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Normalization and partial evaluation
 Applied Semantics, number 2395 in LNCS
, 2002
"... Abstract. We give an introduction to normalization by evaluation and typedirected partial evaluation. We first present normalization by evaluation for a combinatory version of Gödel System T. Then we show normalization by evaluation for typed lambda calculus with β and η conversion. Finally, we int ..."
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Abstract. We give an introduction to normalization by evaluation and typedirected partial evaluation. We first present normalization by evaluation for a combinatory version of Gödel System T. Then we show normalization by evaluation for typed lambda calculus with β and η conversion. Finally, we introduce the notion of binding time, and explain the method of typedirected partial evaluation for a small PCFstyle functional programming language. We give algorithms for both callbyname and callbyvalue versions of this language.
Inclusion Constraints over Nonempty Sets of Trees
, 1997
"... We present a new constraint system called INES. Its constraints are conjunctions of inclusions t1 `t2 between firstorder terms (without set operators) which are interpreted over nonempty sets of trees. The existing systems of set constraints can express INES constraints only if they include ne ..."
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Cited by 14 (5 self)
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We present a new constraint system called INES. Its constraints are conjunctions of inclusions t1 `t2 between firstorder terms (without set operators) which are interpreted over nonempty sets of trees. The existing systems of set constraints can express INES constraints only if they include negation. Their satisfiability problem is NEXPTIMEcomplete. We present an incremental algorithm that solves the satisfiability problem of INES constraints in cubic time. We intend to apply INES constraints for type analysis for a concurrent constraint programming language.
A finite semantics of simplytyped lambda terms for infinite runs of automata
 Procedings of the 20th international Workshop on Computer Science Logic (CSL ’06), volume 4207 of Lecture Notes in Computer Science
, 2006
"... Vol. 3 (3:1) 2007, pp. 1–23 ..."
Operational Aspects of Untyped Normalization by Evaluation
, 2003
"... A purely syntactic and untyped variant of Normalization by Evaluation for the λcalculus... ..."
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A purely syntactic and untyped variant of Normalization by Evaluation for the λcalculus...
Infinite rewriting: from syntax to semantics
 In Processes, Terms and Cycles: Steps on the Road to Infinity: Essays Dedicated to Jan Willem Klop on the Occasion of His 60th Birthday
, 2005
"... Rewriting is the repeated transformation of a structured object according to a set of rules. This simple concept has turned out to have a rich variety of elaborations, giving rise to many different theoretical frameworks for reasoning about computation. Aside from its theoretical importance, rewriti ..."
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Cited by 3 (1 self)
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Rewriting is the repeated transformation of a structured object according to a set of rules. This simple concept has turned out to have a rich variety of elaborations, giving rise to many different theoretical frameworks for reasoning about computation. Aside from its theoretical importance, rewriting has also
Operational Aspects of Normalization by Evaluation
, 2001
"... A purely syntactic and untyped variant of Normalization by Evaluation for the calculus is presented in the framework of a twolevel calculus with rewrite rules to model the inverse of the evaluation functional. Among its operational properties gures a standardization theorem that formally establi ..."
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Cited by 3 (2 self)
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A purely syntactic and untyped variant of Normalization by Evaluation for the calculus is presented in the framework of a twolevel calculus with rewrite rules to model the inverse of the evaluation functional. Among its operational properties gures a standardization theorem that formally establishes adequacy of implementation in functional programming languages. An example implementation in Haskell is provided. The relation to usual typedirected Normalization by Evaluation is highlighted, using a short analysis of expansion that leads to a perspicuous strong normalization and conuence proof for "reduction as a byproduct.
Combinatory Models and Symbolic Computation
 Lecture Notes in Computer Science , Springer Verlag 721
, 1992
"... Weintroduce an algebraic model of computation which is especially useful for the description of computations in analysis. On one level the model allows the representation of algebraic computation and on an other level approximate computation is represented. ..."
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Weintroduce an algebraic model of computation which is especially useful for the description of computations in analysis. On one level the model allows the representation of algebraic computation and on an other level approximate computation is represented.
Interpreting functions as πcalculus processes: a tutorial
, 1999
"... This paper is concerned with the relationship betweencalculus and ��calculus. Thecalculus talks about functions and their applicative behaviour. This contrasts with the ��calculus, that talks about processes and their interactive behaviour. Application is a special form of interaction, and there ..."
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This paper is concerned with the relationship betweencalculus and ��calculus. Thecalculus talks about functions and their applicative behaviour. This contrasts with the ��calculus, that talks about processes and their interactive behaviour. Application is a special form of interaction, and therefore functions can be seen as a special form of processes. We study how the functions of thecalculus (the computable functions) can be represented as ��calculus processes. The ��calculus semantics of a language induces a notion of equality on the terms of that language. We therefore also analyse the equality among functions that is induced by their representation as ��calculus processes. This paper is intended as a tutorial. It however contains some original contributions. The main ones are: the use of wellknown Continuation Passing Style transforms to derive the encodings into ��calculus and prove their correctness; the encoding of typedcalculi.
A Non Functional Calculus: Linear Logic and Concurrency
, 2000
"... this paper to an interaction mechanism inspired to the computational behaviour of proof nets, a deduction system of linear logic [7]. In this setting the conclusion of a derivation is the type of the corresponding proof net. The computational mechanism is cut elimination that can only occur between ..."
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this paper to an interaction mechanism inspired to the computational behaviour of proof nets, a deduction system of linear logic [7]. In this setting the conclusion of a derivation is the type of the corresponding proof net. The computational mechanism is cut elimination that can only occur between terms with the same type. The relationship between proof nets and processes have already been studied in the literature. Abramsky interprets proof as processes and consider a cutelimination as communication paradigm [1]. Similar typed calculi based on linear logic where developed also by Solitro and Valentini [13, 14]. Yuxi Fu [6] studies a computational model in which the role of process and proofs is reversed with respect to the Abramsky's view. The corresponding paradigm is thus communication as cutelimination for classical proofs. Bellin and Scott implements the cutelimination of linear logic in the calculus. We here push forward the work in [13, 14] where : : : . Our approach differ from the one mentioned above in that we move from the mentioned calculi for linear logic and borrow some ideas from cham by Berry and Boudol [3].
NOTES on LAMBDA CALCULUS
"... INTRODUCTION Lambda calculus, invented by Alonzo Church in the 1930s, is a general but syntactically simple model of computation. It was conceived as part of a system of higherorder logic and function theory. The first undecidability results were for lambda calculus; similar results for Turing mac ..."
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INTRODUCTION Lambda calculus, invented by Alonzo Church in the 1930s, is a general but syntactically simple model of computation. It was conceived as part of a system of higherorder logic and function theory. The first undecidability results were for lambda calculus; similar results for Turing machines came later. In addition to its purely mathematical applications, lambda calculus is important in the study of computer programming languages. It has served as a basic linguistic prototype from which LISP, ALGOLlike languages, and functional programming languages have been derived. It also serves as a basic metalanguage for expressing the denotational semantics of programming languages. These notes are a brief introduction to the typefree lambda calculus. Two versions of the typefree lambda calculus are presented: the callbyname (CBN) and the callbyvalue (CBV) calculi. The CBN calculus was the original version of the lambda