Results 1  10
of
27
Light types for polynomial time computation in lambdacalculus
 In Proceedings of the 19th IEEE Syposium on Logic in Computer Science
, 2004
"... We propose a new type system for lambdacalculus ensuring that welltyped programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic ..."
Abstract

Cited by 44 (11 self)
 Add to MetaCart
(Show Context)
We propose a new type system for lambdacalculus ensuring that welltyped programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambdaterms: subject reduction is satisfied and a welltyped term admits a polynomial bound on the reduction by any strategy. Finally we establish that as LAL, DLAL allows to represent all polytime functions. 1
The essence of dataflow programming
 In APLAS
, 2005
"... Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure ..."
Abstract

Cited by 23 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure contextdependent computation. In particular, we develop a generic comonadic interpreter of languages for contextdependent computation and instantiate it for streambased computation. We also discuss distributive laws of a comonad over a monad as a means to structure combinations of effectful and contextdependent computation. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1
Extended CurryHoward Correspondence for a Basic Constructive Modal Logic
 In Proceedings of Methods for Modalities
, 2001
"... this paper. This calculus satises cutelimination, as for instance shown (in a more complicated form) in [Wij90]. This calculus is dierent from what is usually taken as the basic constructive system K, as we do not assume the distribution of possibility (3) over disjunctions neither in its binary f ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
this paper. This calculus satises cutelimination, as for instance shown (in a more complicated form) in [Wij90]. This calculus is dierent from what is usually taken as the basic constructive system K, as we do not assume the distribution of possibility (3) over disjunctions neither in its binary form 3(A _ B) ! (3A _ 3B) nor in its nullary form 3? ! ? The sequent calculus above corresponds to an axiomatic formulation given by axioms for intuitionistic logic, plus axioms: 2(A ! B) ! (2A ! 2B) 2(A ! B) ! (3A ! 3B) 2A3B ! 3(A B) together with rules for Modus Ponens and Necessitation: ` A ! B ` A ` B MP ` A ` 2A Nec Wijesekera proved a Craig interpolation theorem, one of the usual consequences of syntactic cutelimination and produced Kripke, algebraic and topological semantics for a calculus very similar to the one above. The only dierence is that he does assume 3? ! ?. From our \wish list" for logical systems only a natural deduction formulation and a categorical semantics are missing. These we proceed to discuss
Paiva: Constructive CK for Contexts
 Propositional Lax Logic. Information and Computation
, 1997
"... Abstract. This note describes possible world semantics for a constructive modal logic CK. The system CK is weaker than other constructive modal logics K as it does not satisfy distribution of possibility over disjunctions, neither binary (3(A ∨ B) → 3A ∨ 3B) nor nullary (3 ⊥ → ⊥). We are intereste ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
Abstract. This note describes possible world semantics for a constructive modal logic CK. The system CK is weaker than other constructive modal logics K as it does not satisfy distribution of possibility over disjunctions, neither binary (3(A ∨ B) → 3A ∨ 3B) nor nullary (3 ⊥ → ⊥). We are interested in this version of constructive K for its application to contexts in AI [dP03]. However, our previous work on CK described only a categorical semantics [BdPR01] for the system, while most logicians interested in contexts prefer their semantics possible worlds style. This note fills the gap by providing the possible worlds model theory for the constructive modal system CK, showing soundness and completeness of the proposed semantics, as well as the finite model property and (hence) decidability of the system. Wijesekera [Wij90] investigated possible worlds semantics of a system similar to CK, without the binary distribution, but satisfying the nullary one. The semantics presented here for CK is new and considerably simpler than the one of Wijesekera. 1
Coeffects: Unified static analysis of contextdependence
, 2013
"... Monadic effect systems provide a unified way of tracking effects of computations, but there is no unified mechanism for tracking how computations rely on the environment in which they are executed. This is becoming an important problem for modern software – we need to track where distributed comput ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
Monadic effect systems provide a unified way of tracking effects of computations, but there is no unified mechanism for tracking how computations rely on the environment in which they are executed. This is becoming an important problem for modern software – we need to track where distributed computations run, which resources a program uses and how they use other capabilities of the environment. We consider three examples of contextdependence analysis: liveness analysis, tracking the use of implicit parameters (similar to tracking of resource usage in distributed computation), and calculating caching requirements for dataflow programs. Informed by these cases, we present a unified calculus for tracking context dependence in functional languages together with a categorical semantics based on indexed comonads. We believe that indexed comonads are the right foundation for constructing contextaware languages and type systems and that following an approach akin to monads can lead to a widespread use of the concept.
Cut Elimination in Nested Sequents for Intuitionistic Modal Logics
"... Abstract. We present cutfree deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending IK with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents, which allows us to give a uniform cut elimination argument for ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We present cutfree deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending IK with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents, which allows us to give a uniform cut elimination argument for all 15 logic in the intuitionistic S5 cube. 1
Bidirectional Decision Procedures for the Intuitionistic Propositional Modal Logic IS4
"... Abstract. We present a multicontext focused sequent calculus whose derivations are in bijective correspondence with normal natural deductions in the propositional fragment of the intuitionistic modal logic IS4. This calculus, suitable for the enumeration of normal proofs, is the starting point for ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We present a multicontext focused sequent calculus whose derivations are in bijective correspondence with normal natural deductions in the propositional fragment of the intuitionistic modal logic IS4. This calculus, suitable for the enumeration of normal proofs, is the starting point for the development of a sequent calculusbased bidirectional decision procedure for propositional IS4. In this system, relevant derived inference rules are constructed in a forward direction prior to proof search, while derivations constructed using these derived rules are searched over in a backward direction. We also present a variant which searches directly over normal natural deductions. Experimental results show that on most problems, the bidirectional prover is competitive with both conventional backward provers using loopdetection and inverse method provers, significantly outperforming them in a number of cases. 1
The essence of dataflow programming (short version
 Proc. of 3rd Asian Symp. on Programming Languages and Systems, APLAS 2005, v. 3780 of Lect. Notes in Comput. Sci
, 2005
"... Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure contextdependent computation. In particular, we develop a generic comonadic interpreter of languages for contextdependent computation and instantiate it for streambased computation. We also discuss distributive laws of a comonad over a monad as a means to structure combinations of effectful and contextdependent computation. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1
Calculi for intuitionistic normal modal logic
 In Proceedings of Programming and Programming Languages
, 2007
"... This paper provides a callbyname and a callbyvalue term calculus, both of which have a CurryHoward correspondence to the box fragment of the intuitionistic modal logic IK. The strong normalizability and the confluency of the calculi are shown. Moreover, we define a CPS transformation from the c ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
This paper provides a callbyname and a callbyvalue term calculus, both of which have a CurryHoward correspondence to the box fragment of the intuitionistic modal logic IK. The strong normalizability and the confluency of the calculi are shown. Moreover, we define a CPS transformation from the callbyvalue calculus to the callbyname calculus, and show its soundness and completeness. 1
Dialectica and Chu Constructions: Cousins?
 In this Volume
, 2006
"... This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel. The constructions have the same objects, but are rather di#erent in other ways. We discuss similarities and di#erences and prove ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This note investigates two generic constructions used to produce categorical models of linear logic, the Chu construction and the Dialectica construction, in parallel. The constructions have the same objects, but are rather di#erent in other ways. We discuss similarities and di#erences and prove that the dialectica construction can be done over a symmetric monoidal closed basis. We also point out several interesting open problems concerning the Dialectica construction.