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The Implicit Calculus of Constructions Extending Pure Type Systems with an Intersection Type Binder and Subtyping [chapter]

Alexandre Miquel
2001 Lecture Notes in Computer Science  
In this paper, we introduce a new type system, the Implicit Calculus of Constructions, which is a Curry-style variant of the Calculus of Constructions that we extend by adding an intersection type bindercalled  ...  We also illustrate the specificities of this calculus by revisitting the impredicative encodings of the Calculus of Constructions, and we show that their translation into the implicit calculus helps to  ...  The Implicit Calculus of Constructions Syntax From a pure syntactical point of view, the Implicit Calculus of Constructions (ICC)-or, shortly, the implicit calculus-is a Curry-style variant of the Calculus  ... 
doi:10.1007/3-540-45413-6_27 fatcat:2xpmxsobwnfkfepe4n6bwuzwfq

The Implicit Calculus of Constructions as a Programming Language with Dependent Types [chapter]

Bruno Barras, Bruno Bernardo
Foundations of Software Science and Computational Structures  
In this paper, we show how Miquel's Implicit Calculus of Constructions (ICC) can be used as a programming language featuring dependent types.  ...  The point of using ICC * rather than the Calculus of Constructions (the core formalism of the Coq proof assistant) is that all of the static information (types and proof objects) is transparent, in the  ...  A Decidable Implicit Calculus of Constructions Syntax Its syntax is the same that in the standard Calculus of Constructions in Church style, except that we duplicate each operation (product, abstraction  ... 
doi:10.1007/978-3-540-78499-9_26 dblp:conf/fossacs/BarrasB08 fatcat:tbrr6tdambe4dnksim2ydokiwa

Extended Report: The Implicit Calculus [article]

Bruno C. d. S. Oliveira, Tom Schrijvers, Wontae Choi, Wonchan Lee, Kwangkeun Yi
2012 arXiv   pre-print
This paper synthesizes the key ideas of implicits formally in a minimal and general core calculus called the implicit calculus, and it shows how to build source languages supporting implicit instantiation  ...  Ultimately, the implicit calculus provides a formal model of implicits, which can be used by language designers to study and inform implementations of similar mechanisms in their own languages.  ...  Type-directed Encoding of Source Language in λ⇒ Implicit scoping The implicit construct, which has been already informally introduced in Section 1, is the core scoping construct of the source language.  ... 
arXiv:1203.4499v1 fatcat:pykj7uowufhx7peh65ly4x7pum

Page 632 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
In Part II the author gives a very readable general overview of the developments in the subject since 1972, focusing on elementary constructions of models of the A-calculus.  ...  Part I is a previously unpublished 1972 memorandum in which the author presents one of the first constructions of denotational models of the untyped A-calculus and compares his models with the D®-models  ... 

The implicit calculus

Bruno C.d.S. Oliveira, Tom Schrijvers, Wontae Choi, Wonchan Lee, Kwangkeun Yi
2012 Proceedings of the 33rd ACM SIGPLAN conference on Programming Language Design and Implementation - PLDI '12  
This paper synthesizes the key ideas of implicits formally in a minimal and general core calculus called the implicit calculus (λ ?  ...  Ultimately, the implicit calculus provides a formal model of implicits, which can be used by language designers to study and inform implementations of similar mechanisms in their own languages.  ...  ACKNOWLEDGMENTS We are grateful to Ben Delaware, Derek Dreyer, Jeremy Gibbons, Scott Kilpatrick, eta Ziliani, the members of ROPAS and the anonymous reviewers for their comments and suggestions.  ... 
doi:10.1145/2254064.2254070 dblp:conf/pldi/OliveiraSCLY12 fatcat:qutlckzhrva2vinmwbgtix4nz4

The implicit calculus

Bruno C.d.S. Oliveira, Tom Schrijvers, Wontae Choi, Wonchan Lee, Kwangkeun Yi
2012 SIGPLAN notices  
This paper synthesizes the key ideas of implicits formally in a minimal and general core calculus called the implicit calculus (λ ?  ...  Ultimately, the implicit calculus provides a formal model of implicits, which can be used by language designers to study and inform implementations of similar mechanisms in their own languages.  ...  ACKNOWLEDGMENTS We are grateful to Ben Delaware, Derek Dreyer, Jeremy Gibbons, Scott Kilpatrick, eta Ziliani, the members of ROPAS and the anonymous reviewers for their comments and suggestions.  ... 
doi:10.1145/2345156.2254070 fatcat:2tfcedbrinckzitjsmagazk25e

Page 2745 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
Coquand’s “calculus of constructions” is a system of typed 4- calculus in which the second-order polymorphic typed A-calculus can be interpreted.  ...  {For the entire collection see MR 98d:03006. } 98e:03019 03B40 03FS0 Seldin, Jonathan P. (3-CONC; Montreal, PQ) On the proof theory of Coquand’s calculus of constructions. (English summary) Ann.  ... 

