#
FICS 2010 Contributed Talks

**
Abstract: ** We give a model for Nakano's typed lambda
calculus with guarded recursive definitions in a category of
metric spaces. By proving a computational adequacy result
that relates the interpretation with the operational
semantics, we show that the model can be used to reason about
contextual equivalence.

pdf
** Abstract: ** Frame and anti-frame
rules have been proposed as proof rules for modular reasoning about
programs. Frame rules allow one to hide irrelevant
parts of the state during verification, whereas the anti-frame rule
allows one to hide local state from the context. We give a
possible worlds semantics for Chargu{\'e}raud and Pottier's
type and capability system including frame and anti-frame
rules, based on the operational semantics and step-indexed heap
relations. The worlds are constructed as a recursively
defined predicate on a recursively defined metric space,
which provides a considerably simpler alternative compared to a
previous construction.

pdf
Marek Czarnecki.
How fast can the fixpoints in modal mu-calculus be reached?
**
Abstract:
**
We investigate how fast modal mu-formulae may reach their fixpoints. We show a way how to construct for each ordinal number alpha less than omega^2, a formula which reaches its fixpoint in alpha steps. Our approach is based on fuses i.e. finite one--way counters, which allow us to control the number of uses of Box while iterating our formulae.

pdf
Herve Grall. Proving
fixed points

** Abstract: **
We propose a method to characterize the fixed points described in
Tarski's theorem for complete lattices. The method is
proof-theoretic: the least and greatest fixed points
are ``proved'' in some inference system. We
also apply the method to two other fixed point theorems, a
generalization of Tarski's theorem to
chain-complete posets and Bourbaki-Witt's
theorem. Finally, we describe how the method differs from the
traditional iterative method resorting to ordinals.

pdf
** Abstract: **
A recursive program is determined, up to bisimilarity, by the
operation of the recursion body on arbitrary processes, of which it is
a fixpoint. The traditional proof of this fact uses
Howe's method, but that does not tell us how the fixpoint is
obtained.

In this paper, we show that the fixpoint may be
obtained by a least fixpoint procedure iterated through the hierarchy
of countable ordinals, using Groote and Vaandrager's notion of
nested simulation.

pdf
Matteo Mio.
The Equivalence of Game and Denotational Semantics for the Probabilistic mu-calculus.

**
Abstract:
**
We show that the game and denotational semantics of a probabilistic extension of the modal mu calculus coincide.

pdf
Keiko Nakata.
Denotational semantics for lazy initialization of letrec: black holes as exceptions rather than divergence
**
Abstract:
**
We present a denotational semantics for a simply typed
call-by-need letrec calculus, which distinguishes direct cycles,
such as "let rec x = x in x" and "let rec x = y
and y = x + 1 in x", and looping recursion, such as "let
rec f = \lambda x.f x in f 0". In this semantics
the former denote an exception whereas the latter
denotes divergence.

The distinction is motivated by
``lazy evaluation'' as implemented in OCaml via
lazy/force and Racket (formerly PLT Scheme) via delay/force: when
a delayed variable is dereferenced for the first time, it is first
pre-initialized to an exception-raising thunk and is
updated afterward by the value obtained by evaluating the
expression bound to the variable. Any attempt to
dereference the variable during the initialization raises an
exception rather than diverges. This way, lazy
evaluation provides a useful measure to initialize
recursive bindings by exploring a successful initialization order
of the bindings at runtime and by signaling an exception when
there is no such order. It is also used for the
initialization semantics of the object system in the F#
programming language.

The denotational semantics is proved
adequate with respect to a referential operational semantics.

pdf
Andrei Romashchenko.
Fixed Point Argument and Tilings without
Long Range Order

** Abstract:
** Tiling is a classic model of combinatorial structure, whose
global properties are determined by simple local rules. In this paper
we construct tilings with some
specific properties, using self-referential argument
originating in Kleene's recursion theorem. This methods proves to
be very effective though the initial problems under consideration are
purely combinatorial and do not refer explicitly to any
questions of computability.

More specifically,
we attack the problem of long range order formulated by
C.Radin: whether one can determine by local rules such
tilings on the plane in which we loose all information
while traveling between distant areas. We
present a partial answer to Radin's question by
constructing a tile set τ=τ

_{0}∪τ

_{1} (i.e., all tiles in
τ are divided into two disjoint classes of 0-tiles
and 1-tiles) such that every τ-tiling of the plane
corresponds to some configuration in
{0,1}

^{Z2}, where there is no long range order.

pdf
Tarmo Uustalu.
A note on strong dinaturality, initial
algebras and uniform parameterized fixpoint operators
** Abstract: ** I show a basic Yoneda-like
lemma relating strongly dinatural transformations and initial
algebras. Further, I apply it to reprove known results about
unique existence of uniform parameterized fixpoint operators.

pdf
** Abstract:
** We show that: (a) Banach's and Knaster-Tarski's fixed
point theorems are instances of a single theorem with a constructive
proof; (b) Bourbaki-Witt's and Caristi's theorems are
instances of a single theorem that cannot have a constructive proof.

pdf

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Luigi Santocanale

Dernière mise à jour : Tue Aug 24 2010, 11:35:04