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\newcommand{\etalchar}[1]{$^{#1}$}
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\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
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\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
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% \MRhref is called by the amsart/book/proc definition of \MR.
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\providecommand{\MRhref}[2]{%
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\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
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}
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\providecommand{\href}[2]{#2}
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\begin{thebibliography}{dMKA{\etalchar{+}}15}
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|
||||
{http://dx.doi.org/https://doi.org/10.1016/j.jal.2013.04.001}
|
||||
{\path{doi:https://doi.org/10.1016/j.jal.2013.04.001}}.
|
||||
|
||||
\bibitem[{The}18]{redprl}
|
||||
{The RedPRL Development Team}, \emph{{RedPRL} -- the {P}eople's {R}efinement
|
||||
{L}ogic}, 2018, \url{http://www.redprl.org/}.
|
||||
|
||||
\bibitem[{Uni}13]{hottbook}
|
||||
The {Univalent Foundations Program}, \emph{Homotopy type theory: Univalent
|
||||
foundations of mathematics}, \url{http://homotopytypetheory.org/book},
|
||||
Institute for Advanced Study, 2013.
|
||||
|
||||
\bibitem[VAG{\etalchar{+}}]{unimath}
|
||||
Vladimir Voevodsky, Benedikt Ahrens, Daniel Grayson, et~al., \emph{{U}ni{M}ath
|
||||
--- {U}nivalent {M}athematics}, code library,
|
||||
\url{https://github.com/UniMath}.
|
||||
|
||||
\bibitem[vD16]{vandoorn2016proptrunc}
|
||||
Floris van Doorn, \emph{Constructing the propositional truncation using
|
||||
non-recursive hits}, Proceedings of the 5th ACM SIGPLAN Conference on
|
||||
Certified Programs and Proofs, ACM, 2016, pp.~122--129.
|
||||
|
||||
\bibitem[vDvRB17]{vandoorn2017leanhott}
|
||||
Floris van Doorn, Jakob von Raumer, and Ulrik Buchholtz, \emph{Homotopy type
|
||||
theory in lean}, pp.~479--495, Springer, 2017, \href
|
||||
{http://dx.doi.org/10.1007/978-3-319-66107-0_30}
|
||||
{\path{doi:10.1007/978-3-319-66107-0_30}}.
|
||||
|
||||
\bibitem[vG12]{berg2010models}
|
||||
Benno {van den Berg} and Richard Garner, \emph{{Topological and simplicial
|
||||
models of identity types}}, ACM transactions on computational logic (TOCL)
|
||||
\textbf{13} (2012), no.~1, 3.
|
||||
|
||||
\bibitem[Voe06]{voevodsky2006}
|
||||
Vladimir Voevodsky, \emph{A very short note on the homotopy
|
||||
{$\lambda$}-calculus}, online, 2006,
|
||||
\url{http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/Hlambda_short_current.pdf}.
|
||||
|
||||
\bibitem[Voe09]{voevodsky2009typesystems}
|
||||
\bysame, \emph{Notes on type systems}, online, 2009,
|
||||
\url{http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/expressions_current_1.pdf}.
|
||||
|
||||
\bibitem[Voe14]{voevodsky2014univalence}
|
||||
\bysame, \emph{{The equivalence axiom and univalent models of type theory.
|
||||
(Talk at CMU on February 4, 2010)}}, \href {http://arxiv.org/abs/1402.5556}
|
||||
{\path{arXiv:1402.5556}}.
|
||||
|
||||
\bibitem[Voe15]{voevodsky2015lecture}
|
||||
\bysame, \emph{Oxford lectures on {U}ni{M}ath}, filmed by Kohei Kishida,
|
||||
available at \url{https://www.math.ias.edu/vladimir/Lectures}, 2015.
|
||||
|
||||
\bibitem[vR16]{raumer2016doublegroupoids}
|
||||
Jakob von Raumer, \emph{Formalizing double groupoids and cross modules in the
|
||||
lean theorem prover}, Mathematical Software -- ICMS 2016, Springer
|
||||
International Publishing, 2016, pp.~28--33.
|
||||
|
||||
\bibitem[Zha17]{zhan2017auto2}
|
||||
Bohua Zhan, \emph{Formalization of the fundamental group in untyped set theory
|
||||
using auto2}, International Conference on Interactive Theorem Proving,
|
||||
Springer, Springer, 2017, pp.~514--530, \href
|
||||
{http://dx.doi.org/10.1007/978-3-319-66107-0_32}
|
||||
{\path{doi:10.1007/978-3-319-66107-0_32}}.
|
||||
|
||||
\end{thebibliography}
|
||||
BIN
resources/VanDoornDissertation/dissertation.pdf
vendored
Normal file
BIN
resources/VanDoornDissertation/dissertation.pdf
vendored
Normal file
Binary file not shown.
6598
resources/VanDoornDissertation/dissertation.tex
vendored
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6598
resources/VanDoornDissertation/dissertation.tex
vendored
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Load diff
293
resources/VanDoornDissertation/lstlean.tex
vendored
Normal file
293
resources/VanDoornDissertation/lstlean.tex
vendored
Normal file
|
|
@ -0,0 +1,293 @@
|
|||
% Listing style definition for the Lean Theorem Prover.
|
||||
% Defined by Jeremy Avigad, 2015, by modifying Assia Mahboubi's SSR style.
|
||||
% Unicode replacements taken from Olivier Verdier's unixode.sty
|
||||
|
||||
\lstdefinelanguage{lean} {
|
||||
|
||||
% Anything betweeen $ becomes LaTeX math mode
|
||||
mathescape=true,
|
||||
% Comments may or not include Latex commands
|
||||
texcl=false,
|
||||
|
||||
% keywords, list taken from lean-syntax.el
|
||||
morekeywords=[1]{
|
||||
import, prelude, tactic_hint, protected, private, noncomputable, definition, renaming,
|
||||
hiding, exposing, parameter, parameters, begin, begin+, proof, qed, conjecture, constant, constants,
|
||||
hypothesis, lemma, corollary, variable, variables, premise, premises, theory,
|
||||
print, theorem, proposition, example, abbreviation, abstract,
|
||||
open, as, export, override, axiom, axioms, inductive, with, structure, record, universe, universes,
|
||||
alias, help, environment, options, precedence, reserve,
|
||||
match, infix, infixl, infixr, notation, postfix, prefix,
|
||||
tactic_infix, tactic_infixl, tactic_infixr, tactic_notation, tactic_postfix, tactic_prefix,
|
||||
eval, check, coercion, end, reveal, this, suppose,
|
||||
using, namespace, section, fields, find_decl,
|
||||
attribute, local, set_option, extends, include, omit, classes,
|
||||
instances, coercions, metaclasses, raw, migrate, replacing,
|
||||
calc, have, obtains, show, suffices, by, by+, in, at, let, forall, Pi, fun,
|
||||
exists, if, dif, then, else, assume, assert, take,
|
||||
obtain, from, aliases
|
||||
},
|
||||
|
||||
% Sorts
|
||||
morekeywords=[2]{Type, Prop},
|
||||
|
||||
% tactics, list taken from lean-syntax.el
|
||||
morekeywords=[3]{
|
||||
Cond, or_else, then, try, when, assumption, eassumption, rapply,
|
||||
apply, fapply, eapply, rename, intro, intros, all_goals, fold, focus, focus_at,
|
||||
generalize, generalizes, clear, clears, revert, reverts, back, beta, done, exact, rexact,
|
||||
refine, repeat, whnf, rotate, rotate_left, rotate_right, inversion, cases, rewrite,
|
||||
xrewrite, krewrite, blast, simp, esimp, unfold, change, check_expr, contradiction,
|
||||
exfalso, split, existsi, constructor, fconstructor, left, right, injection, congruence, reflexivity,
|
||||
symmetry, transitivity, state, induction, induction_using, fail, append,
|
||||
substvars, now, with_options, with_attributes, with_attrs, note
|
||||
},
|
||||
|
||||
% modifiers, taken from lean-syntax.el
|
||||
% note: 'otherkeywords' is needed because these use a different symbol.
