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CGBlockInfo - Information to generate a block literal.
Definition at line 152 of file CGBlocks.h.
Definition at line 34 of file CGBlocks.cpp.
Definition at line 280 of file CGBlocks.h.
Referenced by computeBlockInfo(), clang::CodeGen::CodeGenFunction::EmitBlockLiteral(), clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockLiteralArgVariable(), findAndRemoveBlockInfo(), findBlockCapturedManagedEntities(), clang::CodeGen::CodeGenFunction::GenerateBlockFunction(), getBlockLayoutInfoString(), and GetGCAttrTypeForType().
Definition at line 281 of file CGBlocks.h.
Referenced by buildBlockDescriptor(), buildGlobalBlock(), clang::CodeGen::CGDebugInfo::EmitDeclareOfArgVariable(), clang::CodeGen::CodeGenFunction::GenerateBlockFunction(), clang::CodeGen::CodeGenFunction::GenerateCopyHelperFunction(), clang::CodeGen::CodeGenFunction::GenerateDestroyHelperFunction(), and getBlockDescriptorName().
Definition at line 270 of file CGBlocks.h.
Referenced by clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockDeclRefVariable(), clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockLiteralArgVariable(), findBlockCapturedManagedEntities(), clang::CodeGen::CodeGenFunction::GetAddrOfBlockDecl(), getBlockLayoutInfoString(), getCaptureFieldType(), and GetGCAttrTypeForType().
Definition at line 273 of file CGBlocks.h.
Definition at line 290 of file CGBlocks.h.
Referenced by buildBlockDescriptor(), clang::CodeGen::CodeGenFunction::EmitBlockLiteral(), getBlockDescriptorName(), and getBlockLayoutInfoString().
Definition at line 246 of file CGBlocks.h.
Referenced by clang::CodeGen::CodeGenFunction::EmitBlockLiteral(), and clang::CodeGen::CodeGenModule::GetAddrOfGlobalBlock().
Definition at line 249 of file CGBlocks.h.
Referenced by buildGlobalBlock(), computeBlockInfo(), clang::CodeGen::CodeGenFunction::GenerateCopyHelperFunction(), clang::CodeGen::CodeGenFunction::GenerateDestroyHelperFunction(), getBlockDescriptorName(), initializeForBlockHeader(), and clang::CodeGen::CodeGenFunction::LoadBlockStruct().
Definition at line 247 of file CGBlocks.h.
Referenced by buildGlobalBlock(), clang::CodeGen::CodeGenFunction::EmitBlockLiteral(), and clang::CodeGen::CodeGenModule::GetAddrOfGlobalBlock().
Definition at line 255 of file CGBlocks.h.
Referenced by computeBlockInfo(), and getBlockLayoutInfoString().
Definition at line 258 of file CGBlocks.h.
Definition at line 248 of file CGBlocks.h.
Referenced by buildBlockDescriptor(), buildGlobalBlock(), computeBlockInfo(), clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockLiteralArgVariable(), getBlockDescriptorName(), GetGCAttrTypeForType(), and initializeForBlockHeader().
CanBeGlobal - True if the block can be global, i.e.
it has no non-constant captures.
Definition at line 218 of file CGBlocks.h.
Referenced by buildGlobalBlock(), computeBlockInfo(), and clang::CodeGen::CodeGenFunction::EmitBlockLiteral().
The mapping of allocated indexes within the block.
Definition at line 242 of file CGBlocks.h.
Referenced by buildBlockDescriptor(), and computeBlockInfo().
Indicates whether an object of a non-external C++ class is captured.
This bit is used to determine the linkage of the block copy/destroy helper functions.
Definition at line 239 of file CGBlocks.h.
Referenced by computeBlockInfo(), clang::CodeGen::CodeGenFunction::GenerateCopyHelperFunction(), and clang::CodeGen::CodeGenFunction::GenerateDestroyHelperFunction().
The field index of 'this' within the block, if there is one.
Definition at line 158 of file CGBlocks.h.
Referenced by buildBlockDescriptor(), and clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockLiteralArgVariable().
Definition at line 250 of file CGBlocks.h.
An instruction which dominates the full-expression that the block is inside.
Definition at line 262 of file CGBlocks.h.
HasCapturedVariableLayout : True if block has captured variables and their layout meta-data has been generated.
Definition at line 234 of file CGBlocks.h.
Referenced by computeBlockInfo(), and clang::CodeGen::CodeGenFunction::EmitBlockLiteral().
HasCXXObject - True if the block's custom copy/dispose functions need to be run even in GC mode.
Definition at line 226 of file CGBlocks.h.
Definition at line 244 of file CGBlocks.h.
Name - The name of the block, kindof.
Definition at line 155 of file CGBlocks.h.
Referenced by clang::CodeGen::CodeGenModule::GetAddrOfGlobalBlock(), getBlockDescriptorName(), and getCopyDestroyHelperFuncName().
True if the block has captures that would necessitate custom copy or dispose helper functions if the block were escaping.
Definition at line 222 of file CGBlocks.h.
Referenced by computeBlockInfo(), and clang::CodeGen::CGDebugInfo::EmitDeclareOfArgVariable().
The next block in the block-info chain.
Invalid if this block info is not part of the CGF's block-info chain, which is true if it corresponds to a global block or a block whose expression has been encountered.
Definition at line 268 of file CGBlocks.h.
Referenced by clang::CodeGen::CodeGenFunction::destroyBlockInfos(), and findAndRemoveBlockInfo().
Definition at line 245 of file CGBlocks.h.
Referenced by computeBlockInfo(), clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockDeclRefVariable(), clang::CodeGen::CGDebugInfo::EmitDeclareOfBlockLiteralArgVariable(), clang::CodeGen::CodeGenFunction::GenerateCopyHelperFunction(), clang::CodeGen::CodeGenFunction::GenerateDestroyHelperFunction(), and getBlockLayoutInfoString().
UsesStret : True if the block uses an stret return.
Mutable because it gets set later in the block-creation process.
Definition at line 230 of file CGBlocks.h.
Referenced by buildGlobalBlock(), clang::CodeGen::CodeGenFunction::EmitBlockLiteral(), and clang::CodeGen::CodeGenFunction::GenerateBlockFunction().


