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14
Soft lambdacalculus: a language for polynomial time computation
 In Proc. FoSSaCS, Springer LNCS 2987
, 2004
"... Abstract. Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambdacalculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time. ..."
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Cited by 19 (2 self)
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Abstract. Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambdacalculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms of this calculus are reducible in polynomial time. We then extend the type system of Soft logic with recursive types. This allows us to consider nonstandard types for representing lists. Using these datatypes we examine the concrete expressiveness of Soft lambdacalculus with the example of the insertion sort algorithm. 1
Theories With SelfApplication and Computational Complexity
 Information and Computation
, 2002
"... Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the early seventies. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: selfapplication is meaningful, but not ne ..."
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Cited by 12 (9 self)
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Applicative theories form the basis of Feferman's systems of explicit mathematics, which have been introduced in the early seventies. In an applicative universe, all individuals may be thought of as operations, which can freely be applied to each other: selfapplication is meaningful, but not necessarily total. It has turned out that theories with selfapplication provide a natural setting for studying notions of abstract computability, especially from a prooftheoretic perspective.
A syntactical analysis of nonsizeincreasing polynomial time computation
, 2002
"... A syntactical proof is given that all functions definable in a certain affine linear typed λcalculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated. ..."
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Cited by 11 (2 self)
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A syntactical proof is given that all functions definable in a certain affine linear typed λcalculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be calculated.
The geometry of linear higherorder recursion
 In Logic in Computer Science, 20th International Symposium, Proceedings
, 2005
"... Linearity and ramification constraints have been widely used to weaken higherorder (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions, as the works by Leivant, Hofmann and others show. This paper shows that finetuning these two cons ..."
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Cited by 9 (4 self)
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Linearity and ramification constraints have been widely used to weaken higherorder (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions, as the works by Leivant, Hofmann and others show. This paper shows that finetuning these two constraints leads to different expressive strengths, some of them lying well beyond polynomial time. This is done by introducing a new semantics, called algebraic context semantics. The framework stems from Gonthier’s original work and turns out to be a versatile and powerful tool for the quantitative analysis of normalization in the lambdacalculus with constants and higherorder recursion. 1
A ProofTheoretic Characterization of the Basic Feasible Functionals
 Theoretical Computer Science
, 2002
"... We provide a natural characterization of the type two MehlhornCookUrquhart basic feasible functionals as the provably total type two functionals of our (classical) applicative theory PT introduced in [27], thus providing a proof of a result claimed in the conclusion of [27]. ..."
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Cited by 7 (6 self)
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We provide a natural characterization of the type two MehlhornCookUrquhart basic feasible functionals as the provably total type two functionals of our (classical) applicative theory PT introduced in [27], thus providing a proof of a result claimed in the conclusion of [27].
Weak theories of operations and types
"... This is a survey paper on various weak systems of Feferman’s explicit mathematics and their proof theory. The strength of the systems considered in measured in terms of their provably terminating operations typically belonging to some natural classes of computational time or space complexity. Keywor ..."
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Cited by 4 (3 self)
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This is a survey paper on various weak systems of Feferman’s explicit mathematics and their proof theory. The strength of the systems considered in measured in terms of their provably terminating operations typically belonging to some natural classes of computational time or space complexity. Keywords: Proof theory, Feferman’s explicit mathematics, applicative theories, higher types, types and names, partial truth, feasible operations 1
Linear Programming Languages
"... Abstract. We formalize SℓPCF, namely a programming language which is able to represent linear function between coherence spaces. We give an interpretation of SℓPCF into the model of linear coherence spaces and we show that such semantics is fully abstract with respect to it. SℓPCF is not syntactical ..."
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Cited by 2 (1 self)
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Abstract. We formalize SℓPCF, namely a programming language which is able to represent linear function between coherence spaces. We give an interpretation of SℓPCF into the model of linear coherence spaces and we show that such semantics is fully abstract with respect to it. SℓPCF is not syntactically linear, namely its programs can contain the same variable more than once. Last, we address the universality problem. 1
Linear Ramified Higher Type Recursion and Parallel Complexity
"... A typed lambda calculus with recursion in all finite types is defined such that the first order terms exactly characterize the parallel complexity class NC. This is achieved by use of the appropriate forms of recursion (concatenation recursion and logarithmic recursion), a ramified type structure an ..."
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Cited by 2 (0 self)
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A typed lambda calculus with recursion in all finite types is defined such that the first order terms exactly characterize the parallel complexity class NC. This is achieved by use of the appropriate forms of recursion (concatenation recursion and logarithmic recursion), a ramified type structure and imposing of a linearity constraint.
Higherorder Interpretations and Program Complexity (Long Version)
, 2012
"... Polynomial interpretations and their generalizations like quasiinterpretations have been used in the setting of firstorder functional languages to design criteria ensuring statically some complexity bounds on programs [1]. This fits in the area of implicit computational complexity, which aims at g ..."
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Cited by 1 (0 self)
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Polynomial interpretations and their generalizations like quasiinterpretations have been used in the setting of firstorder functional languages to design criteria ensuring statically some complexity bounds on programs [1]. This fits in the area of implicit computational complexity, which aims at giving machinefree characterizations of complexity classes. Here we extend this approach to the higherorder setting. For that we consider the notion of simply typed term rewriting systems [2], we define higherorder polynomial interpretations (HOPI) for them and give a criterion based on HOPIs to ensure that a program can be executed in polynomial time. In order to obtain a criterion which is flexible enough to validate some interesting programs using higherorder primitives, we introduce a notion of polynomial quasiinterpretations, coupled with a simple termination criterion based on linear types and pathlike orders. 1