|
||||
% this command doesn't allow us to specify a number -- they are put with [1]
|
||||
otherkeywords={
|
||||
[persistent], [notation], [visible], [instance], [trans_instance],
|
||||
[class], [parsing-only], [coercion], [unfold_full], [constructor],
|
||||
[reducible], [irreducible], [semireducible], [quasireducible], [wf],
|
||||
[whnf], [multiple_instances], [none], [decl], [declaration],
|
||||
[relation], [symm], [subst], [refl], [trans], [simp], [congr],
|
||||
[backward], [forward], [no_pattern], [begin_end], [tactic], [abbreviation],
|
||||
[reducible], [unfold], [alias], [eqv], [intro], [intro!], [elim], [grinder],
|
||||
[localrefinfo], [recursor]
|
||||
},
|
||||
|
||||
% Various symbols
|
||||
literate=
|
||||
{α}{{\ensuremath{\mathrm{\alpha}}}}1
|
||||
{β}{{\ensuremath{\mathrm{\beta}}}}1
|
||||
{γ}{{\ensuremath{\mathrm{\gamma}}}}1
|
||||
{δ}{{\ensuremath{\mathrm{\delta}}}}1
|
||||
{ε}{{\ensuremath{\mathrm{\varepsilon}}}}1
|
||||
{ζ}{{\ensuremath{\mathrm{\zeta}}}}1
|
||||
{η}{{\ensuremath{\mathrm{\eta}}}}1
|
||||
{θ}{{\ensuremath{\mathrm{\theta}}}}1
|
||||
{ι}{{\ensuremath{\mathrm{\iota}}}}1
|
||||
{κ}{{\ensuremath{\mathrm{\kappa}}}}1
|
||||
{μ}{{\ensuremath{\mathrm{\mu}}}}1
|
||||
{ν}{{\ensuremath{\mathrm{\nu}}}}1
|
||||
{ξ}{{\ensuremath{\mathrm{\xi}}}}1
|
||||
{π}{{\ensuremath{\mathrm{\mathnormal{\pi}}}}}1
|
||||
{ρ}{{\ensuremath{\mathrm{\rho}}}}1
|
||||
{σ}{{\ensuremath{\mathrm{\sigma}}}}1
|
||||
{τ}{{\ensuremath{\mathrm{\tau}}}}1
|
||||
{φ}{{\ensuremath{\mathrm{\varphi}}}}1
|
||||
{χ}{{\ensuremath{\mathrm{\chi}}}}1
|
||||
{ψ}{{\ensuremath{\mathrm{\psi}}}}1
|
||||
{ω}{{\ensuremath{\mathrm{\omega}}}}1
|
||||
|
||||
{Γ}{{\ensuremath{\mathrm{\Gamma}}}}1
|
||||
{Δ}{{\ensuremath{\mathrm{\Delta}}}}1
|
||||
{Θ}{{\ensuremath{\mathrm{\Theta}}}}1
|
||||
{Λ}{{\ensuremath{\mathrm{\Lambda}}}}1
|
||||
{Σ}{{\ensuremath{\mathrm{\Sigma}}}}1
|
||||
{Φ}{{\ensuremath{\mathrm{\Phi}}}}1
|
||||
{Ξ}{{\ensuremath{\mathrm{\Xi}}}}1
|
||||
{Ψ}{{\ensuremath{\mathrm{\Psi}}}}1
|
||||
{Ω}{{\ensuremath{\mathrm{\Omega}}}}1
|
||||
|
||||
{ℵ}{{\ensuremath{\aleph}}}1
|
||||
|
||||
{≤}{{\ensuremath{\leq}}}1
|
||||
{≥}{{\ensuremath{\geq}}}1
|
||||
{≠}{{\ensuremath{\neq}}}1
|
||||
{≈}{{\ensuremath{\approx}}}1
|
||||
{≡}{{\ensuremath{\equiv}}}1
|
||||
{≃}{{\ensuremath{\simeq}}}1
|
||||
|
||||
{≤}{{\ensuremath{\leq}}}1
|
||||
{≥}{{\ensuremath{\geq}}}1
|
||||
|
||||
{∂}{{\ensuremath{\partial}}}1
|
||||
{∆}{{\ensuremath{\triangle}}}1 % or \laplace?
|
||||
|
||||
{∫}{{\ensuremath{\int}}}1
|
||||
{∑}{{\ensuremath{\mathrm{\Sigma}}}}1
|
||||
{Π}{{\ensuremath{\mathrm{\Pi}}}}1
|
||||
|
||||
{⊥}{{\ensuremath{\perp}}}1
|
||||
{∞}{{\ensuremath{\infty}}}1
|
||||
{∂}{{\ensuremath{\partial}}}1
|
||||
|
||||
{∓}{{\ensuremath{\mp}}}1
|
||||
{±}{{\ensuremath{\pm}}}1
|
||||
{×}{{\ensuremath{\times}}}1
|
||||
|
||||
{⊕}{{\ensuremath{\oplus}}}1
|
||||
{⊗}{{\ensuremath{\otimes}}}1
|
||||
{⊞}{{\ensuremath{\boxplus}}}1
|
||||
|
||||
{∇}{{\ensuremath{\nabla}}}1
|
||||
{√}{{\ensuremath{\sqrt}}}1
|
||||
|
||||
{⬝}{{\ensuremath{\cdot}}}1
|
||||
{•}{{\ensuremath{\cdot}}}1
|
||||
{∘}{{\ensuremath{\circ}}}1
|
||||
{`}{{\ensuremath{{}^\backprime}}}1
|
||||
{'}{{\ensuremath{{}^\prime}}}1
|
||||
|
||||
%{⁻}{{\ensuremath{^{\textup{\kern1pt\rule{2pt}{0.3pt}\kern-1pt}}}}}1
|
||||
{⁻}{{\ensuremath{^{-}}}}1
|
||||
{▸}{{\ensuremath{\mathsmaller\blacktriangleright}}}1 %% requires package relsize
|
||||
|
||||
{∧}{{\ensuremath{\wedge}}}1
|
||||
{∨}{{\ensuremath{\vee}}}1
|
||||
{¬}{{\ensuremath{\neg}}}1
|
||||
{⊢}{{\ensuremath{\vdash}}}1
|
||||
|
||||
%{⟨}{{\ensuremath{\left\langle}}}1
|
||||
%{⟩}{{\ensuremath{\right\rangle}}}1
|
||||
{⟨}{{\ensuremath{\langle}}}1
|
||||
{⟩}{{\ensuremath{\rangle}}}1
|
||||
|
||||
{↦}{{\ensuremath{\mapsto}}}1
|
||||
{→}{{\ensuremath{\rightarrow}}}1
|
||||
{↔}{{\ensuremath{\leftrightarrow}}}1
|
||||
{⇒}{{\ensuremath{\Rightarrow}}}1
|
||||
{⟹}{{\ensuremath{\Longrightarrow}}}1
|
||||
{⇐}{{\ensuremath{\Leftarrow}}}1
|
||||
{⟸}{{\ensuremath{\Longleftarrow}}}1
|
||||
|
||||
{∩}{{\ensuremath{\cap}}}1
|
||||
{∪}{{\ensuremath{\cup}}}1
|
||||
{⊂}{{\ensuremath{\subseteq}}}1
|
||||
{⊆}{{\ensuremath{\subseteq}}}1
|
||||
{⊄}{{\ensuremath{\nsubseteq}}}1
|
||||
{⊈}{{\ensuremath{\nsubseteq}}}1
|
||||
{⊃}{{\ensuremath{\supseteq}}}1
|
||||
{⊇}{{\ensuremath{\supseteq}}}1
|
||||
{⊅}{{\ensuremath{\nsupseteq}}}1
|
||||
{⊉}{{\ensuremath{\nsupseteq}}}1
|
||||
{∈}{{\ensuremath{\in}}}1
|
||||
{∉}{{\ensuremath{\notin}}}1
|
||||
{∋}{{\ensuremath{\ni}}}1
|
||||
{∌}{{\ensuremath{\notni}}}1
|
||||
{∅}{{\ensuremath{\emptyset}}}1
|
||||
|
||||
{∖}{{\ensuremath{\setminus}}}1
|
||||
{†}{{\ensuremath{\dag}}}1
|
||||
|
||||
{ℕ}{{\ensuremath{\mathbb{N}}}}1
|
||||
{ℤ}{{\ensuremath{\mathbb{Z}}}}1
|
||||
{ℝ}{{\ensuremath{\mathbb{R}}}}1
|
||||
{ℚ}{{\ensuremath{\mathbb{Q}}}}1
|
||||
{ℂ}{{\ensuremath{\mathbb{C}}}}1
|
||||
{⌞}{{\ensuremath{\llcorner}}}1
|
||||
{⌟}{{\ensuremath{\lrcorner}}}1
|
||||
{⦃}{{\ensuremath{\{\!|}}}1
|
||||
{⦄}{{\ensuremath{|\!\}}}}1
|
||||
|
||||
{₁}{{\ensuremath{_1}}}1
|
||||
{₂}{{\ensuremath{_2}}}1
|
||||
{₃}{{\ensuremath{_3}}}1
|
||||
{₄}{{\ensuremath{_4}}}1
|
||||
{₅}{{\ensuremath{_5}}}1
|
||||
{₆}{{\ensuremath{_6}}}1
|
||||
{₇}{{\ensuremath{_7}}}1
|
||||
{₈}{{\ensuremath{_8}}}1
|
||||
{₉}{{\ensuremath{_9}}}1
|
||||
{₀}{{\ensuremath{_0}}}1
|
||||
|
||||
{¹}{{\ensuremath{^1}}}1
|
||||
{²}{{\ensuremath{^2}}}1
|
||||
{³}{{\ensuremath{^3}}}1
|
||||
{⁴}{{\ensuremath{^4}}}1
|
||||
{⁵}{{\ensuremath{^5}}}1
|
||||
{⁶}{{\ensuremath{^6}}}1
|
||||
{⁷}{{\ensuremath{^7}}}1
|
||||
{⁸}{{\ensuremath{^8}}}1
|
||||
{⁹}{{\ensuremath{^9}}}1
|
||||
{⁰}{{\ensuremath{^0}}}1
|
||||
|
||||
|
||||
{ᵒ}{{\textsuperscript{o}}}1