Polymorphic Multi-stage Language with Control Effects [chapter]

Yuichiro Kokaji, Yukiyoshi Kameyama
2011 Lecture Notes in Computer Science  
We show that the proposed calculus satisfies type soundness and type inference. The former is the key to guarantee the absence of scope extrusion -open codes are never generated or executed.  ...  Kameyama, Kiselyov, and Shan proposed a multi-stage calculus with computation effects, but their calculus lacks polymorphism.  ...  We also thank anonymous reviewers for constructive comments. The second author is supported in part by JSPS Grant-in-Aid for Scientific Research (B) 21300005.  ... 
doi:10.1007/978-3-642-25318-8_11 fatcat:tzbgaig4bvfunlmajplqomc3ra

Simplicitly: foundations and applications of implicit function types

Martin Odersky, Olivier Blanvillain, Fengyun Liu, Aggelos Biboudis, Heather Miller, Sandro Stucki
2017 Proceedings of the ACM on Programming Languages  
This paper describes a generalization of implicit parameters to implicit function types, a powerful way to abstract over the context in which some piece of code is run.  ...  Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly.  ...  ACKNOWLEDGMENTS We thank the anonymous reviewers of both the program committee and the artifact evaluation committee for their constructive comments. We gratefully acknowledge funding by the Swiss  ... 
doi:10.1145/3158130 dblp:journals/pacmpl/OderskyBLBMS18 fatcat:o5ij3kfi75ahvcmjxgsyca57dq

Page 3968 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
The paper contains rich supplementary material, especially a survey of differential calculus on an algebra which turns out to be an impor- tant ingredient in all the constructions.  ...  A theorem is stated that the graph of an implicit function is a smooth retract of Lebesgue neighborhoods. Finally, the author shows the  ... 

The calculus of constructions

Thierry Coquand, Gérard Huet
1988 Information and Computation  
The calculus of constructions is a higher-order formalism for constructive proofs in natural deduction style. Every proof is a A-expression, typed with propositions of the underlying logic.  ...  We develop the basic theory of a calculus of constructions, and prove a strong normalization theorem showing that all computations terminate.  ...  Girard for his help and guidance for earlier versions of the formalism. We thank D. Scott for his invitation at Carnegie-Mellon University where the final version of this paper was written.  ... 
doi:10.1016/0890-5401(88)90005-3 fatcat:32jmygi2zzgdbewpgosbbzlnsi

Page 115 of Psychological Review Vol. 67, Issue 2 [page]

1960 Psychological Review  
But it is pre- cisely the laws of classical conditioning that function as the basis for the rules by which we arrive at the consequences of the several implicit definitions.  ...  about model refer ‘al calculus or lationships from some In the language use a theory, the term directly to to a system of re other puters, the the laws of con may a mathemati ele ctre nic com- source such  ... 

Page 2085 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
The implicit function theory is instrumental in the tranformation of optimization prob- lems of a complicated nature to problems of a less complicated nature.  ...  The author shows how to construct nontrivial quasiconvex func- tions with pth-power growth at infinity from known quasiconvex functions. The proofs involve use of maximal functions follow- ing E.  ... 

The Perfect Lambda Syntax

Mikus Vanags, Rudite Cevere
2018 Baltic Journal of Modern Computing  
Different ideas of lambda expression implementation are compared, and the perfect lambda syntax is discovered.  ...  These perfections are characterized by the specific properties. This article presents a review and analysis of a set of characteristics that describe a perfect lambda syntax.  ...  Acknowledgements This research started as a part of Mikus Vanags' PhD thesis "Abstract data processing technologies" available at: https://doi.org/10.22616/lluany/2017. 010 We want to thank to all the  ... 
doi:10.22364/bjmc.2018.6.1.02 fatcat:3ineeukcgvcdfdbehztjnh3yma

Applying Holistic Adult Learning Theory to the Study of Calculus

Reem Jaafar, LaGuardia Community College, City University of New York, Joni Schwartz, LaGuardia Community College-City University of New York
2018 Journal of University Teaching and Learning Practice  
Data collection was from a selective sampling of student reflective survey writing throughout the span of one calculus course.  ...  Data content analysis was both manual and with the aid of NVivo qualitative software by two separate coders.  ...  Doctors often use calculus in the estimation of the progression of the illness. Global mapping is done with the help of calculus. Calculus also used to solve paradoxes.  ... 
doi:10.53761/1.15.3.6 fatcat:gsv7lkz2ifcsjezhcix6f43adu
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