swift-mirror/docs/Generics/generics.tex

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% This source file is part of the Swift.org open source project
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% Copyright (c) 2021 - 2024 Apple Inc. and the Swift project authors
% Licensed under Apache License v2.0 with Runtime Library Exception
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% See https://swift.org/LICENSE.txt for license information
% See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
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% From left to right, each option does the following:
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% - Draw line under chapter/section heading at top of page
% - Next three options force use of serif fonts for part, chapter and section headings
% - Put Bibliography in Table of Contents
% - Use 'flat' ToC style because it looks better with double-digit chapter numbers
% - Use 'fleqn' to left-align display math to make it consistent with the 'quote' environment which I use for tables and diagrams and stuff
%
% - Changing `twoside=semi' to `twoside' is safe. The default mode is meant for reading on-screen. If you make this change, even pages have a narrower left margin, and odd pages have a wider left margin, which looks silly when scrolling vertically, but makes sense if you actually print and bind the book.
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% Packages
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% Fancy drop caps at the start of each chapter.
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\renewcommand\LettrineFontHook{\Zallmanfamily}

% Multiple indices.
\usepackage{imakeidx}

% Theorem-like environments: proposition, example, algorithm, etc.
\usepackage{amsthm}

% For the 'List of Algorithms'. Must load before hyperref.
\usepackage{thmtools}

\renewcommand\thmtformatoptarg[1]{#1}

% thmtools doesn't offer enough customization options, so hack it up to not print "Algorithm" in each line of the "List of Algorithms"
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% We use fleqn to left-align display math by default, but sometimes we want to center
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% Hyperlinks in PDF files. We enable numbering in PDF bookmark titles, and backreferences from bibliography entries, and make the section title in the TOC clickable.
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% More control over PDF bookmarks.
\usepackage{bookmark}

% \uptau for generic parameter notation
\usepackage{upgreek}

% rcases, etc
\usepackage{mathtools}

% Nice horizontal rules in tables: \toprule, \midrule, \bottomrule
\usepackage{booktabs}

% AMS math symbols: \varnothing, \mathbb, etc
\usepackage{amssymb}

% UTF-8 greek letters directly in TeX for verbatim environment
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% TikZ for figures
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\usepackage{tikz-cd}
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\tikzstyle{stage}=[rounded corners, draw=darkgray, thick, fill=lightgray, text centered, outer sep=0.2em]
\tikzstyle{data}=[draw=darkgray, thick, fill=light-gray, text centered, outer sep=0.2em]
\tikzstyle{arrow}=[->,>=stealth]
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\tikzstyle{genericenvlabel}=[fill=white, draw=black, very thick, rounded corners]
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\tikzstyle{OtherEntity}=[draw=black,thick,fill=lighter-gray, outer sep=0.2em]

% \DeclareMathOperator, \boxed, etc
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% Verbatim environment with border and line numbers
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% Extended array environment
\usepackage{array}

% Colors for shaded frames
\usepackage{xcolor}

% Shaded frames for 'More details' boxes in Introduction
\usepackage{mdframed}

% To customize bibliography with \bstctlcite
\usepackage{IEEEtrantools}

% Each chapter is its own file.
\usepackage{subfiles}

% Strikethrough (\st)
\usepackage[normalem]{ulem}

% Line breaks in URLs in bibliography
\usepackage{url}
\def\UrlBreaks{\do\/\do-}

% Text flowing around figures
\usepackage{wrapfig}

% Fancier tables
\usepackage{tabularx}

% Set up hyperref link colors.
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% For printing in black and white:
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% Environments
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% Various theorem-like environments
\theoremstyle{definition}
\newtheorem{definition}{Definition}[chapter]

% Algorithm 12A, 12B, etc.
\newtheorem{algorithm}{Algorithm}[chapter]
\renewcommand\thealgorithm{\thechapter\Alph{algorithm}}

% Use the same counter for all three so you get Definition 12.1, Proposition 12.2, Example 12.3 etc.
\newtheorem{example}[definition]{Example}

% We don't want the statement of the theorem to use italics...
% \theoremstyle{theorem}
\newtheorem{proposition}[definition]{Proposition}
\newtheorem{lemma}[definition]{Lemma}
\newtheorem{corollary}[definition]{Corollary}
\newtheorem{theorem}[definition]{Theorem}

% 'listing' floating environment for source listings
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% 'Verbatim' environment for fancy source listings
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% 'More Details' boxes in Introduction
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% Derived requirements
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% Generic environments in Archetypes

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}{%
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}

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% Macros
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% Cross-references.
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% I use this in a few places.
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% Declared interface type
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% Protocol generic signature
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%%%
% Derived requirements
%%%

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%%%
% Generic signature queries
%%%

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\item \textbf{Query:} \IndexQueryDef{#1}$\texttt{#1}(#2)$

\textbf{Input:} #3

\textbf{Output:} #4

#5
}

%%%
% Type substitution algebra
%%%

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% Conformances
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% Archetypes print [[like this]]. Must be in math mode
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% Generic environment operations
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%%%
% Monoids, etc
%%%

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% Requirement Machine
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%%%
% Math helpers
%%%
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% Old substitution algebra notation
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\newcommand{\ttbox}[1]{\boxed{\mbox{\vphantom{pI\texttt{pI}}\texttt{#1}}}}