|
||||
{ᵖ}{{\textsuperscript{p}}}1
|
||||
|
||||
|
||||
{ₙ}{{\ensuremath{_n}}}1
|
||||
{ₘ}{{\ensuremath{_m}}}1
|
||||
{↑}{{\ensuremath{\uparrow}}}1
|
||||
{↓}{{\ensuremath{\downarrow}}}1
|
||||
|
||||
% {▸}{{\ensuremath{\triangleright}}}1
|
||||
|
||||
{Σ}{{\color{symbolcolor}\ensuremath{\mathrm{\Sigma}}}}1
|
||||
{Π}{{\color{symbolcolor}\ensuremath{\mathrm{\Pi}}}}1
|
||||
{∀}{{\color{symbolcolor}\ensuremath{\forall}}}1
|
||||
{∃}{{\color{symbolcolor}\ensuremath{\exists}}}1
|
||||
{λ}{{\color{symbolcolor}\ensuremath{\mathrm{\lambda}}}}1
|
||||
{Ω}{{\color{symbolcolor}\ensuremath{\mathrm{\Omega}}}}1
|
||||
|
||||
{:=}{{\color{symbolcolor}:=}}1
|
||||
{=}{{\color{symbolcolor}=}}1
|
||||
{<}{{\color{symbolcolor}<}}1
|
||||
{+}{{\color{symbolcolor}+}}1
|
||||
{*}{{\color{symbolcolor}\ensuremath{{}^{*}}}}1,
|
||||
|
||||
% Comments
|
||||
%comment=[s][\itshape \color{commentcolor}]{/-}{-/},
|
||||
morecomment=[s][\color{commentcolor}]{/-}{-/},
|
||||
morecomment=[l][\itshape \color{commentcolor}]{--},
|
||||
|
||||
% Spaces are not displayed as a special character
|
||||
showstringspaces=false,
|
||||
|
||||
% keep spaces
|
||||
keepspaces=true,
|
||||
|
||||
% String delimiters
|
||||
morestring=[b]",
|
||||
morestring=[d],
|
||||
|
||||
% Size of tabulations
|
||||
tabsize=3,
|
||||
|
||||
% Enables ASCII chars 128 to 255
|
||||
extendedchars=false,
|
||||
|
||||
% Case sensitivity
|
||||
sensitive=true,
|
||||
|
||||
% Automatic breaking of long lines
|
||||
breaklines=true,
|
||||
|
||||
% Default style fors listingsred
|
||||
basicstyle=\ttfamily,
|
||||
|
||||
% Position of captions is bottom
|
||||
captionpos=b,
|
||||
|
||||
% Full flexible columns
|
||||
columns=[l]fullflexible,
|
||||
|
||||
|
||||
% Style for (listings') identifiers
|
||||
identifierstyle={\ttfamily\color{black}},
|
||||
% Note : highlighting of Coq identifiers is done through a new
|
||||
% delimiter definition through an lstset at the begining of the
|
||||
% document. Don't know how to do better.
|
||||
|
||||
% Style for declaration keywords
|
||||
keywordstyle=[1]{\ttfamily\color{keywordcolor}},
|
||||
|
||||
% Style for sorts
|
||||
keywordstyle=[2]{\ttfamily\color{sortcolor}},
|
||||
|
||||
% Style for tactics keywords
|
||||
keywordstyle=[3]{\ttfamily\color{tacticcolor}},
|
||||
|
||||
% Style for attributes
|
||||
keywordstyle=[4]{\ttfamily\color{attributecolor}},
|
||||
|
||||
% Style for strings
|
||||
stringstyle=\ttfamily,
|
||||
|
||||
% Style for comments
|
||||
% commentstyle={\ttfamily\footnotesize },
|
||||
|
||||
}
|
||||
783
resources/VanDoornDissertation/macros.tex
vendored
Normal file
783
resources/VanDoornDissertation/macros.tex
vendored
Normal file
|
|
@ -0,0 +1,783 @@
|
|||
%%%% MACROS FOR NOTATION %%%%
|
||||
% Use these for any notation where there are multiple options.
|
||||
% Slightly modified by Floris van Doorn
|
||||
|
||||
%%% Notes and exercise sections
|
||||
\makeatletter
|
||||
\newcommand{\sectionNotes}{\phantomsection\section*{Notes}\addcontentsline{toc}{section}{Notes}\markright{\textsc{\@chapapp{} \thechapter{} Notes}}}
|
||||
\newcommand{\sectionExercises}[1]{\phantomsection\section*{Exercises}\addcontentsline{toc}{section}{Exercises}\markright{\textsc{\@chapapp{} \thechapter{} Exercises}}}
|
||||
\makeatother
|
||||
|
||||
%%% Definitional equality (used infix) %%%
|
||||
\newcommand{\jdeq}{\equiv} % An equality judgment
|
||||
\let\judgeq\jdeq
|
||||
%\newcommand{\defeq}{\coloneqq} % An equality currently being defined
|
||||
\newcommand{\defeq}{\vcentcolon\equiv} % A judgmental equality currently being defined
|
||||
|
||||
%%% Term being defined
|
||||
\newcommand{\define}[1]{\textbf{#1}}
|
||||
|
||||
%%% Vec (for example)
|
||||
|
||||
\newcommand{\Vect}{\ensuremath{\mathsf{Vec}}}
|
||||
\newcommand{\Fin}{\ensuremath{\mathsf{Fin}}}
|
||||
\newcommand{\fmax}{\ensuremath{\mathsf{fmax}}}
|
||||
\newcommand{\seq}[1]{\langle #1\rangle}
|
||||
|
||||
%%% Dependent products %%%
|
||||
\def\prdsym{\textstyle\prod}
|
||||
%% Call the macro like \prd{x,y:A}{p:x=y} with any number of
|
||||
%% arguments. Make sure that whatever comes *after* the call doesn't
|
||||
%% begin with an open-brace, or it will be parsed as another argument.
|
||||
\makeatletter
|
||||
% Currently the macro is configured to produce
|
||||
% {\textstyle\prod}(x:A) \; {\textstyle\prod}(y:B),\
|
||||
% in display-math mode, and
|
||||
% \prod_{(x:A)} \prod_{y:B}
|
||||
% in text-math mode.
|
||||
\def\prd#1{\@ifnextchar\bgroup{\prd@parens{#1}}{\@ifnextchar\sm{\prd@parens{#1}\@eatsm}{\prd@noparens{#1}}}}
|
||||
\def\prd@parens#1{\@ifnextchar\bgroup%
|
||||
{\mathchoice{\@dprd{#1}}{\@tprd{#1}}{\@tprd{#1}}{\@tprd{#1}}\prd@parens}%
|
||||
{\@ifnextchar\sm%
|
||||
{\mathchoice{\@dprd{#1}}{\@tprd{#1}}{\@tprd{#1}}{\@tprd{#1}}\@eatsm}%
|
||||
{\mathchoice{\@dprd{#1}}{\@tprd{#1}}{\@tprd{#1}}{\@tprd{#1}}}}}
|
||||
\def\@eatsm\sm{\sm@parens}
|
||||
\def\prd@noparens#1{\mathchoice{\@dprd@noparens{#1}}{\@tprd{#1}}{\@tprd{#1}}{\@tprd{#1}}}
|
||||
% Helper macros for three styles
|
||||
\def\lprd#1{\@ifnextchar\bgroup{\@lprd{#1}\lprd}{\@@lprd{#1}}}
|
||||
\def\@lprd#1{\mathchoice{{\textstyle\prod}}{\prod}{\prod}{\prod}({\textstyle #1})\;}
|
||||
\def\@@lprd#1{\mathchoice{{\textstyle\prod}}{\prod}{\prod}{\prod}({\textstyle #1}),\ }
|
||||
\def\tprd#1{\@tprd{#1}\@ifnextchar\bgroup{\tprd}{}}
|
||||
\def\@tprd#1{\mathchoice{{\textstyle\prod_{(#1)}}}{\prod_{(#1)}}{\prod_{(#1)}}{\prod_{(#1)}}}
|
||||
\def\dprd#1{\@dprd{#1}\@ifnextchar\bgroup{\dprd}{}}
|
||||
\def\@dprd#1{\prod_{(#1)}\,}
|
||||
\def\@dprd@noparens#1{\prod_{#1}\,}
|
||||
|
||||
%%% Lambda abstractions.