text:
International Journal of Speleology
About This IR
Scholar Commons
Scholar Commons > USF Libraries > Environmental Sustainability > IJS > Vol. 2 (1966) > Iss. 1
Contribution à l'Etude de Bathynella d'Europe: Bathynella natans Vejdovsky, un dilemme à résoudre
Eugène Serban, Institut de Speologie
After a minute study of the structure of the 8th male pereiopod in some Bathynella populations from Romania and England, the structure differences which were found allowed to identify two well individualized kinds of pereiopods; they were named type natans and type stammeri. Taking into account the striking differences between these two types, B. stammeri (Jakobi), which since 1954 is considered to be a subspecies of the natans species, was separated out of the species B. natans sensu Jakobi (1954). The populations understudied were collected in England and Romania, their minute study being the object of an other note, collaboration with T. Gledhill. The facts led to the conclusion that Jakobi's opinion (1954), which dominated the taxonomy of this group, doesn't entirely correspond to the reality, the two taxonomical units being characterized as follows: - Bathynella natans Vejdovsky, characterized by the 8th male pereiopod (fig. I A) with a triangular, well developed anterior plate (fig. 3 A-D-a; 7 A-D), of the same length with the exopodit, a cylindrical internal lobe (fig. 3 A-D-b,) and a little lobe (fig. 3 A-D-c) of a reduced size; - Bathynella stammeri (Jakobi) differing from the first with respect to the anterior pinte (fig. 2 A-D-a; 6A-C) which is rectangular in shape and has a prolongation in the distal outer angle, to the conelike internal lobe (fig. 2 AD-b), and to the little lobe (fig. 2 A-D-d) which is twolobed in this case. After discussion on the relationship between B. catena Vejd. and B. stammeri (Jakobi) it is shown that differences observed in the 8th male pereiopod structure give important indications about the above species to the effect that they are not very closely related. If one takes into account also their wide spreading area, and the individualisation of some populations due to important, characteristic traits - we are obliged to classify them into two different sub-genera. In the first one, the species catena is included - which will keep by this way the very name of the genus, and in the second, termed here Antrobathynella, the species stammeri. In conclusion, what was till now considered as Bathynella natans Vejdovsky sensu Jakobi, was divided into two distinct species — each of them pertaining to two different sub-genera, that is: Bathynella (Bathynella) natans Vejdovsky and Bathynella (Antrobathynella) stammeri (Jakobi). It is demonstrated that the synonymy Jakobi made between B.chappuisi and B. natans is perfectly true under the new conditions too, because it was Delachaux (1919) who rediscovered B.natans Vejd., not Chappuis (1914). The material found by Chappuis in Basel (1914) appears to pertain to B. stammeri (Jakobi) differing both from the individuals from the Grotte de Ver (Delachaux, 1919) and from Prague (Vejdovsky, 1882).
http://dx.doi.org/10.5038/1827-806X.2.1.10
Serban, Eugène. 1966. Contribution à l'Etude de Bathynella d'Europe: Bathynella natans Vejdovsky, un dilemme à résoudre. International Journal of Speleology, 2: 115-132.
Available at: https://scholarcommons.usf.edu/ijs/vol2/iss1/10
Earth Sciences Commons
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Speleogenesis
International Journals of Cave and Karst Science
Acta Carsologica
Cave and Karst Science
Journal of Cave and Karst Science
Karstologia
Travaux de l'Institute de Spéologie Emile Racovitza
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redpajama_set_name: RedPajamaCommonCrawl


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redpajama_set_name: RedPajamaGithub


The Tiny Toy Dump Truck by madscifi makes a fine tchotchke for a presentation, serving to illustrate the risks and rewards of printing flat overhangs without support. A fleet of six printed well, after repairing some failures as those tall, tall rings and posts near the dump bed pivot fell over. I pasted them down in mid-print using ABS slurry, which is not a technique to emulate.
A closer look shows the overhang problem in the dump bed and the broken pillars behind the wheels.
It's in monochrome because the camera choked on that much Safety Orange filament in the image, to the extent that no amount of color correction produced a usable result.


