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Structural recursion with locally scoped names

ANDREW M. PITTS
2011 Journal of functional programming  
The paper is a revised and expanded version of Pitts (Nominal System T. In  ...  The new recursion principle is motivated by the nominal sets notion of 'α-structural recursion', whose use of names and associated freshness side-conditions in recursive definitions formalizes common practice  ...  When making a structurally recursive definition of a function f : Λ → X in terms of functions f 1 : A → X, f 2 : X × X → X and f 3 : A × X → X, one can take advantage of the identification of terms up  ... 
doi:10.1017/s0956796811000116 fatcat:zxrp75duazf45ekoxzeg7v6cbq

Alpha-Structural Recursion and Induction [chapter]

Andrew M. Pitts
2005 Lecture Notes in Computer Science  
This paper explains the idea in as concrete a way as possible and gives a new derivation within higher-order logic of principles of α-structural recursion and induction for α-equivalence classes from the  ...  The nominal approach to abstract syntax deals with the issues of bound names and α-equivalence by considering constructions and properties that are invariant with respect to permuting names.  ...  Thus if some language of interest has been specified as the α-terms for a particular nominal signature and one wishes to define a function on those α-terms specified by an instance of the recursion scheme  ... 
doi:10.1007/11541868_2 fatcat:kc5n3jcbxjecdl2ehrusibxlvi

Alpha-structural recursion and induction

Andrew M. Pitts
2006 Journal of the ACM  
This paper explains the idea in as concrete a way as possible and gives a new derivation within higher-order logic of principles of α-structural recursion and induction for α-equivalence classes from the  ...  The nominal approach to abstract syntax deals with the issues of bound names and α-equivalence by considering constructions and properties that are invariant with respect to permuting names.  ...  Thus if some language of interest has been specified as the α-terms for a particular nominal signature and one wishes to define a function on those α-terms specified by an instance of the recursion scheme  ... 
doi:10.1145/1147954.1147961 fatcat:flhgnqt6xvfsrl7sher53yanti

Rensets and Renaming-Based Recursion for Syntax with Bindings [article]

Andrei Popescu
2022 arXiv   pre-print
a recursively enumerable set of unconditional equations, referring only to the most fundamental term operators: the constructors and renaming.  ...  In particular, renaming is a more fundamental operator than the nominal swapping operator and enjoys a simpler, equationally expressed relationship with the variable freshness predicate.  ...  I am grateful to the IJCAR reviewers for their insightful comments and suggestions, and for pointing out related work.  ... 
arXiv:2205.09233v2 fatcat:az3oi32w6ffo3af2qi4b2svpxq

Recursive nonlinear-system identification using latent variables [article]

Per Mattsson, Dave Zachariah, Petre Stoica
2018 arXiv   pre-print
Finally, we develop a convex majorization technique and show that it enables a recursive identification method.  ...  The method learns parsimonious predictive models and is tested on both synthetic and real nonlinear systems.  ...  Here we consider nominal models on the form y 0 (t) = Θϕ(t), (2) where the p × 1 vector ϕ(t) is a given function of D t−1 and Θ denotes the unknown parameters. Remark 2.  ... 
arXiv:1606.04366v3 fatcat:qk6ggqdblzbhhmw6hb6et5o7ey

A Comparison of NOOP to Structural Domain-Theoretic Models of OOP [article]

Moez A. AbdelGawad
2017 arXiv   pre-print
Leveraging the development of NOOP, the comparison presented in this paper provides a clear and precise mathematical account for the relation between nominal and structural OO type systems.  ...  NOOP is a recently developed domain-theoretic model of OOP that was designed to include full nominal information found in nominally-typed OOP.  ...  of the conclusions in this paper, and to Professor Benjamin Pierce for the feedback he offered on motivating and presenting NOOP.  ... 
arXiv:1603.08648v3 fatcat:3mhtkbo54rdzzj2zfevug5j6rm

Nominal Reasoning Techniques in Coq

Brian Aydemir, Aaron Bohannon, Stephanie Weirich
2007 Electronical Notes in Theoretical Computer Science  
Our axiomatization includes a nominal induction principle and functions for calculating free variables and substitution.  ...  We are currently working on proving the soundness of a primitive recursion combinator and developing a method of generating these axioms and their proof of soundness from a grammar describing the syntax  ...  Note that this function requires that the type atom be infinite and implements "choosing a fresh atom," an operation whose details are typically left unspecified on paper.  ... 
doi:10.1016/j.entcs.2007.01.028 fatcat:ldmfshfj55andf4mtlbbb2bnrm

A Simple Nominal Type Theory

James Cheney
2009 Electronical Notes in Theoretical Computer Science  
This has proven difficult, largely because of complex interactions between nominal logic's name-abstraction operation and ordinary functional abstraction.  ...  This is a first step towards understanding the constructive content of nominal logic and incorporating it into existing constructive logics and type theories.  ...  Thanks are also due to Andrew Pitts, Christian Urban and the anonymous reviewers for detailed comments and suggestions.  ... 
doi:10.1016/j.entcs.2008.12.115 fatcat:x2m436r2w5hvphnptmf2cgz4ya