|
||||
% Each variable being abstracted over is a separate argument. If
|
||||
% there is more than one such argument, they *must* be enclosed in
|
||||
% braces. Arguments can be untyped, as in \lam{x}{y}, or typed with a
|
||||
% colon, as in \lam{x:A}{y:B}. In the latter case, the colons are
|
||||
% automatically noticed and (with current implementation) the space
|
||||
% around the colon is reduced. You can even give more than one variable
|
||||
% the same type, as in \lam{x,y:A}.
|
||||
\def\lam#1{{\lambda}\@lamarg#1:\@endlamarg\@ifnextchar\bgroup{.\,\lam}{.\,}}
|
||||
\def\@lamarg#1:#2\@endlamarg{\if\relax\detokenize{#2}\relax #1\else\@lamvar{\@lameatcolon#2},#1\@endlamvar\fi}
|
||||
\def\@lamvar#1,#2\@endlamvar{(#2\,{:}\,#1)}
|
||||
% \def\@lamvar#1,#2{{#2}^{#1}\@ifnextchar,{.\,{\lambda}\@lamvar{#1}}{\let\@endlamvar\relax}}
|
||||
\def\@lameatcolon#1:{#1}
|
||||
\let\lamt\lam
|
||||
% This version silently eats any typing annotation.
|
||||
\def\lamu#1{{\lambda}\@lamuarg#1:\@endlamuarg\@ifnextchar\bgroup{.\,\lamu}{.\,}}
|
||||
\def\@lamuarg#1:#2\@endlamuarg{#1}
|
||||
|
||||
%%% Dependent products written with \forall, in the same style
|
||||
\def\fall#1{\forall (#1)\@ifnextchar\bgroup{.\,\fall}{.\,}}
|
||||
|
||||
%%% Existential quantifier %%%
|
||||
\def\exis#1{\exists (#1)\@ifnextchar\bgroup{.\,\exis}{.\,}}
|
||||
|
||||
%%% Dependent sums %%%
|
||||
\def\smsym{\textstyle\sum}
|
||||
% Use in the same way as \prd
|
||||
\def\sm#1{\@ifnextchar\bgroup{\sm@parens{#1}}{\@ifnextchar\prd{\sm@parens{#1}\@eatprd}{\sm@noparens{#1}}}}
|
||||
\def\sm@parens#1{\@ifnextchar\bgroup%
|
||||
{\mathchoice{\@dsm{#1}}{\@tsm{#1}}{\@tsm{#1}}{\@tsm{#1}}\sm@parens}%
|
||||
{\@ifnextchar\prd%
|
||||
{\mathchoice{\@dsm{#1}}{\@tsm{#1}}{\@tsm{#1}}{\@tsm{#1}}\@eatprd}%
|
||||
{\mathchoice{\@dsm{#1}}{\@tsm{#1}}{\@tsm{#1}}{\@tsm{#1}}}}}
|
||||
\def\@eatprd\prd{\prd@parens}
|
||||
\def\sm@noparens#1{\mathchoice{\@dsm@noparens{#1}}{\@tsm{#1}}{\@tsm{#1}}{\@tsm{#1}}}
|
||||
\def\lsm#1{\@ifnextchar\bgroup{\@lsm{#1}\lsm}{\@@lsm{#1}}}
|
||||
\def\@lsm#1{\mathchoice{{\textstyle\sum}}{\sum}{\sum}{\sum}({\textstyle #1})\;}
|
||||
\def\@@lsm#1{\mathchoice{{\textstyle\sum}}{\sum}{\sum}{\sum}({\textstyle #1}),\ }
|
||||
\def\tsm#1{\@tsm{#1}\@ifnextchar\bgroup{\tsm}{}}
|
||||
\def\@tsm#1{\mathchoice{{\textstyle\sum_{(#1)}}}{\sum_{(#1)}}{\sum_{(#1)}}{\sum_{(#1)}}}
|
||||
\def\dsm#1{\@dsm{#1}\@ifnextchar\bgroup{\dsm}{}}
|
||||
\def\@dsm#1{\sum_{(#1)}\,}
|
||||
\def\@dsm@noparens#1{\sum_{#1}\,}
|
||||
|
||||
%%% W-types
|
||||
\def\wtypesym{{\mathsf{W}}}
|
||||
\def\wtype#1{\@ifnextchar\bgroup%
|
||||
{\mathchoice{\@twtype{#1}}{\@twtype{#1}}{\@twtype{#1}}{\@twtype{#1}}\wtype}%
|
||||
{\mathchoice{\@twtype{#1}}{\@twtype{#1}}{\@twtype{#1}}{\@twtype{#1}}}}
|
||||
\def\lwtype#1{\@ifnextchar\bgroup{\@lwtype{#1}\lwtype}{\@@lwtype{#1}}}
|
||||
\def\@lwtype#1{\mathchoice{{\textstyle\mathsf{W}}}{\mathsf{W}}{\mathsf{W}}{\mathsf{W}}({\textstyle #1})\;}
|
||||
\def\@@lwtype#1{\mathchoice{{\textstyle\mathsf{W}}}{\mathsf{W}}{\mathsf{W}}{\mathsf{W}}({\textstyle #1}),\ }
|
||||
\def\twtype#1{\@twtype{#1}\@ifnextchar\bgroup{\twtype}{}}
|
||||
\def\@twtype#1{\mathchoice{{\textstyle\mathsf{W}_{(#1)}}}{\mathsf{W}_{(#1)}}{\mathsf{W}_{(#1)}}{\mathsf{W}_{(#1)}}}
|
||||
\def\dwtype#1{\@dwtype{#1}\@ifnextchar\bgroup{\dwtype}{}}
|
||||
\def\@dwtype#1{\mathsf{W}_{(#1)}\,}
|
||||
|
||||
\newcommand{\suppsym}{{\mathsf{sup}}}
|
||||
\newcommand{\supp}{\ensuremath\suppsym\xspace}
|
||||
|
||||
\def\wtypeh#1{\@ifnextchar\bgroup%
|
||||
{\mathchoice{\@lwtypeh{#1}}{\@twtypeh{#1}}{\@twtypeh{#1}}{\@twtypeh{#1}}\wtypeh}%
|
||||
{\mathchoice{\@@lwtypeh{#1}}{\@twtypeh{#1}}{\@twtypeh{#1}}{\@twtypeh{#1}}}}
|
||||
\def\lwtypeh#1{\@ifnextchar\bgroup{\@lwtypeh{#1}\lwtypeh}{\@@lwtypeh{#1}}}
|
||||
\def\@lwtypeh#1{\mathchoice{{\textstyle\mathsf{W}^h}}{\mathsf{W}^h}{\mathsf{W}^h}{\mathsf{W}^h}({\textstyle #1})\;}
|
||||
\def\@@lwtypeh#1{\mathchoice{{\textstyle\mathsf{W}^h}}{\mathsf{W}^h}{\mathsf{W}^h}{\mathsf{W}^h}({\textstyle #1}),\ }
|
||||
\def\twtypeh#1{\@twtypeh{#1}\@ifnextchar\bgroup{\twtypeh}{}}
|
||||
\def\@twtypeh#1{\mathchoice{{\textstyle\mathsf{W}^h_{(#1)}}}{\mathsf{W}^h_{(#1)}}{\mathsf{W}^h_{(#1)}}{\mathsf{W}^h_{(#1)}}}
|
||||
\def\dwtypeh#1{\@dwtypeh{#1}\@ifnextchar\bgroup{\dwtypeh}{}}
|
||||
\def\@dwtypeh#1{\mathsf{W}^h_{(#1)}\,}
|
||||
|
||||
|
||||
\makeatother
|
||||
|
||||
% Other notations related to dependent sums
|
||||
\let\setof\Set % from package 'braket', write \setof{ x:A | P(x) }.
