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Parametrization over inductive relations of a bounded number of variables

1990
*
Annals of Pure and Applied Logic
*

We present

doi:10.1016/0168-0072(90)90043-2
fatcat:2tyfsumnt5b7xpu3x3j4pp6oae
*a**Parametrization*Theorem for (positive elementary)*inductions*that use*a**bounded**number**of**variables*. ... These results involve the complexity*of*the*inductive**relations*-and the complexity*of*the structure or class*of*structures on which these*relations*live. ... But '8 is not*inductive*in*a**bounded**number**of**variables*. Towards contradiction, suppose that Uk = UkC1)*parametrized*all unary %*inductive**relations*. For some K E w, Uk is K-*inductive*. ...##
###
Invariant Generation for Parametrized Systems Using Self-reflection
[chapter]

2012
*
Lecture Notes in Computer Science
*

*Parametrized*systems are concurrent systems consisting

*of*an

*a*priori unbounded

*number*

*of*process instances running the same program. ... In our approach, the key enabler is the notion

*of*

*a*reflective abstraction that we prove has an important correspondence with

*inductive*invariants. ... with

*a*

*bounded*

*number*

*of*resources. . ...

##
###
Syntax for Free: Representing Syntax with Binding Using Parametricity
[chapter]

2009
*
Lecture Notes in Computer Science
*

To demonstrate the proof we have constructed

doi:10.1007/978-3-642-02273-9_5
fatcat:qxwscoc3rbhprdcwgk4expkk5y
*a*model*of**parametric*polymorphism inside the Coq proof assistant. The proof*of*the theorem requires*parametricity**over*Kripke*relations*. ... We show that, in*a**parametric*model*of*polymorphism, the type ∀α.((α → α) → α) → (α → α → α) → α is isomorphic to closed de Bruijn terms. ... The preorder-indexing*of*the*relations*is used to handle the expansion*of*the*number**of*meta-*variables*being used as object-*variables*as we go under binders. ...##
###
On bounding space usage of streams using interpretation analysis

2015
*
Science of Computer Programming
*

The input/output upper

doi:10.1016/j.scico.2015.05.004
fatcat:4tuszuio5zdkpjij7snfq66nce
*bounds*criteria consider instead the*relations*between the*number**of*elements read from the input stream and the*number**of*elements produced on the output stream. ... This contribution can be seen as*a*first step in the development*of**a*methodology aiming at using interpretation properties to ensure space safety properties*of*programs working on streams. ...*a**number**of*output elements*related*to the*number*and the size*of*input read elements. ...##
###
A SAT-based algorithm for reparameterization in symbolic simulation

2004
*
Proceedings of the 41st annual conference on Design automation - DAC '04
*

For large circuits, the reparametrization step often results in

doi:10.1145/996566.996711
dblp:conf/dac/ChauhanCK04
fatcat:pkcmbs2j3fg4lmshzvd5yb54ve
*a*blowup*of*BDDs and is expensive due to*a*large*number**of*quantifications*of*input*variables*involved. ... This paper presents*a*novel SAT-based reparameterization algorithm that is largely immune to the large*number**of*input*variables*that need to be quantified. ...*A*set*of*Boolean vectors*over*the state*variables*represents*a*set*of*states. Consider*a*set S*of*vectors*over*the*variables*V = {v 1 , v 2 , . . . , v n }. ...##
###
A relational framework for higher-order shape analysis

2014
*
SIGPLAN notices
*

We propose the integration

doi:10.1145/2692915.2628159
fatcat:welztkjmdvewvp7o3sunq6yxlq
*of**a**relational*specification framework within*a*dependent type system capable*of*verifying complex invariants*over*the shapes*of*algebraic datatypes. ... Our approach is based on the observation that structural properties*of*such datatypes can often be naturally expressed as*inductively*-defined*relations**over*the recursive structure evident in their definitions ... In contrast,*a**parametric*structural*relation*is*a*structural*relation**over**a*polymorphic data type, that is parameterized by*relations**over*type*variables*in the data type. ...##
###
A relational framework for higher-order shape analysis

2014
*
Proceedings of the 19th ACM SIGPLAN international conference on Functional programming - ICFP '14
*

We propose the integration

doi:10.1145/2628136.2628159
dblp:conf/icfp/KakiJ14
fatcat:ntcadei36vhzrptsywef6hwqmi
*of**a**relational*specification framework within*a*dependent type system capable*of*verifying complex invariants*over*the shapes*of*algebraic datatypes. ... Our approach is based on the observation that structural properties*of*such datatypes can often be naturally expressed as*inductively*-defined*relations**over*the recursive structure evident in their definitions ... In contrast,*a**parametric*structural*relation*is*a*structural*relation**over**a*polymorphic data type, that is parameterized by*relations**over*type*variables*in the data type. ...##
###
Global and Local Space Properties of Stream Programs
[chapter]

