notices  
Standard ML or O'Caml.  ...  To address this question we provide a type-theoretic analysis of the notion of a recursive module in the context of the phase-distinction" formalism for higher-order module systems.  ...  Under the standard type-theoretic interpretation of ML see, for example, Harper and Mitchell 8 , the implementation o f a recursive datatype is an iso-recursive t ype.  ... 
doi:10.1145/301631.301641 fatcat:mc3o56jes5du3denu5msojmt2a

What is a recursive module?

Karl Crary, Robert Harper, Sidd Puri
1999 Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation - PLDI '99  
Standard ML or O'Caml.  ...  To address this question we provide a type-theoretic analysis of the notion of a recursive module in the context of the phase-distinction" formalism for higher-order module systems.  ...  Under the standard type-theoretic interpretation of ML see, for example, Harper and Mitchell 8 , the implementation o f a recursive datatype is an iso-recursive t ype.  ... 
doi:10.1145/301618.301641 dblp:conf/pldi/CraryHP99 fatcat:zh3sex3jg5crlnctgehzulu5iq

Design, analysis and Reasoning about Tools: Abstracts from the Second Workshop (Aalborg, 1992, 20-21 August)

Flemming Nielson
1992 DAIMI Report Series  
This report contains a brief overview of DART as well as abstracts of the 20 talks given at the workshop and a status report of DART as of summer 1992.  ...  The primary aim of the workshop was to increase the awareness of DART participants for each other's work, and to stimulate cooperation between the various groups.  ...  The problem has recently found a satisfactory solution for higherorder functors (in the sense of Standard ML).  ... 
doi:10.7146/dpb.v21i417.6730 fatcat:pwvpx7dapfffhpzvtcy7nkl7sq

On the type structure of standard ML

Robert Harper, John C. Mitchell
1993 ACM Transactions on Programming Languages and Systems  
Standard ML is a useful programming language with a polymorphic type system and a flexible module facility.  ...  One notable feature of the core expression language of ML is that it is implicdy 1988 under the title "The Essence of ML." The work of R.  ...  On the Type Structure of Standard ML . 225 5.4.1 Set-Theoretic Models. If we begin with some model M = (U?, + "", {Dom"la e using standard set-theoretic cartesian product.  ... 
doi:10.1145/169701.169696 fatcat:opmooq52ubhtzp7bkk3q7sqao4
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