Terry looked at me. He said: "Do not underestimate this anger. This anger was the engine that powered Good Omens." I thought of the driven way that Terry wrote, and of the way that he drove the rest of us with him, and I knew that he was right.
There is a fury to Terry Pratchett's writing: it's the fury that was the engine that powered Discworld. It's also the anger at the headmaster who would decide that six-year-old Terry Pratchett would never be smart enough for the 11-plus; anger at pompous critics, and at those who think serious is the opposite of funny; anger at his early American publishers who could not bring his books out successfully.
And that anger, it seems to me, is about Terry's underlying sense of what is fair and what is not. It is that sense of fairness that underlies Terry's work and his writing, and it's what drove him from school to journalism to the press office of the SouthWestern Electricity Board to the position of being one of the best-loved and bestselling writers in the world.
This description of Terry Pratchett reminded me of the character Sam Vimesfrom the Discworld series. Vimes is an idealist, but a committed cynic whose knowledge of human nature constantly reminds him how far off those ideals are. Vimes also has a dark side that comes out when Vimes loses control of his anger, especially when he temporarily lets go of "the Beast" (in the novel Thud!).


text:
Mars is shining big & bright as it comes closest to Earth in 15 years
08:51 PM | 27 Jul, 2018
CALIFORNIA - With scientists recently announcing the exciting discovery of a 'lake' hidden below the ice on Mars' south pole, the Red Planet is seemingly capitalizing on the exciting news by coming closer to Earth than it has in 15 years.
Stargazers will be able to see the planet at its brightest from Friday night through to Monday night, as Mars comes a 'mere' 36 million miles (58 million km) from Earth, according to NASA.
The planet will be easily visible by the naked eye, while those with a telescope may be able to spot details on the planet's surface, such as its ice caps.
However, dust storms currently engulfing the planet may obscure details that are usually visible with telescopes, Widener University astronomer Harry Augensen told the international media.
On the plus side, the Martian dust will better reflect sunlight, making the planet appear even brighter from Earth.
"It's magnificent. It's as bright as an aeroplane landing light," Augensen added. "Not quite as bright as Venus, but still because of the reddish, orange-ish-red colour, you really can't miss it in the sky."
The visit will see Mars come into "opposition," which occurs when Earth lies directly between Mars and the sun, making the sun and Mars appear in opposite directions as viewed from the Earth.
In 2003, Mars came its closest to Earth in 60,000 years – 34.6 million miles – a feat that won't be repeated until August 28, 2287.
People in Australia, Africa, much of Asia, the Middle East, Europe and South America will also be treated to a lunar eclipse (at least part of it) on Friday night, which is expected to last for one hour and 43 minutes.
Three including Pakistani national killed in UAE ...
First locally transmitted Omicron case reported ...
Genocide Watch warns of impending genocide in ...
Saudi Arabia restricts Umrah repetition for ...
Indian minister promises to construct roads ...
Hostage-taker who demanded release of Dr Aafia ...
Fans to nominate 'Hamaray Heroes' for PSL 2022
Three including Pakistani national killed in UAE suspected drone ...
Areeba Habib and husband Saadain spotted dancing at a friend's wedding
Kiara Advani has the perfect birthday wish for rumoured beau Sidharth ...


Specify, in brief, the nature, structure, types of products or service of the business you selected. Examine the information within the company's code of ethical conduct, and choose three (3) key issues from within the document that you believe are critical for success. Provide rationale for the response.
In contrast, for the fifteenth time in as many years, shareholders of Exxon Mobil Corporation voted down a proposed resolution which would have added "sexual orientation" to their non-discrimination policy.
On the issue of bribery, both ConocoPhillips and ExxonMobil by comparison were committed to compliance with regulations. In contrast, both had internal controls in place and functioning.
If ConocoPhillips and ExxonMobil addresses the issues of human rights policies, discrimination and bribery the positive outcomes would be competitive advantage in the industry and marketplace and a more comprehensive systems approach in regards to global sustainability, since industrial, social, and ecological systems are closely linked.
the customer would know that the company cares for social values. 2. What actions should she take regarding the IKEA supply contract with Rangan Exports? A. Marianne Barner should first of all understand the situation thoroughly before taking any steps against Rangan Exports. The Global sourcing always brings with it the social, cultural and regulatory differences which should be dealt with effectively to ensure success in global supply chain. She should seek the assistance of UNICEF, ILO and NGO's….
Compare the challenges to selected business activities within a selected organisation, in two different economic environments. It is very common in large businesses to expand abroad but there are a lot of factors to be considered when planning to start operation in a different country as countries differ depending on their background, policies, infrastructure and stability. In this report I will compare the challenges to business activities within Tesco Plc. In two different economic environments: China….
- stakeholder influence – pag.10 TASK 2 – a - the nature of UK economic system – pag.11 TASK 2 – b - how government manage UK economy – pag.11 – fiscal and monetary policies - pag. 11 – 12 TASK 2 – c - competition policy and regulatory mechanism in UK – pag.12 TASK 3 – a - market structure of Domino's Pizza – pag. 13 TASK 3 – b - market influence in Domino's Pizza – pag. 14 – 15 TASK 3 – c - cultural environment in Domino's Pizza – pag. 15 TASK 4 – a….
------------------------------------------------- BUSINESS COMMUNICATION Semester 1 2011-2012 Module Leader Ms. Kirti Bhatia Communication Process and Challenges In Global Busienss Environment Submitted By: Kanishk Matta Executive Summary In this report, generic form of communication process is described and types of communication are also there to help the reader get an idea of communication to start with. Thereafter, prominent barriers in communication faced by global firms are elaborated to give the reader….