2010
*
Lecture Notes in Computer Science
*

We study global and local upper

doi:10.1007/978-3-642-15331-0_4
fatcat:ynhlrebaajdu5hbs5onhzhsrha
*bounds*properties*of*both theoretical and practical interests guaranteeing that the size*of*each output stream element is*bounded*by*a*function in the maximal size*of*the ... In this paper, we study semantic interpretation criteria in order to ensure safety and complexity properties*of*first order Haskell like programs on streams. ... The*parametrized*assignment*of**a**variable*x is defined by*a*fresh*variable*X ranking*over*R + . ...##
###
Revisiting Reachability in Timed Automata
[article]

2017
*
arXiv
*
pre-print

We revisit

arXiv:1702.03450v2
fatcat:jfqgafejabebzkz53uqueq5e4a
*a*fundamental result in real-time verification, namely that the binary reachability*relation*between configurations*of**a*given timed automaton is definable in linear arithmetic*over*the integers ... In this paper we give*a*new and simpler proof*of*this result, building on the well-known reachability analysis*of*timed automata involving difference*bound*matrices. ... Given*a*parameter valuation ξ, we define*a*satisfaction*relation*|ù ξ between configurations*of**A*and PTRL formulas by*induction**over*the structure*of*formulas. ...##
###
The Girard–Reynolds isomorphism

2003
*
Information and Computation
*

It also extends to

doi:10.1016/s0890-5401(03)00141-x
fatcat:aubcjde6avgolmbve7kbkr465y
*a*correspondence between second-order intuitionistic logic with quantifiers*over*proposition*variables*and second-order typed lambda calculus with quantifiers*over*type*variables*, which ... However, we show that in the presence*of*Reynolds's*parametricity*property that this is indeed the case, for propositions corresponding to*inductive*definitions*of*naturals or other algebraic types. ... Acknowledgments My thanks to Andrew Pitts, Jon Riecke, and referees*of*POPL 1999, LICS 2000, TACS 2001, and Information and Computation; with particular thanks to Andrew Pitts and some*of*the referees ...##
###
Page 6391 of Mathematical Reviews Vol. , Issue 91M
[page]

1991
*
Mathematical Reviews
*

Bulitko (Odessa)
91m:03048 03D70 03D75
McColm, Gregory L. (1-SFL)

*Parametrization**over**inductive**relations**of**a**bounded**number**of**variables*. Ann. Pure Appl. Logic 48 (1990), no. 2, 103-134. ...*A*key complexity measure is the property*of*being k-*inductive*, i.e.*inductive*via*a*definition using at most k*variables*, free and*bound*. ...##
###
The Girard–Reynolds isomorphism (second edition)

2007
*
Theoretical Computer Science
*

Reynolds proved an Abstraction Theorem: every term in F2 satisfies

doi:10.1016/j.tcs.2006.12.042
fatcat:qp3znp5lpraitaygmw3ay763ye
*a*suitable notion*of*logical*relation*; and formulated*a*notion*of**parametricity*satisfied by well-behaved models. ... Reynolds additionally proved an Abstraction Theorem: every term in F2 satisfies*a*suitable notion*of*logical*relation*; and formulated*a*notion*of**parametricity*satisfied by well-behaved models. ... Acknowledgements My thanks to Rasmus Møgelberg, Martin Odersky, Andrew Pitts, Gordon Plotkin, Jon Riecke, Colin Runciman, Clemens Szyperski, René Vestergaard, to referees*of*POPL 1999, LICS 2000, TACS ...##
###
Variant parametric types

2006
*
ACM Transactions on Programming Languages and Systems
*

For instance,

doi:10.1145/1152649.1152650
fatcat:lttuadsjlvgkbfh3gz3zmwigea
*a*method that only reads the elements*of**a*container*of**numbers*can be easily modified so as to accept containers*of*integers, floating point*numbers*, or any subtype*of*the*number*type. ... By exploiting variant*parametric*types,*a*programmer can write generic code abstractions working on*a*wide range*of**parametric*types in*a*safe way. ... ACKNOWLEDGMENTS We thank anonymous reviewers for useful comments, Gilad Bracha and Benjamin Pierce for helping us clarify about*related*work, and David Griswold and people involved in the development*of*...##
###
Parameter Synthesis Algorithms for Parametric Interval Markov Chains
[chapter]

2018
*
Lecture Notes in Computer Science
*

In particular, we introduce

doi:10.1007/978-3-319-92612-4_7
fatcat:2k754m6janhgrdcjbowld7kcci
*a*co-*inductive*definition*of*consistency, which improves and simplifies previous*inductive*definitions considerably. ... We provide*a*sharper upper*bound*, based on the longest simple path in the IMC. ... They acknowledge the support*of*the Van Gogh project PAMPAS, that partly covered their mutual research visits. ...##
###
SPEED: Symbolic Complexity Bound Analysis
[chapter]

2009
*
Lecture Notes in Computer Science
*

The SPEED project addresses the problem

doi:10.1007/978-3-642-02658-4_7
fatcat:h5hf2uaohzaf7oonfqlkcfjh7y
*of*computing symbolic computational complexity*bounds**of*procedures in terms*of*their inputs. ... We discuss some*of*the challenges that arise and present various orthogonal/complementary techniques recently developed in the SPEED project for addressing these challenges. ... We thank Varun Aggarwala and Aditya Nori for providing useful feedback on*a*draft*of*this paper. ...
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