|
||||
% \newcommand{\pair}{\ensuremath{\mathsf{pair}}\xspace}
|
||||
\newcommand{\tup}[2]{(#1,#2)}
|
||||
\newcommand{\proj}[1]{\ensuremath{\mathsf{pr}_{#1}}\xspace}
|
||||
\newcommand{\fst}{\ensuremath{\proj1}\xspace}
|
||||
\newcommand{\snd}{\ensuremath{\proj2}\xspace}
|
||||
\newcommand{\ac}{\ensuremath{\mathsf{ac}}\xspace} % not needed in symbol index
|
||||
\newcommand{\un}{\ensuremath{\mathsf{upun}}\xspace} % not needed in symbol index, uniqueness principle for unit type
|
||||
|
||||
%%% recursor and induction
|
||||
\newcommand{\rec}[1]{\mathsf{rec}_{#1}}
|
||||
\newcommand{\ind}[1]{\mathsf{ind}_{#1}}
|
||||
\newcommand{\indid}[1]{\ind{=_{#1}}} % (Martin-Lof) path induction principle for identity types
|
||||
\newcommand{\indidb}[1]{\ind{=_{#1}}'} % (Paulin-Mohring) based path induction principle for identity types
|
||||
|
||||
%%% the uniqueness principle for product types, formerly called surjective pairing and named \spr:
|
||||
\newcommand{\uppt}{\ensuremath{\mathsf{uppt}}\xspace}
|
||||
|
||||
% Paths in pairs
|
||||
\newcommand{\pairpath}{\ensuremath{\mathsf{pair}^{\mathord{=}}}\xspace}
|
||||
% \newcommand{\projpath}[1]{\proj{#1}^{\mathord{=}}}
|
||||
\newcommand{\projpath}[1]{\ensuremath{\apfunc{\proj{#1}}}\xspace}
|
||||
|
||||
%%% For quotients %%%
|
||||
%\newcommand{\pairr}[1]{{\langle #1\rangle}}
|
||||
\newcommand{\pairr}[1]{{\mathopen{}(#1)\mathclose{}}}
|
||||
\newcommand{\Pairr}[1]{{\mathopen{}\left(#1\right)\mathclose{}}}
|
||||
|
||||
% \newcommand{\type}{\ensuremath{\mathsf{Type}}} % this command is overridden below, so it's commented out
|
||||
\newcommand{\im}{\ensuremath{\mathsf{im}}} % the image
|
||||
|
||||
%%% 2D path operations
|
||||
\newcommand{\leftwhisker}{\mathbin{{\ct}_{\ell}}}
|
||||
\newcommand{\rightwhisker}{\mathbin{{\ct}_{r}}}
|
||||
\newcommand{\hct}{\star}
|
||||
|
||||
%%% modalities %%%
|
||||
\newcommand{\modal}{\ensuremath{\ocircle}}
|
||||
\let\reflect\modal
|
||||
\newcommand{\modaltype}{\ensuremath{\type_\modal}}
|
||||
% \newcommand{\ism}[1]{\ensuremath{\mathsf{is}_{#1}}}
|
||||
% \newcommand{\ismodal}{\ism{\modal}}
|
||||
% \newcommand{\existsmodal}{\ensuremath{{\exists}_{\modal}}}
|
||||
% \newcommand{\existsmodalunique}{\ensuremath{{\exists!}_{\modal}}}
|
||||
% \newcommand{\modalfunc}{\textsf{\modal-fun}}
|
||||
% \newcommand{\Ecirc}{\ensuremath{\mathsf{E}_\modal}}
|
||||
% \newcommand{\Mcirc}{\ensuremath{\mathsf{M}_\modal}}
|
||||
\newcommand{\mreturn}{\ensuremath{\eta}}
|
||||
\let\project\mreturn
|
||||
%\newcommand{\mbind}[1]{\ensuremath{\hat{#1}}}
|
||||
\newcommand{\ext}{\mathsf{ext}}
|
||||
%\newcommand{\mmap}[1]{\ensuremath{\bar{#1}}}
|
||||
%\newcommand{\mjoin}{\ensuremath{\mreturn^{-1}}}
|
||||
% Subuniverse
|
||||
\renewcommand{\P}{\ensuremath{\type_{P}}\xspace}
|
||||
|
||||
%%% Localizations
|
||||
% \newcommand{\islocal}[1]{\ensuremath{\mathsf{islocal}_{#1}}\xspace}
|
||||
% \newcommand{\loc}[1]{\ensuremath{\mathcal{L}_{#1}}\xspace}
|
||||
|
||||
%%% Identity types %%%
|
||||
\newcommand{\idsym}{{=}}
|
||||
% \newcommand{\id}[3][]{\ensuremath{#2 =_{#1} #3}\xspace}
|
||||
\newcommand{\idtype}[3][]{\ensuremath{\mathsf{Id}_{#1}(#2,#3)}\xspace}
|
||||
\newcommand{\idtypevar}[1]{\ensuremath{\mathsf{Id}_{#1}}\xspace}
|
||||
% A propositional equality currently being defined
|
||||
\newcommand{\defid}{\coloneqq}
|
||||
|
||||
%%% Dependent paths
|
||||
\newcommand{\dpath}[4]{#3 =^{#1}_{#2} #4}
|
||||
|
||||
%%% singleton
|
||||
% \newcommand{\sgl}{\ensuremath{\mathsf{sgl}}\xspace}
|
||||
% \newcommand{\sctr}{\ensuremath{\mathsf{sctr}}\xspace}
|
||||
|
||||
%%% Reflexivity terms %%%
|
||||
% \newcommand{\reflsym}{{\mathsf{refl}}}
|
||||
% \newcommand{\refl}[1]{\ensuremath{\mathsf{refl}_{#1}}\xspace}
|
||||
|
||||
%%% Path concatenation (used infix, in diagrammatic order) %%%
|
||||
\newcommand{\ct}{%
|
||||
\mathchoice{\mathbin{\raisebox{0.5ex}{$\displaystyle\centerdot$}}}%
|
||||
{\mathbin{\raisebox{0.5ex}{$\centerdot$}}}%
|
||||
{\mathbin{\raisebox{0.25ex}{$\scriptstyle\,\centerdot\,$}}}%
|
||||
{\mathbin{\raisebox{0.1ex}{$\scriptscriptstyle\,\centerdot\,$}}}
|
||||
}
|
||||
|
||||
%%% Path reversal %%%
|
||||
\newcommand{\opp}[1]{\mathord{{#1}^{-1}}}
|
||||
\let\rev\opp
|
||||
|
||||
%%% Transport (covariant) %%%
|
||||
\newcommand{\trans}[2]{\ensuremath{{#1}_{*}\mathopen{}\left({#2}\right)\mathclose{}}\xspace}
|
||||
\let\Trans\trans
|
||||
%\newcommand{\Trans}[2]{\ensuremath{{#1}_{*}\left({#2}\right)}\xspace}
|
||||
\newcommand{\transf}[1]{\ensuremath{{#1}_{*}}\xspace} % Without argument
|
||||
%\newcommand{\transport}[2]{\ensuremath{\mathsf{transport}_{*} \: {#2}\xspace}}
|
||||
\newcommand{\transfib}[3]{\ensuremath{\mathsf{transport}^{#1}(#2,#3)\xspace}}
|
||||
\newcommand{\Transfib}[3]{\ensuremath{\mathsf{transport}^{#1}\Big(#2,\, #3\Big)\xspace}}
|
||||
\newcommand{\transfibf}[1]{\ensuremath{\mathsf{transport}^{#1}\xspace}}
|
||||
|
||||
%%% 2D transport
|
||||
\newcommand{\transtwo}[2]{\ensuremath{\mathsf{transport}^2\mathopen{}\left({#1},{#2}\right)\mathclose{}}\xspace}
|
||||
|
||||
%%% Constant transport
|
||||
\newcommand{\transconst}[3]{\ensuremath{\mathsf{transportconst}}^{#1}_{#2}(#3)\xspace}
|
||||
\newcommand{\transconstf}{\ensuremath{\mathsf{transportconst}}\xspace}
|
||||
|
||||
%%% Map on paths %%%
|
||||
\newcommand{\mapfunc}[1]{\ensuremath{\mathsf{ap}_{#1}}\xspace} % Without argument
|
||||
\newcommand{\map}[2]{\ensuremath{{#1}\mathopen{}\left({#2}\right)\mathclose{}}\xspace}
|
||||
\let\Ap\map
|
||||
%\newcommand{\Ap}[2]{\ensuremath{{#1}\left({#2}\right)}\xspace}
|
||||
\newcommand{\mapdepfunc}[1]{\ensuremath{\mathsf{apd}_{#1}}\xspace} % Without argument
|
||||
% \newcommand{\mapdep}[2]{\ensuremath{{#1}\llparenthesis{#2}\rrparenthesis}\xspace}
|
||||
\newcommand{\mapdep}[2]{\ensuremath{\mapdepfunc{#1}\mathopen{}\left(#2\right)\mathclose{}}\xspace}
|
||||
\let\apfunc\mapfunc
|
||||
\let\ap\map
|
||||
