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14
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 ..."
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Cited by 18 (3 self)
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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 ..."
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Cited by 10 (2 self)
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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
Constructive CK for Contexts
 In Proceedings of the First Workshop on Context Representation and Reasoning, CONTEXT’05
, 2005
"... 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 (✸(A ∨ B) → ✸A ∨ ✸B) nor nullary (✸ ⊥ → ⊥). We are intereste ..."
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Cited by 5 (2 self)
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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 (✸(A ∨ B) → ✸A ∨ ✸B) nor nullary (✸ ⊥ → ⊥). 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
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 ..."
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Cited by 2 (1 self)
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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
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 ..."
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Cited by 2 (0 self)
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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
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 ..."
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Cited by 1 (1 self)
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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
Callbyname and callbyvalue in normal modal logic
"... Abstract. This paper provides a callbyname and a callbyvalue calculus, both of which have a CurryHoward correspondence to the minimal normal logic K. The calculi are extensions of the λµcalculi, and their semantics are given by CPS transformations into a calculus corresponding to the intuition ..."
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Abstract. This paper provides a callbyname and a callbyvalue calculus, both of which have a CurryHoward correspondence to the minimal normal logic K. The calculi are extensions of the λµcalculi, and their semantics are given by CPS transformations into a calculus corresponding to the intuitionistic fragment of K. The duality between callbyname and callbyvalue with modalities is investigated in our calculi. 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 ..."
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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.
An institutional view on categorical logic and the CurryHowardTaitisomorphism
"... We introduce a generic notion of propositional categorical logic and provide a construction of an institution with proofs out of such a logic, following the CurryHowardTait paradigm. We then prove logicindependent soundness and completeness theorems. The framework is instantiated with a number ..."
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Cited by 1 (1 self)
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We introduce a generic notion of propositional categorical logic and provide a construction of an institution with proofs out of such a logic, following the CurryHowardTait paradigm. We then prove logicindependent soundness and completeness theorems. The framework is instantiated with a number of examples: classical, intuitionistic, linear and modal propositional logics. Finally, we speculate how this framework may be extended beyond the propositional case.
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 ..."
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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