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Stratified Bounded Affine Logic for Logarithmic Space
"... A number of complexity classes, most notably PTIME, have been characterised by subsystems of linear logic. In this paper we show that the functions computable in logarithmic space can also be characterised by a restricted version of linear logic. We introduce Stratified Bounded Affine Logic (SBAL), ..."
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Cited by 8 (0 self)
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A number of complexity classes, most notably PTIME, have been characterised by subsystems of linear logic. In this paper we show that the functions computable in logarithmic space can also be characterised by a restricted version of linear logic. We introduce Stratified Bounded Affine Logic (SBAL), a restricted version of Bounded Linear Logic, in which not only the modality! but also the universal quantifier is bounded by a resource polynomial. We show that the proofs of certain sequents in SBAL represent exactly the functions computable logarithmic space. The proof that SBALproofs can be compiled to LOGSPACE functions rests on modelling computation by interaction dialogues in the style of game semantics. We formulate the compilation of SBALproofs to spaceefficient programs as an interpretation in a realisability model, in which realisers are taken from a Geometry of Interaction situation.
The Weak Lambda Calculus as a Reasonable Machine
, 2006
"... We define a new cost model for the callbyvalue lambdacalculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the callbyvalue lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial propertie ..."
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Cited by 4 (2 self)
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We define a new cost model for the callbyvalue lambdacalculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the callbyvalue lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial properties of usual betareduction, without any reference to a specific machine or evaluator. In particular, the cost of a single beta reduction is proportional to the difference between the size of the redex and the size of the reduct. In this way, the total cost of normalizing a lambda term will take into account the size of all intermediate results (as well as the number of steps to normal form).
HigherOrder Functional Reactive Programming in Bounded Space
"... Functional reactive programming (FRP) is an elegant and successful approach to programming reactive systems declaratively. The high levels of abstraction and expressivity that make FRP attractive as a programming model do, however, often lead to programs whose resource usage is excessive and hard to ..."
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Cited by 3 (1 self)
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Functional reactive programming (FRP) is an elegant and successful approach to programming reactive systems declaratively. The high levels of abstraction and expressivity that make FRP attractive as a programming model do, however, often lead to programs whose resource usage is excessive and hard to predict. In this paper, we address the problem of space leaks in discretetime functional reactive programs. We present a functional reactive programming language that statically bounds the size of the dataflow graph a reactive program creates, while still permitting use of higherorder functions and highertype streams such as streams of streams. We achieve this with a novel linear type theory that both controls allocation and ensures that all recursive definitions are wellfounded. We also give a denotational semantics for our language by combining recent work on metric spaces for the interpretation of higherorder causal functions with lengthspace models of spacebounded computation. The resulting category is doubly closed and hence forms a model of the logic of bunched implications.
Realizability and implicit PTIME characterization
"... 2 DIAL∀l µ l 4 2.1 The dual typing system............................ 4 2.2 Data structures and notations......................... 5 ..."
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2 DIAL∀l µ l 4 2.1 The dual typing system............................ 4 2.2 Data structures and notations......................... 5
An Invariant Cost Model for the Lambda Calculus
, 2005
"... We define a new cost model for the callbyvalue lambdacalculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the callbyvalue lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial properties ..."
Abstract
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We define a new cost model for the callbyvalue lambdacalculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the callbyvalue lambdacalculus can simulate each other within a polynomial time overhead. The model only relies on combinatorial properties of usual betareduction, without any reference to a specific machine or evaluator. In particular, the cost of a single beta reduction is proportional to the difference between the size of the redex and the size of the reduct. In this way, the total cost of normalizing a lambda term will take into account the size of all intermediate results (as well as the number of steps to normal form). 1