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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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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
A Dependent Type Theory with Names and Binding
 In Proceedings of the 2004 Computer Science Logic Conference, number 3210 in Lecture notes in Computer Science
, 2004
"... We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on FraenkelMostowski (FM) set theory how to address this through firstclass names: in this paper we present a dependent type theory for prog ..."
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Cited by 15 (1 self)
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We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on FraenkelMostowski (FM) set theory how to address this through firstclass names: in this paper we present a dependent type theory for programming and reasoning with such names. Our development is based on a categorical axiomatisation of names, with freshness as its central notion. An associated adjunction captures constructions known from FM theory: the freshness quantifier N , namebinding, and unique choice of fresh names. The Schanuel topos  the category underlying FM set theory  is an instance of this axiomatisation.
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
Tiering as a Recursion Technique
 Bulletin of Symbolic Logic
"... I survey the syntactic technique of tiering which can be used to restrict the power of a recursion scheme. I show how various results can be obtained entirely proof theoretically without the use of a model of computation. The essence of the method is to move between explicit numerals and simulated ( ..."
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Cited by 3 (0 self)
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I survey the syntactic technique of tiering which can be used to restrict the power of a recursion scheme. I show how various results can be obtained entirely proof theoretically without the use of a model of computation. The essence of the method is to move between explicit numerals and simulated (Church) numerals.
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.
The computational SLR: a logic for reasoning about computational indistinguishability
"... Abstract. Computational indistinguishability is a notion in complexitytheoretic cryptography and is used to define many security criteria. However, in traditional cryptography, proving computational indistinguishability is usually informal and becomes errorprone when cryptographic constructions ar ..."
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Abstract. Computational indistinguishability is a notion in complexitytheoretic cryptography and is used to define many security criteria. However, in traditional cryptography, proving computational indistinguishability is usually informal and becomes errorprone when cryptographic constructions are complex. This paper presents a formal proof system based on an extension of Hofmann’s SLR language, which can capture probabilistic polynomialtime computations through typing and is sufficient for expressing cryptographic constructions. We in particular define rules that justify directly the computational indistinguishability between programs and prove that these rules are sound with respect to the settheoretic semantics, hence the standard definition of security. We also show that it is applicable in cryptography by verifying, in our proof system, Goldreich and Micali’s construction of pseudorandom generator, and the equivalence between nextbit unpredictability and pseudorandomness. 1
Type Systems for ResourceBounded Programming and Compilation: Case for Support
"... Introduction Recent decades have seen a gradual move from lowlevel programming languages such as assembler, Basic, and COBOL to highlevel languages such as C++, Haskell, Java, and ML. Highlevel languages provide abstraction layers and powerful programming idioms, making it much easier to impleme ..."
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Introduction Recent decades have seen a gradual move from lowlevel programming languages such as assembler, Basic, and COBOL to highlevel languages such as C++, Haskell, Java, and ML. Highlevel languages provide abstraction layers and powerful programming idioms, making it much easier to implement and analyse complicated algorithms. At the beginning, lack of efficiency prevented the use of these languages in reallife applications, but nowadays powerful hardware and efficient compilers make highlevel programming languages the method of choice for most applications. Nonetheless, efficiency concerns are still paramount when computing resources are limited, such as in embedded and realtime systems, or for applications to be run across the internet. For embedded and realtime systems, programmers use assembler code (or assemblerclose fragments of `C') to ensure a close control over resource consumption. For internet applications, highlevel languages such as Java ar
Cause and Effect: Type Systems for Effects and Dependencies
, 2005
"... Formal framework for reasoning about programs are important not only for automated tools but also for programmers. Type systems have proven an enormously popular framework for validating static analyses of programs, as well as for documenting their interfaces for programmers. However, most type syst ..."
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Cited by 1 (0 self)
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Formal framework for reasoning about programs are important not only for automated tools but also for programmers. Type systems have proven an enormously popular framework for validating static analyses of programs, as well as for documenting their interfaces for programmers. However, most type systems used in practice today fail to capture many essential aspect of p behavior dependencie of programs The considerabl c i pas twenty years int developing that captu e information I pape examin compa contrast connec mbe o highly influentia p ototy ica system capturing dependencies Specifically w classi e typ system a onceive fo l canonical example o pendenc system system informationflow di moda systems c (co)monadi e fec dependenc discipline linear system p e easonin abou state esou Finally als esen calculus provide insight possibili fo a unified account for all of these systems.
HigherOrder Linear Ramified Recurrence
, 2004
"... HigherOrder Linear Ramified Recurrence (HOLRR) is a linear (affine) calculus  every variable occurs at most once  extended with a recursive scheme on free algebras. Two simple conditions on type derivations enforce both polytime completeness and a strong notion of polytime soundness on typ ..."
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Cited by 1 (1 self)
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HigherOrder Linear Ramified Recurrence (HOLRR) is a linear (affine) calculus  every variable occurs at most once  extended with a recursive scheme on free algebras. Two simple conditions on type derivations enforce both polytime completeness and a strong notion of polytime soundness on typeable terms. Completeness for PTIME holds by embedding Leivant's ramified recurrence on words into HOLRR. Soundness is established at all types  and not only for first order terms. Type connectives are limited to tensor and linear implication.