Today on the Offense-Defense Blog we're going to be discussing the main differences between our Football Training Programs and those of our competition.
There are many important things that set us apart from other local and national camp-focused companies, and knowing these differences is going to be crucial in making the right choice when deciding where to focus your time following this season.
O-D: At Offense-Defense we build our coaching staff from the highest level of talent available, from D1 College coaches to current and retired NFL veterans. In fact, O-D is one of the top employers of football coaches during the off-season each year. Competition: Local youth and sometimes high school coaches, usually parents of one of the campers.
O-D: We rank players on the camp level, regionally, and nationally at each one of our events throughout the year. Beyond simply a name and number on a list, this provides valuable feedback to the players and family about where they stand compared to the competition. Competition: No rankings.
O-D: Offense-Defense uses a hybrid of Pro Style evaluations, as well as a proprietary, dynamic algorithm we've developed over the last 47 years of training Youth, High School, and College level athletes. Many of players we have trained have even used our evaluations as part of their applications for College athletic programs. Competition: No evaluations or occasionally an abridged review of limited value.
O-D: We offer a variety of postseason events in the fall, including tournaments within our own football league (ODFL), as well as the biggest event of them all, the Offense-Defense All-American Bowl, which has been held in such esteemed venues as AT&T Stadium (Cowboys, Dallas), NRG Stadium (Texans, Houston), Citrus Bowl Stadium (various Bowl Games, Orlando), and many more over the last 11 years. Competition: No postseason options, or transparently profit-based pay-to-play tournaments.
O-D: Varying levels of contact, in compliance with local High School Association rules, and tailored to the specific training the athlete is receiving, including full-contact, modified-contact, and non-contact, with the health and safety of each athlete being our #1 priority ALWAYS. Competition: Non-contact training, which leads to much higher risk of injury and concussion during practices and gametime.
O-D: Our high profile events all feature dozens of college scouts from local and regional programs, we well as a variety of recruiting organization who report to athletic departments nationally. Competition: No college scouts or recruiters.
O-D: The first step of getting a scholarship is getting recruited. Every football program has different ways of handing out their scholarships, and we'll connect you with the right Coaches and Athletic directors within our personnel network to help you make your college dreams a reality. Competition: No scholarship assistance.
Head over to O-D.com today to get started on your journey to greatness!


FASTENINGS » DF Truss with Steel Plate Flush Bracket, Morehouse MacDonald & Assoc. Inc.
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text:
\section{Introduction}
\label{sec:introduction}

Serverless computing~\cite{Jonas2019}, also known as Functions-as-a-Service,
narrows the development of Cloud applications to the definition and
composition of stateless functions, while the provider handles the deployment,
scaling, and balancing of the host infrastructure.
Hence, although a bit of a misnomer --- as servers are of course involved ---
the ``less'' in serverless refers to the removal of some server-related
concerns, namely, their \emph{maintenance}, \emph{scaling}, and expenses
related to a sub-optimal management (\eg idle servers).
Essentially, serverless pushes to the extreme the per-usage model of Cloud
Computing: in serverless, users pay only for the computing resources used at
each function invocation. This is why recent
reports~\cite{HellersteinFGSS19,Jonas2019} address serverless computing as the
actual realisation of the long-standing promise of the Cloud to deliver
\emph{computation as a commodity}.
AWS Lambda~\cite{aws_lambda}, launched in 2014, is the first and most
widely-used serverless implementation, however many players like Google,
Microsoft, Apache, IBM, and also open-source communities recently joined the
serverless
market~\cite{apache_openwhisk,microsoft_azure_functions,google_cloud_functions,ironio_ironFunctions,openlambda,ibm_functions}.
Current serverless proposals support the definition of functions --- written
in mainstream languages such as Go, Java, Javascript or Python --- activated
by specific events in the system, like a user request to a web gateway, the
delivery of content from a message broker or a notification from a database.
The serverless infrastructure transparently handles the instantiation of
functions, as well as monitoring, logging, and fault tolerance.

Serverless offerings have become more and more common, yet the technology is
still in its infancy and presents
limitations~\cite{baldini2017serverless,Jonas2019,HellersteinFGSS19} which
hinder its wide adoption. For example, current serverless implementations
favour operational flexibility (asynchrony and scalability) over developer
control (function composition).
Concretely, they do not support the direct composition of functions, which must
call some stateful service in the infrastructure (\eg a message broker) which
will take care of triggering an event bound to the callee. On the one hand,
that limitation is beneficial, since programmers must develop their functions
as highly fine-grained, re-usable components (reminiscent of service-oriented
architectures and microservices~\cite{DragoniGLMMMS17}). On the other hand,
such openness and fine granularity increases the complexity of the system:
programmers cannot assume sequential consistency or serialisability among their
functions, which complicates reasoning on the semantics of the transformations
applied to the global state of their architecture. This holds true also when
estimating resource usage/costs, due to the complexity of unfolding all
possible concurrent computations.

The above criticisms pushed us to investigate a core calculus for
serverless computing, to reason on the paradigm, to model desirable features of future
implementations, and to formalise guarantees over programs. In
\cref{sec:calculus} we introduce the Serverless Kernel Calculus (SKC); as far
as we know, the first core formal model for serverless computing. SKC\ combines ideas
from both the $\lambda$-calculus (for functions) and the $\pi$-calculus (for
communication). In \cref{sec:calculus}, we also extend SKC{} to capture
limitations of current serverless implementations. In \cref{sec:example} we use
our extension to model a real-world serverless architecture~\cite{tailor},
implemented on AWS Lambda. Finally, in \cref{sec:discussion} we discuss future
developments of SKC{}.