\let\apdfunc\mapdepfunc
|
||||
\let\apd\mapdep
|
||||
|
||||
%%% 2D map on paths
|
||||
\newcommand{\aptwofunc}[1]{\ensuremath{\mathsf{ap}^2_{#1}}\xspace}
|
||||
\newcommand{\aptwo}[2]{\ensuremath{\aptwofunc{#1}\mathopen{}\left({#2}\right)\mathclose{}}\xspace}
|
||||
\newcommand{\apdtwofunc}[1]{\ensuremath{\mathsf{apd}^2_{#1}}\xspace}
|
||||
\newcommand{\apdtwo}[2]{\ensuremath{\apdtwofunc{#1}\mathopen{}\left(#2\right)\mathclose{}}\xspace}
|
||||
|
||||
%%% Identity functions %%%
|
||||
\newcommand{\idfunc}[1][]{\ensuremath{\mathsf{id}_{#1}}\xspace}
|
||||
|
||||
%%% Homotopies (written infix) %%%
|
||||
\newcommand{\htpy}{\sim}
|
||||
|
||||
%%% Other meanings of \sim
|
||||
\newcommand{\bisim}{\sim} % bisimulation
|
||||
\newcommand{\eqr}{\sim} % an equivalence relation
|
||||
|
||||
%%% Equivalence types %%%
|
||||
\newcommand{\eqv}[2]{\ensuremath{#1 \simeq #2}\xspace}
|
||||
\newcommand{\eqvspaced}[2]{\ensuremath{#1 \;\simeq\; #2}\xspace}
|
||||
\newcommand{\eqvsym}{\simeq} % infix symbol
|
||||
\newcommand{\texteqv}[2]{\ensuremath{\mathsf{Equiv}(#1,#2)}\xspace}
|
||||
\newcommand{\isequiv}{\ensuremath{\mathsf{isequiv}}}
|
||||
\newcommand{\qinv}{\ensuremath{\mathsf{qinv}}}
|
||||
\newcommand{\ishae}{\ensuremath{\mathsf{ishae}}}
|
||||
\newcommand{\linv}{\ensuremath{\mathsf{linv}}}
|
||||
\newcommand{\rinv}{\ensuremath{\mathsf{rinv}}}
|
||||
\newcommand{\biinv}{\ensuremath{\mathsf{biinv}}}
|
||||
\newcommand{\lcoh}[3]{\mathsf{lcoh}_{#1}(#2,#3)}
|
||||
\newcommand{\rcoh}[3]{\mathsf{rcoh}_{#1}(#2,#3)}
|
||||
\newcommand{\hfib}[2]{{\mathsf{fib}}_{#1}(#2)}
|
||||
|
||||
%%% Map on total spaces %%%
|
||||
\newcommand{\total}[1]{\ensuremath{\mathsf{total}(#1)}}
|
||||
|
||||
%%% Universe types %%%
|
||||
%\newcommand{\type}{\ensuremath{\mathsf{Type}}\xspace}
|
||||
\newcommand{\UU}{\ensuremath{\mathcal{U}}\xspace}
|
||||
\let\bbU\UU
|
||||
\let\type\UU
|
||||
% Universes of truncated types
|
||||
\newcommand{\typele}[1]{\ensuremath{{#1}\text-\mathsf{Type}}\xspace}
|
||||
\newcommand{\typeleU}[1]{\ensuremath{{#1}\text-\mathsf{Type}_\UU}\xspace}
|
||||
\newcommand{\typelep}[1]{\ensuremath{{(#1)}\text-\mathsf{Type}}\xspace}
|
||||
\newcommand{\typelepU}[1]{\ensuremath{{(#1)}\text-\mathsf{Type}_\UU}\xspace}
|
||||
\let\ntype\typele
|
||||
\let\ntypeU\typeleU
|
||||
\let\ntypep\typelep
|
||||
\let\ntypepU\typelepU
|
||||
\newcommand{\set}{\ensuremath{\mathsf{Set}}\xspace}
|
||||
\newcommand{\setU}{\ensuremath{\mathsf{Set}_\UU}\xspace}
|
||||
\newcommand{\prop}{\ensuremath{\mathsf{Prop}}\xspace}
|
||||
\newcommand{\propU}{\ensuremath{\mathsf{Prop}_\UU}\xspace}
|
||||
%Pointed types
|
||||
\newcommand{\pointed}[1]{\ensuremath{#1_\bullet}}
|
||||
|
||||
%%% Ordinals and cardinals
|
||||
\newcommand{\card}{\ensuremath{\mathsf{Card}}\xspace}
|
||||
\newcommand{\ord}{\ensuremath{\mathsf{Ord}}\xspace}
|
||||
\newcommand{\ordsl}[2]{{#1}_{/#2}}
|
||||
|
||||
%%% Univalence
|
||||
\newcommand{\ua}{\ensuremath{\mathsf{ua}}\xspace} % the inverse of idtoeqv
|
||||
\newcommand{\idtoeqv}{\ensuremath{\mathsf{idtoeqv}}\xspace}
|
||||
\newcommand{\univalence}{\ensuremath{\mathsf{univalence}}\xspace} % the full axiom
|
||||
|
||||
%%% Truncation levels
|
||||
\newcommand{\iscontr}{\ensuremath{\mathsf{isContr}}}
|
||||
\newcommand{\contr}{\ensuremath{\mathsf{contr}}} % The path to the center of contraction
|
||||
\newcommand{\isset}{\ensuremath{\mathsf{isSet}}}
|
||||
\newcommand{\isprop}{\ensuremath{\mathsf{isProp}}}
|
||||
% h-propositions
|
||||
% \newcommand{\anhprop}{a mere proposition\xspace}
|
||||
% \newcommand{\hprops}{mere propositions\xspace}
|
||||
|
||||
%%% Homotopy fibers %%%
|
||||
%\newcommand{\hfiber}[2]{\ensuremath{\mathsf{hFiber}(#1,#2)}\xspace}
|
||||
\let\hfiber\hfib
|
||||
|
||||
%%% Bracket/squash/truncation types %%%
|
||||
% \newcommand{\brck}[1]{\textsf{mere}(#1)}
|
||||
% \newcommand{\Brck}[1]{\textsf{mere}\Big(#1\Big)}
|
||||
% \newcommand{\trunc}[2]{\tau_{#1}(#2)}
|
||||
% \newcommand{\Trunc}[2]{\tau_{#1}\Big(#2\Big)}
|
||||
% \newcommand{\truncf}[1]{\tau_{#1}}
|
||||
%\newcommand{\trunc}[2]{\Vert #2\Vert_{#1}}
|
||||
\newcommand{\trunc}[2]{\mathopen{}\left\Vert #2\right\Vert_{#1}\mathclose{}}
|
||||
\newcommand{\ttrunc}[2]{\bigl\Vert #2\bigr\Vert_{#1}}
|
||||
\newcommand{\Trunc}[2]{\Bigl\Vert #2\Bigr\Vert_{#1}}
|
||||
\newcommand{\truncf}[1]{\Vert \blank \Vert_{#1}}
|
||||
\newcommand{\tproj}[3][]{\mathopen{}\left|#3\right|_{#2}^{#1}\mathclose{}}
|
||||
\newcommand{\tprojf}[2][]{|\blank|_{#2}^{#1}}
|
||||
\def\pizero{\trunc0}
|
||||
%\newcommand{\brck}[1]{\trunc{-1}{#1}}
|
||||
%\newcommand{\Brck}[1]{\Trunc{-1}{#1}}
|
||||
%\newcommand{\bproj}[1]{\tproj{-1}{#1}}
|
||||
%\newcommand{\bprojf}{\tprojf{-1}}
|
||||
|
||||
\newcommand{\brck}[1]{\trunc{}{#1}}
|
||||
\newcommand{\bbrck}[1]{\ttrunc{}{#1}}
|
||||
\newcommand{\Brck}[1]{\Trunc{}{#1}}
|
||||
\newcommand{\bproj}[1]{\tproj{}{#1}}
|
||||
\newcommand{\bprojf}{\tprojf{}}
|
||||
|
||||
% Big parentheses
|
||||
\newcommand{\Parens}[1]{\Bigl(#1\Bigr)}
|
||||
|
||||
% Projection and extension for truncations
|
||||
\let\extendsmb\ext
|
||||
\newcommand{\extend}[1]{\extendsmb(#1)}
|
||||
|
||||
%
|
||||
%%% The empty type
|
||||
\newcommand{\emptyt}{\ensuremath{\mathbf{0}}\xspace}
|
||||
|
||||
%%% The unit type
|
||||
\newcommand{\unit}{\ensuremath{\mathbf{1}}\xspace}
|
||||
\newcommand{\ttt}{\ensuremath{\star}\xspace}
|
||||
|
||||
%%% The two-element type
|
||||
\newcommand{\bool}{\ensuremath{\mathbf{2}}\xspace}
|
||||
\newcommand{\btrue}{{1_{\bool}}}
|
||||
\newcommand{\bfalse}{{0_{\bool}}}
|
||||
|
||||
%%% Injections into binary sums and pushouts
|
||||
\newcommand{\inlsym}{{\mathsf{inl}}}
|
||||
\newcommand{\inrsym}{{\mathsf{inr}}}
|
||||
\newcommand{\inl}{\ensuremath\inlsym\xspace}
|
||||
\newcommand{\inr}{\ensuremath\inrsym\xspace}
|
||||
|
||||
%%% The segment of the interval
|
||||
\newcommand{\seg}{\ensuremath{\mathsf{seg}}\xspace}
|
||||
|
||||
