7,993 research outputs found
Needed Computations Shortcutting Needed Steps
We define a compilation scheme for a constructor-based, strongly-sequential,
graph rewriting system which shortcuts some needed steps. The object code is
another constructor-based graph rewriting system. This system is normalizing
for the original system when using an innermost strategy. Consequently, the
object code can be easily implemented by eager functions in a variety of
programming languages. We modify this object code in a way that avoids total or
partial construction of the contracta of some needed steps of a computation.
When computing normal forms in this way, both memory consumption and execution
time are reduced compared to ordinary rewriting computations in the original
system.Comment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681
On Constructor Rewrite Systems and the Lambda Calculus
We prove that orthogonal constructor term rewrite systems and lambda-calculus
with weak (i.e., no reduction is allowed under the scope of a
lambda-abstraction) call-by-value reduction can simulate each other with a
linear overhead. In particular, weak call-by- value beta-reduction can be
simulated by an orthogonal constructor term rewrite system in the same number
of reduction steps. Conversely, each reduction in a term rewrite system can be
simulated by a constant number of beta-reduction steps. This is relevant to
implicit computational complexity, because the number of beta steps to normal
form is polynomially related to the actual cost (that is, as performed on a
Turing machine) of normalization, under weak call-by-value reduction.
Orthogonal constructor term rewrite systems and lambda-calculus are thus both
polynomially related to Turing machines, taking as notion of cost their natural
parameters.Comment: 27 pages. arXiv admin note: substantial text overlap with
arXiv:0904.412
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
On Sharing, Memoization, and Polynomial Time (Long Version)
We study how the adoption of an evaluation mechanism with sharing and
memoization impacts the class of functions which can be computed in polynomial
time. We first show how a natural cost model in which lookup for an already
computed value has no cost is indeed invariant. As a corollary, we then prove
that the most general notion of ramified recurrence is sound for polynomial
time, this way settling an open problem in implicit computational complexity
Polygraphs for termination of left-linear term rewriting systems
We present a methodology for proving termination of left-linear term
rewriting systems (TRSs) by using Albert Burroni's polygraphs, a kind of
rewriting systems on algebraic circuits. We translate the considered TRS into a
polygraph of minimal size whose termination is proven with a polygraphic
interpretation, then we get back the property on the TRS. We recall Yves
Lafont's general translation of TRSs into polygraphs and known links between
their termination properties. We give several conditions on the original TRS,
including being a first-order functional program, that ensure that we can
reduce the size of the polygraphic translation. We also prove sufficient
conditions on the polygraphic interpretations of a minimal translation to imply
termination of the original TRS. Examples are given to compare this method with
usual polynomial interpretations.Comment: 15 page
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