\section{A Serverless Kernel Calculus}
\label{sec:calculus}

\looseness=-1
Our kernel calculus defines a serverless architecture as a pair
$\plat{S} {\env D}$, where $S$ is the system of \emph{running functions} and
$\env D$ is a \emph{definition repository}, containing function
definitions. The repository $\env D$ is a partial function from function
names $\code f$ to function bodies $M$.
$M$ includes function application (\code{$M$\ $M$'}), asynchronous execution of
new functions (\code{async\ $M$}), function names \code{f}, and values $V$.
Values include variables \code{x}, $\lambda$-abstractions
\code{\\x.$M$}, named
\emph{futures}~\cite{baker1977,halstead1985,NiehrenSS06} \code{$c$}, and the
unit value \code{()}. A system $S$ contains \emph{running functions} $\evalp{c}
{M}$, where $c$ will contain the result of the computation of the function
$M$. Systems can be composed in parallel $\mathbin{\texttt{|}}$ and include the empty system
$\texttt{0}$. Futures can be restricted in systems via $\res{c} {S}$.%
\begin{align*}
S, S' \Coloneqq {} &
  \evalp{c}{M} \mid
  S \mathbin{\texttt{|}} S' \mid
  \res{c}{S} \mid
  \texttt{0}
  &
  \mbox{(Systems)}
\\
M,M' \Coloneqq {} &
  \code{$M$\ $M$'} \mid
  \code{async\ $M$} \mid
  \code{f} \mid
  V
  &
\mbox{(Functions)}
\\
V,V' \Coloneqq {} &
  \code{x} \mid
  \code{\\x.$M$} \mid
  \code{$c$} \mid
  \code{()} &
\mbox{(Values)}
\end{align*}
We assume futures to appear only at runtime and not in initial systems.
Moreover, we consider a standard structural congruence $\congr$ that supports
changing the scope of restrictions to avoid name capture, and where parallel
composition is associative, commutative, and has $\texttt{0}$ as neutral element.
\begin{align*}
\res{c}{\res{c'}{S}} \congr \res{c'}{\res{c}{S}}
\qquad
\res{c}{(S \mathbin{\texttt{|}} S')} \congr \res{c}{S} \mathbin{\texttt{|}} S' \qquad\text{if }  c \not\in \mathop{\mathrm{fn}}(S')
\\
S \congr S \mathbin{\texttt{|}} \texttt{0}
\qquad
S \mathbin{\texttt{|}} S' \congr S' \mathbin{\texttt{|}} S
\qquad
(S \mathbin{\texttt{|}} S') \mathbin{\texttt{|}} S'' \congr S \mathbin{\texttt{|}} (S' \mathbin{\texttt{|}} S'')
\end{align*}
We define the semantics of our calculus using evaluation contexts
$\mathcal{E}$ and $\mathcal{E}_{\lambda}$, to evaluate, respectively,
systems and functions.
\begin{align*}
	\mathcal{E} {} \Coloneqq
	       \evalp{c}{\mathcal{E}_{\lambda}}
	  %
   \hspace{5em}
	\mathcal{E}_{\lambda} {} \Coloneqq
		     [-]
 		\mid \code{(\\x.$M$)$\mathcal{E}_{\lambda}$}
		\mid \code{$\mathcal{E}_{\lambda}$ $M$}
\end{align*}
\looseness=-1
We report in \cref{fig:reduction} the semantics of serverless architectures $
\plat{S} {\env D}$, expressed as reduction rules. Rule \rname{$\beta$} is the
traditional function application of $\lambda$-calculus. Rule
\rname{ret} retrieves the body of function \code{f} from the definition
repository $\env{D}$. Rule \rname{async} models the execution of new
functions: it creates a fresh future $c$ and, in parallel, it
executes function $M$ so that $c$ will store the evaluation of
$M$. When the evaluation of a function reduces to a value, rule
\rname{push} returns the value to the associated future and removes
both the terminated function and its restriction. Rules
\rname{str}, \rname{res}, and \rname{lpar} perform the closure under,
respectively, structural congruence, restriction, and parallel
composition.
\begin{figure}[t]
\begin{spreadlines}{2pt}
\begin{gather*}
\scalemath{.88}{
\infer[\rname{$\beta$}]
{\plat{\mathcal{E}[\code{(\\x.$M$)\ $V$}]}{\env D}
\reducesto
\plat{\mathcal{E}[M\{V/\code{x}\}]}{\env D}}
{}
}
\qquad
\scalemath{.88}{
\infer[\rname{ret}]
{\plat{\mathcal{E}[\code{f}]}{\env D} \reducesto \plat{\mathcal{E}[M]}{\env D}}
{\env D(\code{f})=M}
}
\\
\scalemath{.88}{
\infer[\rname{async}]{
\plat{\mathcal{E}[\code{async\ $M$}]}{\env D}
\reducesto
\plat{\res{c}{(\mathcal{E}[c] \mathbin{\texttt{|}} \evalp{c}{\code{$M$}})}}{\env D}
}{c \notin \mathop{\mathrm{fn}}(M)}
}
\quad
\scalemath{.88}{
\infer[\rname{push}]
{\plat{\res{c}{(S \mathbin{\texttt{|}} \evalp{c}{V})}}{\env D} \reducesto \plat{S\{V/c\}}{\env D}}
{}
}
\\
\scalemath{.88}{
  \infer[\rname{str}]
	{\plat{S_0}{\env D} \reducesto \plat{S_1}{\env D'}}
	{S_0 \congr S_0'
	&\plat{S_0'}{\env D} \reducesto \plat{S_1'}{\env D'}
	&S_1' \congr S_1}
}
\\
\scalemath{.88}{
\infer[\rname{res}]
	{\plat{\res{c}{S}}{\env D} \reducesto \plat{\res{c}{S'}}{\env D'}}
	{\plat{S}{\env D} \reducesto \plat{S'}{\env D'}}
}
\qquad
\scalemath{.88}{
\infer[\rname{lpar}]
	{\plat{S_1 \mathbin{\texttt{|}} S_2}{\env D} \reducesto \plat{S_1' \mathbin{\texttt{|}} S_2}{\env D'}}
	{\plat{S_1}{\env D} \reducesto \plat{S_1'}{\env D'}}
}
\end{gather*}
\end{spreadlines}
\caption{SKC{} reduction semantics.}\label{fig:reduction}
\end{figure}
We include in SKC{} standard components (conditionals, \etc) and extend evaluation contexts ($\mathcal{E}$) accordingly:
\begin{gather*}
M \Coloneqq {} \dots \mid \code{if {}$M$ then {}$M$' else {}$M$''}
 \mid \code{fst {}$M$} \mid \code{snd {}$M$}
\\
V \Coloneqq {} \dots \mid \code{True} \mid \code{False} \mid \code{
($V$,$V$')}
\end{gather*}
We define standard macros for \code{fix}point, \code{let} and \code{let}
\code{rec} declarations, and pairs.
\begin{gather*}
\code{fix} \defeq \code{\\f.(\\x.f(xx))(\\x.f(xx))}
\qquad
\code{let x =\ $M$ in\ $M$'} \defeq \code{(\\x.$M$')\ $M$}
\\
\code{let rec x =\ $M$ in\ $M$'} \defeq
\code{let x =\ fix \\x.$M$ in\ $M$'}
\\
\code{\\(x,y).M} \defeq \code{\\z.(\\x.\\y.M) (fst z) (snd z)}
\end{gather*}

