21,640 research outputs found
Work it, wrap it, fix it, fold it
The worker/wrapper transformation is a general-purpose technique for refactoring recursive programs to improve their performance. The two previous approaches to formalising the technique were based upon different recursion operators and different correctness conditions. In this paper we show how these two approaches can be generalised in a uniform manner by combining their correctness conditions, extend the theory with new conditions that are both necessary and sufficient to ensure the correctness of the worker/wrapper technique, and explore the benefits that result. All the proofs have been mechanically verified using the Agda system
Second-Order Functions and Theorems in ACL2
SOFT ('Second-Order Functions and Theorems') is a tool to mimic second-order
functions and theorems in the first-order logic of ACL2. Second-order functions
are mimicked by first-order functions that reference explicitly designated
uninterpreted functions that mimic function variables. First-order theorems
over these second-order functions mimic second-order theorems universally
quantified over function variables. Instances of second-order functions and
theorems are systematically generated by replacing function variables with
functions. SOFT can be used to carry out program refinement inside ACL2, by
constructing a sequence of increasingly stronger second-order predicates over
one or more target functions: the sequence starts with a predicate that
specifies requirements for the target functions, and ends with a predicate that
provides executable definitions for the target functions.Comment: In Proceedings ACL2 2015, arXiv:1509.0552
Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
We investigate orientifolds of type II string theory on K3 and Calabi-Yau
3-folds with intersecting D-branes wrapping special Lagrangian cycles. We
determine quite generically the chiral massless spectrum in terms of
topological invariants and discuss both orbifold examples and algebraic
realizations in detail. Intriguingly, the developed techniques provide an
elegant way to figure out the chiral sector of orientifold models without
computing any explicit string partition function. As a new example we derive a
non-supersymmetric Standard-like Model from an orientifold of type IIA on the
quintic Calabi-Yau 3-fold with wrapped D6-branes. In the case of supersymmetric
intersecting brane models on Calabi-Yau manifolds we discuss the D-term and
F-term potentials, the effective gauge couplings and the Green-Schwarz
mechanism. The mirror symmetric formulation of this construction is provided
within type IIB theory. We finally include a short discussion about the lift of
these models from type IIB on K3 to F-theory and from type IIA on Calabi-Yau
3-folds to M-theory on G_2 manifolds.Comment: 82 pages, harvmac, 5 figures. v2: references added. v3: T^6
orientifold corrected, JHEP versio
Calabi-Yau 3-folds from 2-folds
We consider type IIA string theory on a Calabi-Yau 2-fold with D6-branes
wrapping 2-cycles in the 2-fold. We find a complete set of conditions on the
supergravity solution for any given wrapped brane configuration in terms of
SU(2) structures. We reduce the problem of finding a supergravity solution for
the wrapped branes to finding a harmonic function on RCY. We then
lift this solution to 11-dimensions as a product of R and a
Calabi-Yau 3-fold. We show how the metric on the 3-fold is determined in terms
of the wrapped brane solution. We write down the distinguished (3,0) form and
the K{\"a}hler form of the 3-fold in terms of structures defined on the base
2-d complex manifold. We discuss the topology of the 3-fold in terms of the
D6-branes and the underlying 2-fold. We show that in addition to the
non-trivial cycles inherited from the underlying 2-fold there are new
2-cycles. We construct closed (1,1) forms corresponding to these new cycles. We
also display some explicit examples. One of our examples is that of D6-branes
wrapping the 2-cycle in an A ALE space, the resulting 3-fold has
, where is the number of D6-branes.Comment: 30 page
Moving Five-Branes in Low-Energy Heterotic M-Theory
We construct cosmological solutions of four-dimensional effective heterotic
M-theory with a moving five-brane and evolving dilaton and T modulus. It is
shown that the five-brane generates a transition between two asymptotic
rolling-radii solutions. Moreover, the five-brane motion always drives the
solutions towards strong coupling asymptotically. We present an explicit
example of a negative-time branch solution which ends in a brane collision
accompanied by a small-instanton transition. The five-dimensional origin of
some of our solutions is also discussed.Comment: 16 pages, Latex, 3 eps figure
The String Landscape, the Swampland, and the Missing Corner
We give a brief overview of the string landscape and techniques used to
construct string compactifications. We then explain how this motivates the
notion of the swampland and review a number of conjectures that attempt to
characterize theories in the swampland. We also compare holography in the
context of superstrings with the similar, but much simpler case of topological
string theory. For topological strings, there is a direct definition of
topological gravity based on a sum over a "quantum gravitational foam." In this
context, holography is the statement of an identification between a gravity and
gauge theory, both of which are defined independently of one another. This
points to a missing corner in string dualities which suggests the search for a
direct definition of quantum theory of gravity rather than relying on its
strongly coupled holographic dual as an adequate substitute (Based on TASI 2017
lectures given by C. Vafa)
The HERMIT in the Tree
This paper describes our experience using the HERMIT tool- kit to apply well-known transformations to the internal core language of the Glasgow Haskell Compiler. HERMIT provides several mechanisms to support writing general-purpose transformations: a domain-specific language for strategic programming specialized to GHC's core language, a library of primitive rewrites, and a shell-style{based scripting language for interactive and batch usage. There are many program transformation techniques that have been described in the literature but have not been mechanized and made available inside GHC - either because they are too specialized to include in a general-purpose compiler, or because the developers' interest is in theory rather than implementation. The mechanization process can often reveal pragmatic obstacles that are glossed over in pen-and-paper proofs; understanding and removing these obstacles is our concern. Using HERMIT, we implement eleven examples of three program transformations, report on our experience, and describe improvements made in the process
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