%%% Free groups
|
||||
\newcommand{\freegroup}[1]{F(#1)}
|
||||
\newcommand{\freegroupx}[1]{F'(#1)} % the "other" free group
|
||||
|
||||
%%% Glue of a pushout
|
||||
\newcommand{\glue}{\mathsf{glue}}
|
||||
|
||||
%%% Circles and spheres
|
||||
\newcommand{\Sn}{\mathbb{S}}
|
||||
\newcommand{\base}{\ensuremath{\mathsf{base}}\xspace}
|
||||
\newcommand{\lloop}{\ensuremath{\mathsf{loop}}\xspace}
|
||||
\newcommand{\surf}{\ensuremath{\mathsf{surf}}\xspace}
|
||||
|
||||
%%% Suspension
|
||||
\newcommand{\susp}{\Sigma}
|
||||
\newcommand{\north}{\mathsf{N}}
|
||||
\newcommand{\south}{\mathsf{S}}
|
||||
\newcommand{\merid}{\mathsf{merid}}
|
||||
|
||||
%%% Blanks (shorthand for lambda abstractions)
|
||||
\newcommand{\blank}{\mathord{\hspace{1pt}\text{--}\hspace{1pt}}}
|
||||
|
||||
%%% Nameless objects
|
||||
\newcommand{\nameless}{\mathord{\hspace{1pt}\underline{\hspace{1ex}}\hspace{1pt}}}
|
||||
|
||||
%%% Some decorations
|
||||
%\newcommand{\bbU}{\ensuremath{\mathbb{U}}\xspace}
|
||||
% \newcommand{\bbB}{\ensuremath{\mathbb{B}}\xspace}
|
||||
\newcommand{\bbP}{\ensuremath{\mathbb{P}}\xspace}
|
||||
|
||||
%%% Some categories
|
||||
\newcommand{\uset}{\ensuremath{\mathcal{S}et}\xspace}
|
||||
\newcommand{\ucat}{\ensuremath{{\mathcal{C}at}}\xspace}
|
||||
\newcommand{\urel}{\ensuremath{\mathcal{R}el}\xspace}
|
||||
\newcommand{\uhilb}{\ensuremath{\mathcal{H}ilb}\xspace}
|
||||
\newcommand{\utype}{\ensuremath{\mathcal{T}\!ype}\xspace}
|
||||
|
||||
% Pullback corner
|
||||
%\newbox\pbbox
|
||||
%\setbox\pbbox=\hbox{\xy \POS(65,0)\ar@{-} (0,0) \ar@{-} (65,65)\endxy}
|
||||
%\def\pb{\save[]+<3.5mm,-3.5mm>*{\copy\pbbox} \restore}
|
||||
|
||||
% Macros for the categories chapter
|
||||
% \newcommand{\inv}[1]{{#1}^{-1}}
|
||||
\newcommand{\idtoiso}{\ensuremath{\mathsf{idtoiso}}\xspace}
|
||||
\newcommand{\isotoid}{\ensuremath{\mathsf{isotoid}}\xspace}
|
||||
\newcommand{\op}{^{\mathrm{op}}}
|
||||
\newcommand{\y}{\ensuremath{\mathbf{y}}\xspace}
|
||||
\newcommand{\dgr}[1]{{#1}^{\dagger}}
|
||||
\newcommand{\unitaryiso}{\mathrel{\cong^\dagger}}
|
||||
\newcommand{\cteqv}[2]{\ensuremath{#1 \simeq #2}\xspace}
|
||||
\newcommand{\cteqvsym}{\simeq} % Symbol for equivalence of categories
|
||||
|
||||
%%% Natural numbers
|
||||
\newcommand{\N}{\ensuremath{\mathbb{N}}\xspace}
|
||||
%\newcommand{\N}{\textbf{N}}
|
||||
\let\nat\N
|
||||
\newcommand{\natp}{\ensuremath{\nat'}\xspace} % alternative nat in induction chapter
|
||||
|
||||
\newcommand{\zerop}{\ensuremath{0'}\xspace} % alternative zero in induction chapter
|
||||
\newcommand{\suc}{\mathsf{succ}}
|
||||
\newcommand{\sucp}{\ensuremath{\suc'}\xspace} % alternative suc in induction chapter
|
||||
\newcommand{\add}{\mathsf{add}}
|
||||
\newcommand{\ack}{\mathsf{ack}}
|
||||
\newcommand{\ite}{\mathsf{iter}}
|
||||
\newcommand{\assoc}{\mathsf{assoc}}
|
||||
\newcommand{\dbl}{\ensuremath{\mathsf{double}}}
|
||||
\newcommand{\dblp}{\ensuremath{\dbl'}\xspace} % alternative double in induction chapter
|
||||
|
||||
|
||||
%%% Lists
|
||||
\newcommand{\lst}[1]{\mathsf{List}(#1)}
|
||||
\newcommand{\nil}{\mathsf{nil}}
|
||||
\newcommand{\cons}{\mathsf{cons}}
|
||||
|
||||
%%% Vectors of given length, used in induction chapter
|
||||
\newcommand{\vect}[2]{\ensuremath{\mathsf{Vec}_{#1}(#2)}\xspace}
|
||||
|
||||
%%% Integers
|
||||
\newcommand{\Z}{\ensuremath{\mathbb{Z}}\xspace}
|
||||
\newcommand{\Zsuc}{\mathsf{succ}}
|
||||
\newcommand{\Zpred}{\mathsf{pred}}
|
||||
|
||||
%%% Rationals
|
||||
\newcommand{\Q}{\ensuremath{\mathbb{Q}}\xspace}
|
||||
|
||||
%%% Function extensionality
|
||||
\newcommand{\funext}{\mathsf{funext}}
|
||||
\newcommand{\happly}{\mathsf{happly}}
|
||||
|
||||
%%% A naturality lemma
|
||||
\newcommand{\com}[3]{\mathsf{swap}_{#1,#2}(#3)}
|
||||
|
||||
%%% Code/encode/decode
|
||||
\newcommand{\code}{\ensuremath{\mathsf{code}}\xspace}
|
||||
\newcommand{\encode}{\ensuremath{\mathsf{encode}}\xspace}
|
||||
\newcommand{\decode}{\ensuremath{\mathsf{decode}}\xspace}
|
||||
|
||||
% Function definition with domain and codomain
|
||||
\newcommand{\function}[4]{\left\{\begin{array}{rcl}#1 &
|
||||
\longrightarrow & #2 \\ #3 & \longmapsto & #4 \end{array}\right.}
|
||||
|
||||
%%% Cones and cocones
|
||||
\newcommand{\cone}[2]{\mathsf{cone}_{#1}(#2)}
|
||||
\newcommand{\cocone}[2]{\mathsf{cocone}_{#1}(#2)}
|
||||
% Apply a function to a cocone
|
||||
\newcommand{\composecocone}[2]{#1\circ#2}
|
||||
\newcommand{\composecone}[2]{#2\circ#1}
|
||||
%%% Diagrams
|
||||
\newcommand{\Ddiag}{\mathscr{D}}
|
||||
|
||||
%%% (pointed) mapping spaces
|
||||
\newcommand{\Map}{\mathsf{Map}}
|
||||
|
||||
%%% The interval
|
||||
\newcommand{\interval}{\ensuremath{I}\xspace}
|
||||
\newcommand{\izero}{\ensuremath{0_{\interval}}\xspace}
|
||||
\newcommand{\ione}{\ensuremath{1_{\interval}}\xspace}
|
||||
|
||||
%%% Arrows
|
||||
\newcommand{\epi}{\ensuremath{\twoheadrightarrow}}
|
||||
\newcommand{\mono}{\ensuremath{\rightarrowtail}}
|
||||
|
||||
%%% Sets
|
||||
\newcommand{\bin}{\ensuremath{\mathrel{\widetilde{\in}}}}
|
||||
|
||||
%%% Semigroup structure
|
||||
\newcommand{\semigroupstrsym}{\ensuremath{\mathsf{SemigroupStr}}}
|
||||
\newcommand{\semigroupstr}[1]{\ensuremath{\mathsf{SemigroupStr}}(#1)}
|
||||
\newcommand{\semigroup}[0]{\ensuremath{\mathsf{Semigroup}}}
|
||||
|
||||
%%% Macros for the formal type theory
|
||||
\newcommand{\emptyctx}{\ensuremath{\cdot}}
|
||||
\newcommand{\production}{\vcentcolon\vcentcolon=}
|
||||
\newcommand{\conv}{\downarrow}
|
||||
\newcommand{\ctx}{\ensuremath{\mathsf{ctx}}}
|
||||
\newcommand{\wfctx}[1]{#1\ \ctx}
|
||||
\newcommand{\oftp}[3]{#1 \vdash #2 : #3}
|
||||
\newcommand{\jdeqtp}[4]{#1 \vdash #2 \jdeq #3 : #4}
|
||||
\newcommand{\judg}[2]{#1 \vdash #2}
|
||||
\newcommand{\tmtp}[2]{#1 \mathord{:} #2}
|
||||
|
||||
% rule names
|
||||
\newcommand{\form}{\textsc{form}}
|
||||
\newcommand{\intro}{\textsc{intro}}
|
||||