\subsection{SKC{}$_\sigma$ - A stateful extension of SKC{}}
\label{sub:stateful_skc}

SKC{} considers static definition repositories, \ie no rules mutate the state
of $\env{D}$. We now present SKC{}$_\sigma$, an extension of SKC{} which
includes two primitives to define transformations on definition repositories.
As shown in \cref{sec:example}, SKC{}$_\sigma$ is powerful enough to encode
stateful services, like databases and message queues.
\begin{align*}
M,M' \Coloneqq {} & \dots \mid \code{set f\ $M$}  \mid \code{take f}
\end{align*}
The first primitive included in SKC{}$_\sigma$ is \code{set f\ $M$}, which
updates the definition repository $\env{D}$ to map \code{f} to $M$: users can
use the \code{set} primitive to deploy new function definitions or
update/override existing ones. The second primitive is \code{take f}, which
removes the definition of \code{f} from $\env{D}$, returning it to the
caller. We report below the semantics of the new primitives.
\begin{spreadlines}{1pt}
\begin{gather*}
\scalemath{.88}{\infer[\rname{set}]
{\plat{\mathcal{E}[\code{set f {}$M$}]}{\env{D}}
\reducesto
\plat{\mathcal{E}[\code{f}]}{\env{D}[\code{f|-> }$M$]}}
{\texttt{futures}(M) = \emptyset}}
\\
\scalemath{.88}{\infer[\rname{take}]
{\plat{\mathcal{E}[\code{take f}]}{\env{D}}
\reducesto
\plat{\mathcal{E}[\code{let rec f=$M$ in\ $M$}]}{\undeff{\env{D}}{\code{f}}}}
{\env{D}(\code{f}) = M}}
\end{gather*}
\end{spreadlines}
The only restriction on the application of rule \rname{set} is that the body
$M$ of the newly deployed function $\code f$ does not contain futures
(\texttt{futures}($M$) is the set of futures occurring in $M$). This preserves
the semantics of restriction of futures in function evaluations (\cf rules
\rname{async} and \rname{push}). In the reductum, the rule returns the name of
the deployed function, useful to invoke it in the continuation.
Rule \rname{take} removes the definition $M$ of a deployed function $
\code f$. For simplicity, we define $\rname{take}$ applicable only if
$\code f$ is defined. In the reductum, the caller of the \code{take} obtains
the \code{rec}ursive \code{let} declaration of the function (useful for
internal application) while the association for $\code f$ is removed from $\env D$ by function $\texttt{undef}$.

\subsection{SKC{}$_{\mathtt e}$ - Event-based function composition in SKC{}}
\label{sub:events_skc}
We present an idiom of SKC{}, called SKC{}$_{\mathtt e}$, which
models event-based function composition.  SKC{}$_{\mathtt e}$
captures one of the main limitations of current serverless vendors:
the lack of support for direct function invocation, replaced by an
event-handling/event-triggering invocation model. Indeed, current
serverless implementations, such as AWS Lambda, work as follows: they
include
 infrastructural stateful services, such as API
gateways, that we can model using our stateful extension
SKC{}$_{\mathtt \sigma}$, and these services throw
events. User-defined functions are invoked as handlers of these
events. User-defined functions can then invoke the infrastructural
services above. Notably, a user-defined function cannot directly
invoke another user-defined function. We will see an instance of the
event-based pattern in \Cref{sec:example}, while we describe below
event handling mechanisms.