% GitHub links in 'Source Code Reference' sections
\newcommand{\SourceFile}[1]{\href{https://github.com/swiftlang/swift/tree/main/#1}{\texttt{#1}}}

% Note: \apiref{foo}{bar} must be followed by a newline, because of a quirk with \noindent
\def\apiref#1#2
{\bigskip\hrule\nobreak\vskip 3pt\noindent\texttt{\vphantom{p}#1}\hfill\textsl{#2}\par\nobreak\vskip 3pt\hrule\vskip 3pt\noindent}

% Type parameter and conformance path graph
\tikzstyle{root} = [rounded corners, fill=lightgray, outer sep=0.1em]
\tikzstyle{interior} = [rounded corners, fill=light-gray, outer sep=0.1em]

% Protocol dependency graph
\tikzstyle{protocol} = [rounded corners, fill=light-gray]

% Title page logo

\newcommand{\GenericsLogo}{
\begin{center}
\begin{tikzpicture}[x=2cm, y=2cm]
\foreach \a in {0,1,2,3,4,5} {
  \foreach \b in {0,1,2,3,4,5} {
    \node (A\a B\b) [circle, draw, very thick, outer sep=0.4em] at (\a,\b) {};
  }
}

\foreach \a in {0,1,2,3,4,5} {
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  \path [arrow, very thick] (A\a B2) edge (A\a B1);
  \path [arrow, very thick] (A\a B0) edge (A\a B1);
}

\foreach \a in {0,1,2,3,4} {
  \pgfmathtruncatemacro\aa{\a+1}
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    \path [arrow, very thick] (A\a B\b) edge (A\aa B\b);
  }
}
\end{tikzpicture}
\end{center}
}

% I don't like boldface page numbers in the table of contents.
\RedeclareSectionCommands[tocpagenumberformat=]{chapter}
\RedeclareSectionCommands[tocpagenumberformat=]{part}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Index
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\indexsetup{othercode=\footnotesize}

% We have a main index and one for command line flags.

% generics.ist configures letter headings in the index.
\makeindex[intoc,options=-s generics]
\makeindex[intoc,name=flags,title=Command Line Flags,columns=1,options=-s generics]

% \Index is used instead of \index for entries with custom formatting, eg
%
%   \Index{foo bar@foo \texttt{bar}}
%
% because for some reason, a mix of \IndexDefinition or \IndexSource with \index doesn't get collated correctly.
\newcommand{\Index}[1]{\index{#1|textrm}}

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% Add an entry to the command line flag index with the right formatting
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% Used for -debug-requirement-machine=... flags
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% Derivation steps
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\newcommand{\IndexStepTwo}[2]{\index{#1 derivation step@\textsc{#1} derivation step!#2}}
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% Sets in the type substitution algebra
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\newcommand{\IndexSetDefinition}[2]{\index{#1@$#2$|textbf}}

% Swift version history
\newcommand{\IndexSwift}[1]{\index{Swift!#1}\index{history}}

% Generic signature queries
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\newcommand{\IndexQuerySource}[1]{\IndexSource{#1()@$\texttt{#1}()$}}
\newcommand{\IndexQuery}[1]{\Index{#1()@$\texttt{#1}()$}}

\newcommand{\IndexSelf}{\Index{protocol Self type@protocol \tSelf\ type}}

% Normally a seealso index entry elides the page number, but sometimes we want index entries that look like this:
%
% foo, 123
%    see also bar
%
% The trick is to make a fake subentry and format it with this macro to prevent it from showing up.
%
% The above example would be generated by: \index{foo}\index{foo!z@\igobble|seealso{bar}}
%
% The 'z' should sort after every other 'real' subentry, if any.
\def\igobble#1 {}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title Page
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\titlehead{\GenericsLogo}
\title{Compiling Swift Generics}
\author{Slava Pestov}

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\begin{document}

\maketitle

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% Let's Go!
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% Table of Contents
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\tableofcontents

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% The Good Stuff
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\subfile{chapters/preface}

\part{Syntax}\label{part syntax}

\subfile{chapters/introduction}

\subfile{chapters/compilation-model}

\subfile{chapters/types}

\subfile{chapters/declarations}

\part{Semantics}\label{part semantics}

\subfile{chapters/generic-signatures}

\subfile{chapters/substitution-maps}

\subfile{chapters/conformances}

\subfile{chapters/archetypes}

\subfile{chapters/type-resolution}

\part{Specialties}\label{part specialties}

\subfile{chapters/extensions}

\subfile{chapters/building-generic-signatures}

\subfile{chapters/conformance-paths}

\subfile{chapters/opaque-return-types}

\subfile{chapters/existential-types}

\part{The Requirement Machine}\label{part rqm}

\subfile{chapters/basic-operation}

\subfile{chapters/monoids}

\subfile{chapters/symbols-terms-and-rules}

\subfile{chapters/completion}

\subfile{chapters/property-map}

\subfile{chapters/concrete-conformances}

\subfile{chapters/rule-minimization}

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\appendix

\subfile{chapters/math-summary}

\subfile{chapters/derived-requirements-summary}

\subfile{chapters/type-substitution-summary}

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% Postmatter
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% Index
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