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Extending the Loop Language with HigherOrder Procedural Variables
 Special issue of ACM TOCL on Implicit Computational Complexity
, 2010
"... We extend Meyer and Ritchie’s Loop language with higherorder procedures and procedural variables and we show that the resulting programming language (called Loop ω) is a natural imperative counterpart of Gödel System T. The argument is twofold: 1. we define a translation of the Loop ω language int ..."
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Cited by 9 (6 self)
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We extend Meyer and Ritchie’s Loop language with higherorder procedures and procedural variables and we show that the resulting programming language (called Loop ω) is a natural imperative counterpart of Gödel System T. The argument is twofold: 1. we define a translation of the Loop ω language into System T and we prove that this translation actually provides a lockstep simulation, 2. using a converse translation, we show that Loop ω is expressive enough to encode any term of System T. Moreover, we define the “iteration rank ” of a Loop ω program, which corresponds to the classical notion of “recursion rank ” in System T, and we show that both translations preserve ranks. Two applications of these results in the area of implicit complexity are described. 1
Classes of Algorithms: Formalization and Comparison
, 2012
"... We discuss two questions about algorithmic completeness (in the operational sense). First, how to get a mathematical characterization of the classes of algorithms associated to the diverse computation models? Second, how to define a robust and satisfactory notion of primitive recursive algorithm? We ..."
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We discuss two questions about algorithmic completeness (in the operational sense). First, how to get a mathematical characterization of the classes of algorithms associated to the diverse computation models? Second, how to define a robust and satisfactory notion of primitive recursive algorithm? We propose solutions based on Gurevich’s Abstract State Machines. Contents 1
for HigherOrder Procedural Variables
, 2009
"... We formally specified the type system and operational semantics of Loop ω with Ott and Isabelle/HOL proof assistant. Moreover, both the type system and the semantics of Loop ω have been tested using Isabelle/HOL program extraction facility for inductively defined relations. In particular, the progra ..."
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We formally specified the type system and operational semantics of Loop ω with Ott and Isabelle/HOL proof assistant. Moreover, both the type system and the semantics of Loop ω have been tested using Isabelle/HOL program extraction facility for inductively defined relations. In particular, the program that computes the Ackermann function type checks and behaves as expected. The main difference (apart from the choice of an Adalike concrete syntax) with Loop ω comes from the treatment of parameter passing. Indeed, since Ott does not currently fully support αconversion, we rephrased the operational semantics with explicit aliasing in order to implement the out parameter passing mode.
Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A COMPLETE CHARACTERIZATION OF PRIMITIVE RECURSIVE INTENSIONAL BEHAVIOURS
"... Abstract. We give a complete characterization of the class of functions that are the intensional behaviours of Primitive Recursive algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unari ..."
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Abstract. We give a complete characterization of the class of functions that are the intensional behaviours of Primitive Recursive algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers. AMS Subject Classification. — Give AMS classification codes —. 1.