431 research outputs found
The Biequivalence of Locally Cartesian Closed Categories and Martin-L\"of Type Theories
Seely's paper "Locally cartesian closed categories and type theory" contains
a well-known result in categorical type theory: that the category of locally
cartesian closed categories is equivalent to the category of Martin-L\"of type
theories with Pi-types, Sigma-types and extensional identity types. However,
Seely's proof relies on the problematic assumption that substitution in types
can be interpreted by pullbacks. Here we prove a corrected version of Seely's
theorem: that the B\'enabou-Hofmann interpretation of Martin-L\"of type theory
in locally cartesian closed categories yields a biequivalence of 2-categories.
To facilitate the technical development we employ categories with families as a
substitute for syntactic Martin-L\"of type theories. As a second result we
prove that if we remove Pi-types the resulting categories with families are
biequivalent to left exact categories.Comment: TLCA 2011 - 10th Typed Lambda Calculi and Applications, Novi Sad :
Serbia (2011
The Hierarchical Formation of the Galactic Disk
I review the results of recent cosmological simulations of galaxy formation
that highlight the importance of satellite accretion in the formation of
galactic disks. Tidal debris of disrupted satellites may contribute to the disk
component if they are compact enough to survive the decay and circularization
of the orbit as dynamical friction brings the satellite into the disk plane.
This process may add a small but non-negligible fraction of stars to the thin
and thick disks, and reconcile the presence of very old stars with the
protracted merging history expected in a hierarchically clustering universe. I
discuss various lines of evidence which suggest that this process may have been
important during the formation of the Galactic disk.Comment: paper to be read at the "Penetrating Bars through Masks of Cosmic
Dust" conference in South Afric
Smart Choices and the Selection Monad
Describing systems in terms of choices and their resulting costs and rewards
offers the promise of freeing algorithm designers and programmers from
specifying how those choices should be made; in implementations, the choices
can be realized by optimization techniques and, increasingly, by machine
learning methods. We study this approach from a programming-language
perspective. We define two small languages that support decision-making
abstractions: one with choices and rewards, and the other additionally with
probabilities. We give both operational and denotational semantics.
In the case of the second language we consider three denotational semantics,
with varying degrees of correlation between possible program values and
expected rewards. The operational semantics combine the usual semantics of
standard constructs with optimization over spaces of possible execution
strategies.
The denotational semantics, which are compositional and can also be viewed as
an implementation by translation to a simpler language, rely on the selection
monad, to handle choice, combined with an auxiliary monad, to handle other
effects such as rewards or probability.
We establish adequacy theorems that the two semantics coincide in all cases.
We also prove full abstraction at ground types, with varying notions of
observation in the probabilistic case corresponding to the various degrees of
correlation. We present axioms for choice combined with rewards and
probability, establishing completeness at ground types for the case of rewards
without probability
A space division multiplexed free-space-optical communication system that can auto-locate and fully self align with a remote transceiver
Free-Space Optical (FSO) systems offer the ability to distribute high speed digital links into remote and rural communities where terrain, installation cost or infrastructure security pose critical hurdles to deployment. A challenge in any point-to-point FSO system is initiating and maintaining optical alignment from the sender to the receiver. In this paper we propose and demonstrate a low-complexity self-aligning FSO prototype that can completely self-align with no requirement for initial manual positioning and could therefore form the opto-mechanical basis for a mesh network of optical transceivers. The prototype utilises off-the-shelf consumer electrical components and a bespoke alignment algorithm. We demonstrate an eight fibre spatially multiplexed link with a loss of 15âdB over 210âm
Relay: A New IR for Machine Learning Frameworks
Machine learning powers diverse services in industry including search,
translation, recommendation systems, and security. The scale and importance of
these models require that they be efficient, expressive, and portable across an
array of heterogeneous hardware devices. These constraints are often at odds;
in order to better accommodate them we propose a new high-level intermediate
representation (IR) called Relay. Relay is being designed as a
purely-functional, statically-typed language with the goal of balancing
efficient compilation, expressiveness, and portability. We discuss the goals of
Relay and highlight its important design constraints. Our prototype is part of
the open source NNVM compiler framework, which powers Amazon's deep learning
framework MxNet
Subtyping and Parametricity
In this paper we study the interaction of subtyping and parametricity. We describe a logic for a programming language with parametric polymorphism and subtyping. The logic supports the formal definition and use of relational parametricity. We give two models for it, and compare it with other formal systems for the same language. In particular, we examine the "Penn interpretation" of subtyping as implicit coercion. Without subtyping, parametricity yields, for example, an encoding of abstract types and of initial algebras, with the corresponding proof principles of simulation and induction. With subtyping, we obtain partially abstract types and certain initial order-sorted algebras, and may derive proof principles for them. 1 Introduction A function is polymorphic if it works on inputs of several types. We may distinguish various notions of polymorphism, particularly parametric polymorphism (e.g. [Rey83]) and subtype polymorphism (e.g. [CW85]). These may exist in isolation, as in ML [MT..
