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Normalization by Evaluation with Typed Abstract Syntax

Olivier Danvy, Morten Rhiger, Kristoffer H. Rose
2001 BRICS Report Series  
<p>We present a simple way to implement typed abstract syntax for the<br />lambda calculus in Haskell, using phantom types, and we specify <br />normalization by evaluation (i.e., type-directed partial  ...  Proving that normalization by evaluation preserves<br /> types and yields normal forms then reduces to type-checking the<br />specification.</p>  ...  Acknowledgments: A preliminary and longer version of this article is available in the proceedings of FLOPS 2001 [11] . We would like to thank Simon Peyton Jones for identifying phantom types in it.  ... 
doi:10.7146/brics.v8i16.20473 fatcat:mipjem5ccve4lbaw5a5oskoqii

Towards Normalization by Evaluation for the βη-Calculus of Constructions [chapter]

Andreas Abel
2010 Lecture Notes in Computer Science  
In Section 3 we define normalization by evaluation for CoC using partial applicative structures, and we specify a type inference algorithm.  ...  The normalization algorithm evaluates terms into a semantic domain, and reifies the values back to terms in normal form.  ...  The author acknowledges the support of INRIA through a guest researcher fellowship.  ... 
doi:10.1007/978-3-642-12251-4_17 fatcat:gjroecnajzgl3oskh2x5kqyr4y

Type Theory Should Eat Itself

James Chapman
2009 Electronical Notes in Theoretical Computer Science  
In this paper I present a partial formalisation of a normaliser for type theory in Agda [22] ; extending previous work on big-step normalisation [2, 1] .  ...  The normaliser in written as an environment machine. Only the computational behaviour of the normaliser is presented omitting details of termination.  ...  Acknowledgement I would like to thank Nils Anders Danielsson, Thorsten Altenkirch, Wouter Swiestra, Nicolas Oury and the anonymous referees for their helpful comments.  ... 
doi:10.1016/j.entcs.2008.12.114 fatcat:xkpwes6dpndlxej7wqnweuh2ri

Completeness of Global Evaluation Logic [chapter]

Sergey Goncharov, Lutz Schröder, Till Mossakowski
2006 Lecture Notes in Computer Science  
A basic role is played here by global evaluation logic, concerned with formulae which may be thought of as being universally quantified over the state space; this formalism is the fundament of more advanced  ...  Monads serve the abstract encapsulation of side effects in semantics and functional programming.  ...  Acknowledgements This work forms part of the DFG-funded project HasCASL (KR 1191/7-1 and KR 1191/7-2) and the project HOL-MDL funded by the FNK of the University of Bremen.  ... 
doi:10.1007/11821069_39 fatcat:x34mtae7jnfkjo43ql4jfswuk4

New equations for neutral terms

Guillaume Allais, Conor McBride, Pierre Boutillier
2013 Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming - DTP '13  
The definitional equality of an intensional type theory is its test of type compatibility.  ...  We propose a way to decide theories which supplement evaluation with 'ν-rules', rearranging the neutral parts of normal forms, and report a successful initial experiment.  ...  Acknowledgements We would like to thank the anonymous reviewers for their helpful comments and suggestions as well as Stevan Andjelkovic for carefully reading our draft.  ... 
doi:10.1145/2502409.2502411 dblp:conf/icfp/AllaisMB13 fatcat:eselyun5jzg6nagt7ltfmkxxoq

Some normalization properties of martin-löf's type theory, and applications [chapter]

David A. Basin, Douglas J. Howe
1991 Lecture Notes in Computer Science  
For the latter application we point out some advantages to be gained by working in a more expressive type theory.  ...  For type theories such as LF, such properties can be established via an analysis of normal forms and types.  ...  between proofs and terms of the type theory.  ... 
doi:10.1007/3-540-54415-1_60 fatcat:3s2533qtijhpzb7ajc32dsqliu

On the orthogonality of assignments and procedures in Algol

Stephen Weeks, Matthias Felleisen
1993 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '93  
We appreciate comments by Robert Cartwright, Ian Mason, Amr Sabry, and John Gateley on an early draft.  ...  tension of a simple imperative programming language with a call-by-name functional language.  ...  First, it proves that the language's calculus is indeed the extension of a term rewriting systems for a simple imperative language with a typed A- calculus.  ... 
doi:10.1145/158511.158523 dblp:conf/popl/WeeksF93 fatcat:frja7j6vwjemxgpbojgk573aba

Comparison of ISO-GUM, draft GUM Supplement 1 and Bayesian statistics using simple linear calibration

