8,726 research outputs found
Relational Parametricity and Control
We study the equational theory of Parigot's second-order
λμ-calculus in connection with a call-by-name continuation-passing
style (CPS) translation into a fragment of the second-order λ-calculus.
It is observed that the relational parametricity on the target calculus induces
a natural notion of equivalence on the λμ-terms. On the other hand,
the unconstrained relational parametricity on the λμ-calculus turns
out to be inconsistent with this CPS semantics. Following these facts, we
propose to formulate the relational parametricity on the λμ-calculus
in a constrained way, which might be called ``focal parametricity''.Comment: 22 pages, for Logical Methods in Computer Scienc
Edge contraction on dual ribbon graphs and 2D TQFT
We present a new set of axioms for 2D TQFT formulated on the category of cell
graphs with edge-contraction operations as morphisms. We construct a functor
from this category to the endofunctor category consisting of Frobenius
algebras. Edge-contraction operations correspond to natural transformations of
endofunctors, which are compatible with the Frobenius algebra structure. Given
a Frobenius algebra A, every cell graph determines an element of the symmetric
tensor algebra defined over the dual space A*. We show that the
edge-contraction axioms make this assignment depending only on the topological
type of the cell graph, but not on the graph itself. Thus the functor generates
the TQFT corresponding to A.Comment: accepted in Journal of Algebra (22 pages, 13 figures
Classification of integrable super-systems using the SsTools environment
A classification problem is proposed for supersymmetric evolutionary PDE that
satisfy the assumptions of nonlinearity and nondegeneracy. Four classes of
nonlinear coupled boson-fermion systems are discovered under the homogeneity
assumption |f|=|b|=|D_t|=1/2. The syntax of the Reduce package SsTools, which
was used for intermediate computations, and the applicability of its procedures
to the calculus of super-PDE are described.Comment: MSC 35Q53,37K05,37K10,81T40; PACS 02.30.Ik,02.70.Wz,12.60.Jv; Comput.
Phys. Commun. (2007), 26 pages (accepted
Some applications of logic to feasibility in higher types
In this paper we demonstrate that the class of basic feasible functionals has
recursion theoretic properties which naturally generalize the corresponding
properties of the class of feasible functions. We also improve the Kapron -
Cook result on mashine representation of basic feasible functionals. Our proofs
are based on essential applications of logic. We introduce a weak fragment of
second order arithmetic with second order variables ranging over functions from
N into N which suitably characterizes basic feasible functionals, and show that
it is a useful tool for investigating the properties of basic feasible
functionals. In particular, we provide an example how one can extract feasible
"programs" from mathematical proofs which use non-feasible functionals (like
second order polynomials)
Extending the Calculus of Constructions with Tarski's fix-point theorem
We propose to use Tarski's least fixpoint theorem as a basis to define
recursive functions in the calculus of inductive constructions. This widens the
class of functions that can be modeled in type-theory based theorem proving
tool to potentially non-terminating functions. This is only possible if we
extend the logical framework by adding the axioms that correspond to classical
logic. We claim that the extended framework makes it possible to reason about
terminating and non-terminating computations and we show that common facilities
of the calculus of inductive construction, like program extraction can be
extended to also handle the new functions
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
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