1,568 research outputs found
Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach
We present an extension of the second-order logic AF2 with iso-style
inductive and coinductive definitions specifically designed to extract programs
from proofs a la Krivine-Parigot by means of primitive (co)recursion
principles. Our logic includes primitive constructors of least and greatest
fixed points of predicate transformers, but contrary to the common approach, we
do not restrict ourselves to positive operators to ensure monotonicity, instead
we use the Mendler-style, motivated here by the concept of monotonization of an
arbitrary operator on a complete lattice. We prove an adequacy theorem with
respect to a realizability semantics based on saturated sets and
saturated-valued functions and as a consequence we obtain the strong
normalization property for the proof-term reduction, an important feature which
is absent in previous related work.Comment: In Proceedings LSFA 2011, arXiv:1203.542
Abstract Interpretation with Unfoldings
We present and evaluate a technique for computing path-sensitive interference
conditions during abstract interpretation of concurrent programs. In lieu of
fixed point computation, we use prime event structures to compactly represent
causal dependence and interference between sequences of transformers. Our main
contribution is an unfolding algorithm that uses a new notion of independence
to avoid redundant transformer application, thread-local fixed points to reduce
the size of the unfolding, and a novel cutoff criterion based on subsumption to
guarantee termination of the analysis. Our experiments show that the abstract
unfolding produces an order of magnitude fewer false alarms than a mature
abstract interpreter, while being several orders of magnitude faster than
solver-based tools that have the same precision.Comment: Extended version of the paper (with the same title and authors) to
appear at CAV 201
From coinductive proofs to exact real arithmetic: theory and applications
Based on a new coinductive characterization of continuous functions we
extract certified programs for exact real number computation from constructive
proofs. The extracted programs construct and combine exact real number
algorithms with respect to the binary signed digit representation of real
numbers. The data type corresponding to the coinductive definition of
continuous functions consists of finitely branching non-wellfounded trees
describing when the algorithm writes and reads digits. We discuss several
examples including the extraction of programs for polynomials up to degree two
and the definite integral of continuous maps
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