103,406 research outputs found
The C++0x "Concepts" Effort
C++0x is the working title for the revision of the ISO standard of the C++
programming language that was originally planned for release in 2009 but that
was delayed to 2011. The largest language extension in C++0x was "concepts",
that is, a collection of features for constraining template parameters. In
September of 2008, the C++ standards committee voted the concepts extension
into C++0x, but then in July of 2009, the committee voted the concepts
extension back out of C++0x.
This article is my account of the technical challenges and debates within the
"concepts" effort in the years 2003 to 2009. To provide some background, the
article also describes the design space for constrained parametric
polymorphism, or what is colloquially know as constrained generics. While this
article is meant to be generally accessible, the writing is aimed toward
readers with background in functional programming and programming language
theory. This article grew out of a lecture at the Spring School on Generic and
Indexed Programming at the University of Oxford, March 2010
Formal Component-Based Semantics
One of the proposed solutions for improving the scalability of semantics of
programming languages is Component-Based Semantics, introduced by Peter D.
Mosses. It is expected that this framework can also be used effectively for
modular meta theoretic reasoning. This paper presents a formalization of
Component-Based Semantics in the theorem prover Coq. It is based on Modular
SOS, a variant of SOS, and makes essential use of dependent types, while
profiting from type classes. This formalization constitutes a contribution
towards modular meta theoretic formalizations in theorem provers. As a small
example, a modular proof of determinism of a mini-language is developed.Comment: In Proceedings SOS 2011, arXiv:1108.279
Reasoning about modular datatypes with Mendler induction
In functional programming, datatypes a la carte provide a convenient modular
representation of recursive datatypes, based on their initial algebra
semantics. Unfortunately it is highly challenging to implement this technique
in proof assistants that are based on type theory, like Coq. The reason is that
it involves type definitions, such as those of type-level fixpoint operators,
that are not strictly positive. The known work-around of impredicative
encodings is problematic, insofar as it impedes conventional inductive
reasoning. Weak induction principles can be used instead, but they considerably
complicate proofs.
This paper proposes a novel and simpler technique to reason inductively about
impredicative encodings, based on Mendler-style induction. This technique
involves dispensing with dependent induction, ensuring that datatypes can be
lifted to predicates and relying on relational formulations. A case study on
proving subject reduction for structural operational semantics illustrates that
the approach enables modular proofs, and that these proofs are essentially
similar to conventional ones.Comment: In Proceedings FICS 2015, arXiv:1509.0282
Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus
Chern-Simons formulation of 2+1 dimensional Einstein gravity with a negative
cosmological constant is investigated when the spacetime has the topology . The physical phase space is shown to be a direct product of two
sub-phase spaces each of which is a non-Hausdorff manifold plus a set with
nonzero codimensions. Spacetime geometrical interpretation of each point in the
phase space is also given and we explain the 1 to 2 correspondence with the ADM
formalism from the geometrical viewpoint. In quantizing this theory, we
construct a "modified phase space" which is a cotangnt bundle on a torus. We
also provide a modular invariant inner product and investigate the relation to
the quantum theory which is directly related to the spinor representation of
the ADM formalism. (This paper is the revised version of a previous
paper(hep-th/9312151). The wrong discussion on the topology of the phase space
is corrected.)Comment: latex 28 page
Axion Couplings and Effective Cut-Offs in Superstring Compactifications
We use the linear supermultiplet formalism of supergravity to study axion
couplings and chiral anomalies in the context of field-theoretical Lagrangians
describing orbifold compactifications beyond the classical approximation. By
matching amplitudes computed in the effective low energy theory with the
results of string loop calculations we determine the appropriate counterterm in
this effective theory that assures modular invariance to all loop order. We use
supersymmetry consistency constraints to identify the correct ultra-violet
cut-offs for the effective low energy theory. Our results have a simple
interpretation in terms of two-loop unification of gauge coupling constants at
the string scale.Comment: 25 page
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