Raghu Kacker, Blaza Toman, Ding Huang
2006 Metrologia  
We consider both small and large uncertainties for the Type B input variables. We use each of the three approaches to quantify the uncertainty in measurement for each of the three scenarios.  ...  For illustration, we use a measurement equation for simple linear calibration that includes both Type A and Type B input variables.  ...  Acknowledgments This paper was developed after a panel discussion organized by Ding Huang at the 2004 meeting of the National Conference of Standards Laboratories International (www.ncsli.org) held in  ... 
doi:10.1088/0026-1394/43/4/s02 fatcat:dsafjqsg5fdw5icacigv7lwjji

New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized [article]

Guillaume Allais, Pierre Boutillier, Conor McBride
2013 arXiv   pre-print
The definitional equality of an intensional type theory is its test of type compatibility.  ...  We propose a way to decide theories which supplement evaluation with 'ν-rules', rearranging the neutral parts of normal forms, and report a successful initial experiment.  ...  Type directed partial evaluation (or normalization by evaluation) is a way to compute the canonical forms by using the evaluation mechanism of the host language whilst exploiting the available type information  ... 
arXiv:1304.0809v3 fatcat:w55zw2s4fzasvkjzmwdpj7qglu

New evaluations for multiaxial-stress properties of ceramic materials

Joseph Marin
1966 Experimental mechanics  
In Part B of this paper, new macroscopic engineering-type theories for combined-stress behavior are  ...  Part A of this paper outlines new experiments that are needed to evaluate the mechanical properties and to confirm theories proposed in Part B.  ...  by a quadratic function of the normal stress on this plane.  ... 
doi:10.1007/bf02326145 fatcat:plu244iruzcxvfqfp4tdvjb5ey

2. The decision-making context [chapter]

1996 Whither Civil Engineering?  
The results indicate that all works can be done by simple computation, the effectiveness is proved; and the order based on the comprehensive scores is in line with the actual situations, which proves the  ...  Taking the new product line project of company X for example, the approach based on information entropy theory is utilized to test the effectiveness, robustness and applicability of the method.  ...  From all of the computation processes, the works could be implemented not only by simple software but by simple hand computation, which proves the approach to be effective.  ... 
doi:10.1680/wce.25646.0002 fatcat:36huetwbhjfuzmyuerao6ouvoq

Automatically Finding Theory Morphisms for Knowledge Management [chapter]

Dennis Müller, Michael Kohlhase, Florian Rabe
2018 Lecture Notes in Computer Science  
As they induce new theorems in the target theory for any of the source theory, theory morphisms are high-value elements of a modular formal library.  ...  Usually, theory morphisms are manually encoded, but this practice requires authors who are familiar with source and target theories at the same time, which limits the scalability of the manual approach  ...  Acknowledgments The authors gratefully acknowledge financial support from the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541) and the DFG-funded project OAF: An Open Archive  ... 
doi:10.1007/978-3-319-96812-4_18 fatcat:llu3cu4cqjbdbi6e6udbknequa

Design and Implementation of the Andromeda Proof Assistant [article]

Andrej Bauer, Gaëtan Gilbert, Philipp G. Haselwarter, Matija Pretnar, Christopher A. Stone
2018 arXiv   pre-print
The only trusted component of Andromeda is a minimalist nucleus (an implementation of the inference rules of an object-level type theory), which controls construction and decomposition of type-theoretic  ...  To demonstrate the flexibility of this system structure, we implemented a nucleus consisting of dependent type theory with equality reflection.  ...  However, LCF and many of its descendants use Church's simple type theory [6] , whereas Andromeda is based on the dependent type theory of Martin-Löf [17] .  ... 
arXiv:1802.06217v1 fatcat:ioweq2oekfg5lba4d62alrln74

Page 447 of Journal of Chemical Physics Vol. 32, Issue 2 [page]

1960 Journal of Chemical Physics  
Phys. 31, 139 (1959). the physical basis of the theory and to develop ap- proximate methods of numerical evaluation. II.  ...  The frequency » is related to the con- tributing normal modes of frequencies {»,;} by v= Diaty?/Dia?, (2) with a; the contribution of the ith normal mode to a motion along the direction g,.  ... 

The "monster" study

Franklin H. Silverman
1988 Journal of Fluency Disorders  
He stated the following: In a semantic theory of stuttering, emphasis is placed upon the self-reflexive process of abstracting, the general mechanism of evaluation, by virtue of which any organism reacts  ...  which have been described by these writers as essentially effortless, "unconscious," simple repetition of syllables, words, and phrases.  ... 
doi:10.1016/0094-730x(88)90049-6 fatcat:z22lbwxlg5e33md3obcuan4zmy
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