Perencanaan dan Pembuatan Sistem Alarm Mobil dengan Memanfaatkan Mikrokontroler
Dengan
menfaatkan
mikrokontroller
AT89C51
dan
variannya
AT89C2051
dibuat
alarm
mobil
dengan
kode
pembuka
yang
dapat
berubah-ubah
dari
waktu
ke
waktu.
Untuk
mengubah-ubah
kode
pembuka
itu
digunakan
metode
pengubahan
kode
tertentu
dan
setiap
kali
kode
pembuka
akan
dikirim,
selalu
diacak
dengan
sebuah
kode
pengacak.
Dengan
demikian
akan
sangat
sulit
bagi
orang
lain
mengetahui
kode
pembuka
alarm
ini.
Selain
itu
alarm
ini
dapat
mendeteksi
perubahan
suhu
didalam
mobil,
sehingga
bila
ada
orang
lain
masuk
kedalam
mobil
tanpa
mengganggu
sensor
switch
pintu
alarm
akan
berbunyi.
Sensor
lain
yang
tersedia
adalah
sensor
switch
pintu,
bagasi,
dan
kap
mesin.
Juga
terdapat
sensor
yang
dapat
mendeteksi
kontak
mobil.
Satu
lagi
kehebatan
alarm
ini
adalah
dapat
mengingat
keadaan
terakhinya.
Jadi
bila
ada
yang
memutus
aki
mobil
untuk
masuk
kedalam
mobil,
maka
saat
aki
disambung
kembali
untuk
menghidupkan
mobil
alarm
akan
berbunyi
dan
mesin
tidak
bisa
dihidupkan.
Pada
perencanaan
sistem
ini
pembahasannya meliputi
perangkat
keras
dan
perangkat
lunak
sistem,
serta
kemungkinan
pengembangannya
pada
suatu
sistem
yang
lebih
besar
Smart Choices and the Selection Monad
Describing systems in terms of choices and their resulting costs and rewards
offers the promise of freeing algorithm designers and programmers from
specifying how those choices should be made; in implementations, the choices
can be realized by optimization techniques and, increasingly, by
machine-learning methods. We study this approach from a programming-language
perspective. We define two small languages that support decision-making
abstractions: one with choices and rewards, and the other additionally with
probabilities. We give both operational and denotational semantics.
In the case of the second language we consider three denotational semantics,
with varying degrees of correlation between possible program values and
expected rewards. The operational semantics combine the usual semantics of
standard constructs with optimization over spaces of possible execution
strategies. The denotational semantics, which are compositional, rely on the
selection monad, to handle choice, augmented with an auxiliary monad to handle
other effects, such as rewards or probability.
We establish adequacy theorems that the two semantics coincide in all cases.
We also prove full abstraction at base types, with varying notions of
observation in the probabilistic case corresponding to the various degrees of
correlation. We present axioms for choice combined with rewards and
probability, establishing completeness at base types for the case of rewards
without probability
A Per Model of Polymorphism and Recursive Types
A model of Reynoldsâ polymorphic lambda calculus is provided, which also allows the recursive
definition of elements and types. The technique
is to use a good class of partial equivalence relations over a certain cpo. This allows the combination of inverse-limits for recursion and intersection for polymorphism
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