We model events (\code{e} and variations thereof) inside SKC{} as function names associated
with peculiar function bodies in the repository $\env{D}$ that asynchronously
evaluate the corresponding event handler and discard the handler result. For
convenience, \emph{i}) we package the asynchronous call of an event handler in
the helper function \code{callHandler} below (hereafter, we assume that
$\env{D}$ contains \code{callHandler}) and \emph{ii}) we write \code{_} for
unused variable symbols in binding constructs.
\[
	\code{callHandler} \mapsto \code{\\h.\\x.let _ = async (h () x) in ()}
\]
Event \code{e} is defined in $\env D$ as $\code{e} \mapsto \code{callHandler \\_.h$\textsubscript{e}$}$ and its event handler as $\code{h$_\text{e}$} \mapsto \code{$M_\text{e}$}$; we wrap the name $\code{h$_\text{e}$}$ in a lambda abstraction to avoid expansion (via \rname{Ret}) since function names are not values.
Raising an event \code{e} with some parameter \code{v} results in
asynchronously executing the corresponding handler, as shown by the derivation
below (we abbreviate $\plat{S}{\env{D}}\reducesto \plat{S'}{\env{D}}$ as
$S \reducesto_{\env{D}} S'$ and label reductions with the
names of the most relevant applied rules).
\begin{spreadlines}{0em}
\[\scalemath{.88}{\begin{array}{l}
\hl{\code{e v}}
\reducesto[\rname{ret}]_{\env{D}}
\hl{\code{callHandler \\_.h$_\text{e}$ v}}
\reducesto[\rname{ret}]_{\env{D}}
\hl{\code{(\\h.\\x.let _=async (h () x) in ()) \\_.h$_\text{e}$ v}}
\\
\reducesto[\rname{$\beta$},\rname{$\beta$}]_{\env{D}}
\hl{\code{let _=async (\\_.h$_e$ () v) in ()}} %
\reducesto[\rname{async}]_{\env{D}}
\hl{$\res{c}{(\code{let _=$c$ in ()} \mathbin{\texttt{|}} \evalp{c}{\code{\\_.h$_e$ () v}})}$}
\\
\reducesto[\rname{$\beta$},\rname{$\beta$}]_{\env{D}}
\hl{$\res{c}{(\code{()} \mathbin{\texttt{|}} \evalp{c}{\code{h$_e$ v}})}$}
\reducesto[\rname{ret}]_{\env{D}}
\hl{$\code{()} \mathbin{\texttt{|}} \res{c}{(\evalp{c}{\code{$M_\text{e}$ v}})}$}
\end{array}}\]
\end{spreadlines}

\section{An Illustrative Example}
\label{sec:example}

\begin{figure}[tb]
 \centering
  \includegraphics[width=.8\textwidth]{images/tailor_extract.pdf}
  \noindent\hfil\rule{0.5\textwidth}{.4pt}\vspace{1em}\hfil
  \includegraphics[width=.8\textwidth]{images/tailor_circled.jpg}
 \caption{
  Scheme of the Autodesk Tailor system. Top, excerpt
  considered in the example. Bottom, full architecture (circled elements
  belong to the excerpt).}
 \label{fig:tailor}
\end{figure}
Let SKC{}$_{\sigma \mathtt e}$ be the compound of SKC{}$_\sigma$ and
SKC{}$_{\mathtt e}$ presented in \cref{sec:calculus}. Here, we illustrate how
SKC{}$_{\sigma {\mathtt e}}$ can capture real-world serverless systems by
encoding a relevant portion (depicted in \cref{fig:tailor}) of
Tailor~\cite{tailor}, an architecture for user registration, developed by
Autodesk over AWS Lambda.
Tailor mixes serverless functions with vendor-specific services: \textit{API
Gateways}, key-value databases (\textit{DynamoDB}), and queue-based
notification services (\textit{SNS}). In the architecture, each function
defines a fragment of the logic of a user-registration procedure, like the
initiation of registration requests (\code{talr-receptionist}), request
validation (\code{talr-validator}), \etc.
To model \cref{fig:tailor} in SKC{}$_{\sigma \code e}$, first, we install in
$\env{D}$ the event handlers for the \textit{API Gateway}, the
\textit{DynamoDB}, and \textit{SNS} services\footnote{We omit the name of the
function called by $\code{e}_\texttt{SNS}$, excluded in the excerpt of
\cref{fig:tailor}.}:
\begin{gather*}
\hl{\code{e$_{\text{API}}$}} \mapsto \code{callHandler(talr-receptionist) }
\qquad
\hl{\code{e$_{\text{SNS}}$}} \mapsto \code{callHandler([...]) }
\\
\hl{\code{e$_{\text{DDB}}$}} \mapsto \code{callHandler(talr-validator)}
\end{gather*}
Then, we define the functions called by the handlers installed above, using
the same names of the \emph{AWS Lambda} functions in \cref{fig:tailor}.
Handler \code{e$_{\text{API}}$} calls function \code{talr-receptionist}, which
validates the request and inserts the information of the user in the key/value
database. For brevity, we omit the behaviour of \code{talr-receptionist} in
case of invalid requests and the definition of auxiliary functions
\code{validate_request}, \code{get_key}, \code{get_value} in $\env D$:
\begin{align*}
\hl{\code{talr-receptionist}}
\mapsto {} &
\code{\\x.if validate_request x then}
\\ &
\quad\code{write_db (get_key x,get_value x) else [...]}
\end{align*}
Handler \code{e$_{\text{DDB}}$} invokes function \code{talr-validator}, which
retrieves from the database the \code{status} of task \code{x}, checks if it is
complete, and sends a notification on \emph{SNS}. We omit the definitions of
functions \code{check} and \code{compose_msg} and of the \code{else} branch.