Demand For Money: Implications for The Conduct of Monetary Policy in Kenya

Moses M. Sichei, Anne W. Kamau
2012 International Journal of Economics and Finance  
Price, real GDP, nominal 91-Day Treasury bill rate, nominal interbank rate, nominal deposit rate and foreign interest rate affected the long-run demand for money functions to different degrees.  ...  Dynamic frameworks are used to estimate and uncover parsimonious and empirically stable demand for money functions.  ...  The nominal deposit rate (own-return on money) has a positive effect on the demand for all the real money balances.  ... 
doi:10.5539/ijef.v4n8p72 fatcat:cdjgo5vaw5dzhct6zkiooki2ja

Tube-Based Robust Economic Model Predictive Control on Dissipative Systems with Generalized Optimal Regimes of Operation

Zihang Dong, David Angeli
2018 2018 IEEE Conference on Decision and Control (CDC)  
Recursive feasibility and an a-priori upper bound to the closed-loop asymptotic average performance are ensured.  ...  The proposed algorithm minimizes a modified economic objective function which considers the worst cost within a tube around the solution of the associated nominal system.  ...  and a weighting function on nominal initial state.  ... 
doi:10.1109/cdc.2018.8619325 dblp:conf/cdc/DongA18 fatcat:mglko5nhbraflcesaxhw3gyizi

A Recursion Combinator for Nominal Datatypes Implemented in Isabelle/HOL [chapter]

Christian Urban, Stefan Berghofer
2006 Lecture Notes in Computer Science  
Pitts stated some general conditions under which functions over alpha-equivalence classes can be defined by a form of structural recursion and gave a clever proof for the existence of a primitive-recursion  ...  We give a version of this proof that works directly over nominal datatypes and does not rely upon auxiliary constructions.  ...  Acknowledgements: We are very grateful to Andrew Pitts and Michael Norrish for the many discussions with them on the subject of the paper. The first  ... 
doi:10.1007/11814771_41 fatcat:auaivy6ub5godmcbmjmhrf2534

Completeness in PVS of a Nominal Unification Algorithm

Mauricio Ayala-Rincón, Maribel Fernández, Ana Cristina Rocha-Oliveira
2016 Electronical Notes in Theoretical Computer Science  
Also, in our specification, instead of applying simplification rules to unification and freshness constraints, we recursively build solutions for the original problem through a straightforward functional  ...  Functional nominal computation can be modelled through nominal rewriting, in which α-equivalence, nominal matching and nominal unification play an important role.  ...  Nominal unification algorithm In order to construct a nominal unification algorithm as a recursive function in the specification language of PVS, it is necessary to provide a recognisable answer in cases  ... 
doi:10.1016/j.entcs.2016.06.005 fatcat:pgsndhnpbfd5nlpbjht7qo3fge

Robust Control of Markov Decision Processes with Uncertain Transition Matrices

Arnab Nilim, Laurent El Ghaoui
2005 Operations Research  
We use to denote the support function of a set ⊆ R n , with for v ∈ R n , v = sup p T v p ∈ .  ...  recursion that is almost the same as that of the classical recursion.  ...  The authors are grateful to Dimitris Bertsimas for pointing out a mistake in an earlier version of the paper, and to Alain Haurie for his very detailed comments.  ... 
doi:10.1287/opre.1050.0216 fatcat:sdopm7bnkfdg7cpnpjsixrff2a

Elements of complex structures, where recursion isn't [chapter]

Masayoshi Shibatani
2009 Typological Studies in Language  
In both generative and typological studies, the relativization site has been considered to be one of the places where recursion of sentences takes place.  ...  This paper examines a number of wide-spread patterns of relativization around the globe and argues that what have been identified as relative clauses/sentences are in fact nominalized entities, lacking  ...  process, which, as noted above, simply juxtaposes a (head) nominal and an argument nominalized expression with a gap in appositive syntagm. 2 2.  ... 
doi:10.1075/tsl.85.07ele fatcat:xwy4ylazqbfhrp62c353qtxpxm

Towards nominal computation

Mikolaj Bojanczyk, Laurent Braud, Bartek Klin, Slawomir Lasota
2012 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '12  
Nominal sets are a different kind of set theory, with a more relaxed notion of finiteness. They offer an elegant formalism for describing λ-terms modulo α-conversion, or automata on data words.  ...  The key idea is that it includes a native type for finite sets in the nominal sense. To illustrate the power of our language, we write short programs that process automata on data words.  ...  We are grateful to Andrew Pitts, Dan Ghica, Paweł Urzyczyn and the anonymous referees, whose constructive comments lead to a great improvement of the presentation of this paper.  ... 
doi:10.1145/2103656.2103704 dblp:conf/popl/BojanczykBKL12 fatcat:ghzi2hxx5bgbzb43cuchpqnrie
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