\begin{align*}
\hl{\code{talr-validator}} \mapsto {} &
\code{\\x.let status = read_db x in} \\ &
\code{if check status then push (compose_msg x) else [...]}
\end{align*}
We conclude illustrating the definitions of functions \code{write_db},
\code{read_db}, and \code{push} in $\env D$, which exemplify how
SKC{}$_{\sigma \mathtt{e}}$ can encode stateful, event-triggering services.
Keys are represented as function names and values are stored in $\env{D}$; thus keys are passed around wrapped in lambda abstractions (\code{\\_.k}) as done for events.
\begin{gather*}
\hl{\code{write_db}} \mapsto \code{\\(x,v).e$_{\text{DDB}}$ (set (x ())
v)}
\quad
\hl{\code{read_db}} \mapsto \code{\\x.x ()}
\\
\hl{\code{push}} \mapsto \code{\\(x,v).e$_{
\text{SNS}}$ (set (x ()) v)}
\end{gather*}
Function \code{write_db} takes a key (wrapped as $\code{x} = \code{\\_.k}$) and a value $\code v$ as parameters, writes on the database by \code{set}ting to $\code v$ the body of a function called $\code k$, and notifies the write, invoking \code{e$_{\text{DDB}}$}\footnote{%
More involved variants of the database are possible. \Eg to avoid clashes
among services using the same key for different elements, we can either use
scoping or prefix key names with service names
--- \eg Tailor uses service-specific tables in \emph{DynamoDB}.
}.
Function \code{read_db} simply unwraps the key thus enabling retrieval from $\env{D}$.
Similarly to \code{write_db}, function \code{push} publishes (\code{set}) a
message $\code v$ on an \textit{SNS} topic (represented as a function name) and triggers \code{e$_{\text{SNS}}$}.

\begin{remark}
The example illustrates how SKC{} can capture (but not be restricted by) one
of the most prominent limitations of current serverless
platform~\cite{HellersteinFGSS19}, \ie that \emph{i}) user-defined functions
can be only invoked by raising an event that executes a new function (as done
by \code{callHandler}, using the \code{async} primitive) and \emph{ii})
functions can invoke other functions only by interacting with some
event-triggering infrastructural service (\eg a database, represented by
function \code{write_db}, or a notification queue, represented by function
\code{push}).
\end{remark}

\section{Discussion and Conclusion}
\label{sec:discussion}
We propose SKC, the first core formal model to reason on serverless computing.
While the design of SKC\ strives for minimality, it captures the main
ingredients~\cite{HellersteinFGSS19,Jonas2019} of serverless architectures:
\emph{i}) the deployment and instantiation of event-triggered, stateless
functions and \emph{ii}) the desiderata of direct function-to-function
invocation based on futures --- in \cref{sec:example} we
show how this mechanism is powerful enough to cover also the current setting
of serverless vendors, where function invocation must rely on third-party
services that handle event triggering.

Futures~\cite{baker1977,halstead1985}, which are the main communication
mechanism in SKC{}, are becoming one of the de-facto standards in
asynchronous systems~\cite{Goetz06,ECMAScript2018,Summerfield13,Williams17}.
We considered using named channels
(as in CCS/$\pi$-calculus~\cite{Milner80,Sangiorgi01}) instead of futures,
but we found them too general for the needs of the serverless model (they are
bi-directional and re-usable). Besides, futures can encode
channels~\cite{NiehrenSS06}.

\looseness=-1
The work closest to ours is~\cite{JPBDMSBG19}, appeared during the submission
of this work, in the form of a technical report. It presents a detailed operational semantics that captures the low-level
details of current serverless implementations (\eg cold/warm components, storage, and transactions are primitive features of their model) whereas SKC{} identifies a kernel model of serverless computing.
Another work close to SKC is~\cite{NiehrenSS06}, where the authors introduce a
$\lambda$-calculus with futures. Since the aim of~\cite{NiehrenSS06} is to
formalise and reason on a concurrent extension of Standard ML, their calculus
is more involved than SKC{}, as it contains primitive operators (handlers and
cells) to encode safe non-deterministic concurrent operations, which can be
encoded as macros in SKC{}. An interesting research direction is to
investigate which results from~\cite{JPBDMSBG19,NiehrenSS06} can be adapted to
SKC{}.

\looseness=-1
Being the first core framework to reason on serverless architectures, SKC
{} opens multiple avenues of future research.
For example, current serverless technologies offer little guarantee on
sequential execution across functions, which compels the investigation of new
tools to enforce sequential consistency~\cite{Lamport79} or
serialisability~\cite{Papadimitriou79} of the transformations of the global
state~\cite{HellersteinFGSS19}. That challenge can be tackled developing
static analysis techniques and type disciplines~\cite{HuttelLVCCDMPRT16,AnconaBB0CDGGGH16} for SKC{}.
Another direction concerns programming models, which should give to programmers
an overview over the overall logic of the distributed functions and capture the
loosely-consistent execution model of serverless~\cite{HellersteinFGSS19}.
Choreographic Programming~\cite{Montesi15,Cruz-FilipeM16} is a promising
candidate for that task, as choreographies are designed to capture the global
interactions in distributed systems~\cite{Kavantzas05}, and recent
results~\cite{CarboneM13,PredaGGLM16,GiallorenzoMG18} confirmed their
applicability to microservices~\cite{DragoniGLMMMS17}, a neighbouring domain
to
that of serverless architectures.  Other possible research directions, that we
do not discuss for space constraints, include monitoring, various kinds of
security analysis including ``self-DDoS
attacks''~\cite{serverless_out_of_control,beware_runonstartup,serverless_a_lesson_learned}
and performance analysis.  This last one is particularly relevant in the
per-usage model of serverless architectures, yet requires to extend SKC{} with an explicit notion of time in order to support quantitative behavioural reasoning for timed systems \cite{brengos:lmcs2019,brengos:concur2016}.

\phantomsection
\label{structure:end-of-mainmatter}

redpajama_set_name: RedPajamaArXiv