\newcommand{\elim}{\textsc{elim}}
|
||||
\newcommand{\comp}{\textsc{comp}}
|
||||
\newcommand{\uniq}{\textsc{uniq}}
|
||||
\newcommand{\Weak}{\mathsf{Wkg}}
|
||||
\newcommand{\Vble}{\mathsf{Vble}}
|
||||
\newcommand{\Exch}{\mathsf{Exch}}
|
||||
\newcommand{\Subst}{\mathsf{Subst}}
|
||||
|
||||
%%% Macros for HITs
|
||||
\newcommand{\cc}{\mathsf{c}}
|
||||
\newcommand{\pp}{\mathsf{p}}
|
||||
\newcommand{\cct}{\widetilde{\mathsf{c}}}
|
||||
\newcommand{\ppt}{\widetilde{\mathsf{p}}}
|
||||
\newcommand{\Wtil}{\ensuremath{\widetilde{W}}\xspace}
|
||||
|
||||
%%% Macros for n-types
|
||||
\newcommand{\istype}[1]{\mathsf{is}\mbox{-}{#1}\mbox{-}\mathsf{type}}
|
||||
\newcommand{\nplusone}{\ensuremath{(n+1)}}
|
||||
\newcommand{\nminusone}{\ensuremath{(n-1)}}
|
||||
% \newcommand{\fact}{\mathsf{fact}}
|
||||
|
||||
%%% Macros for homotopy
|
||||
\newcommand{\kbar}{\overline{k}} % Used in van Kampen's theorem
|
||||
|
||||
%%% Macros for induction
|
||||
\newcommand{\natw}{\ensuremath{\mathbf{N^w}}\xspace}
|
||||
\newcommand{\zerow}{\ensuremath{0^\mathbf{w}}\xspace}
|
||||
\newcommand{\sucw}{\ensuremath{\mathbf{s^w}}\xspace}
|
||||
\newcommand{\nalg}{\nat\mathsf{Alg}}
|
||||
\newcommand{\nhom}{\nat\mathsf{Hom}}
|
||||
\newcommand{\ishinitw}{\mathsf{isHinit}_{\mathsf{W}}}
|
||||
\newcommand{\ishinitn}{\mathsf{isHinit}_\nat}
|
||||
\newcommand{\w}{\mathsf{W}}
|
||||
\newcommand{\walg}{\w\mathsf{Alg}}
|
||||
\newcommand{\whom}{\w\mathsf{Hom}}
|
||||
|
||||
%%% Macros for real numbers
|
||||
\newcommand{\RC}{\ensuremath{\mathbb{R}_\mathsf{c}}\xspace} % Cauchy
|
||||
\newcommand{\RD}{\ensuremath{\mathbb{R}_\mathsf{d}}\xspace} % Dedekind
|
||||
\newcommand{\R}{\ensuremath{\mathbb{R}}\xspace} % Either
|
||||
\newcommand{\barRD}{\ensuremath{\bar{\mathbb{R}}_\mathsf{d}}\xspace} % Dedekind completion of Dedekind
|
||||
|
||||
\newcommand{\close}[1]{\sim_{#1}} % Relation of closeness
|
||||
\newcommand{\closesym}{\mathord\sim}
|
||||
\newcommand{\rclim}{\mathsf{lim}} % HIT constructor for Cauchy reals
|
||||
\newcommand{\rcrat}{\mathsf{rat}} % Embedding of rationals into Cauchy reals
|
||||
\newcommand{\rceq}{\mathsf{eq}_{\RC}} % HIT path constructor
|
||||
\newcommand{\CAP}{\mathcal{C}} % The type of Cauchy approximations
|
||||
\newcommand{\Qp}{\Q_{+}}
|
||||
\newcommand{\apart}{\mathrel{\#}} % apartness
|
||||
\newcommand{\dcut}{\mathsf{isCut}} % Dedekind cut
|
||||
\newcommand{\cover}{\triangleleft} % inductive cover
|
||||
\newcommand{\intfam}[3]{(#2, \lam{#1} #3)} % family of rational intervals
|
||||
|
||||
% Macros for the Cauchy reals construction
|
||||
\newcommand{\bsim}{\frown}
|
||||
\newcommand{\bbsim}{\smile}
|
||||
|
||||
\newcommand{\hapx}{\diamondsuit\approx}
|
||||
\newcommand{\hapname}{\diamondsuit}
|
||||
\newcommand{\hapxb}{\heartsuit\approx}
|
||||
\newcommand{\hapbname}{\heartsuit}
|
||||
\newcommand{\tap}[1]{\bullet\approx_{#1}\triangle}
|
||||
\newcommand{\tapname}{\triangle}
|
||||
\newcommand{\tapb}[1]{\bullet\approx_{#1}\square}
|
||||
\newcommand{\tapbname}{\square}
|
||||
|
||||
%%% Macros for surreals
|
||||
\newcommand{\NO}{\ensuremath{\mathsf{No}}\xspace}
|
||||
\newcommand{\surr}[2]{\{\,#1\,\big|\,#2\,\}}
|
||||
\newcommand{\LL}{\mathcal{L}}
|
||||
\newcommand{\RR}{\mathcal{R}}
|
||||
\newcommand{\noeq}{\mathsf{eq}_{\NO}} % HIT path constructor
|
||||
|
||||
\newcommand{\ble}{\trianglelefteqslant}
|
||||
\newcommand{\blt}{\vartriangleleft}
|
||||
\newcommand{\bble}{\sqsubseteq}
|
||||
\newcommand{\bblt}{\sqsubset}
|
||||
|
||||
\newcommand{\hle}{\diamondsuit\preceq}
|
||||
\newcommand{\hlt}{\diamondsuit\prec}
|
||||
\newcommand{\hlname}{\diamondsuit}
|
||||
\newcommand{\hleb}{\heartsuit\preceq}
|
||||
\newcommand{\hltb}{\heartsuit\prec}
|
||||
\newcommand{\hlbname}{\heartsuit}
|
||||
% \newcommand{\tle}{(\bullet\preceq\triangle)}
|
||||
% \newcommand{\tlt}{(\bullet\prec\triangle)}
|
||||
\newcommand{\tle}{\triangle\preceq}
|
||||
\newcommand{\tlt}{\triangle\prec}
|
||||
\newcommand{\tlname}{\triangle}
|
||||
% \newcommand{\tleb}{(\bullet\preceq\square)}
|
||||
% \newcommand{\tltb}{(\bullet\prec\square)}
|
||||
\newcommand{\tleb}{\square\preceq}
|
||||
\newcommand{\tltb}{\square\prec}
|
||||
\newcommand{\tlbname}{\square}
|
||||
|
||||
%%% Macros for set theory
|
||||
\newcommand{\vset}{\mathsf{set}} % point constructor for cummulative hierarchy V
|
||||
\def\cd{\tproj0}
|
||||
\newcommand{\inj}{\ensuremath{\mathsf{inj}}} % type of injections
|
||||
\newcommand{\acc}{\ensuremath{\mathsf{acc}}} % accessibility
|
||||
|
||||
\newcommand{\atMostOne}{\mathsf{atMostOne}}
|
||||
|
||||
\newcommand{\power}[1]{\mathcal{P}(#1)} % power set
|
||||
\newcommand{\powerp}[1]{\mathcal{P}_+(#1)} % inhabited power set
|
||||
|
||||
%%%% THEOREM ENVIRONMENTS %%%%
|
||||
|
||||
% Hyperref includes the command \autoref{...} which is like \ref{...}
|
||||
% except that it automatically inserts the type of the thing you're
|
||||
% referring to, e.g. it produces "Theorem 3.8" instead of just "3.8"
|
||||
% (and makes the whole thing a hyperlink). This saves a slight amount
|
||||
% of typing, but more importantly it means that if you decide later on
|
||||
% that 3.8 should be a Lemma or a Definition instead of a Theorem, you
|
||||
% don't have to change the name in all the places you referred to it.
|
||||
|
||||
% The following hack improves on this by using the same counter for
|
||||
% all theorem-type environments, so that after Theorem 1.1 comes
|
||||
% Corollary 1.2 rather than Corollary 1.1. This makes it much easier
|
||||
% for the reader to find a particular theorem when flipping through
|
||||
% the document.
|
||||
\makeatletter
|
||||
\def\defthm#1#2#3{%
|
||||
%% Ensure all theorem types are numbered with the same counter
|
||||
\newaliascnt{#1}{thm}
|
||||
\newtheorem{#1}[#1]{#2}
|
||||
\aliascntresetthe{#1}
|
||||
%% This command tells cleveref's \cref what to call things
|
||||
\crefname{#1}{#2}{#3}}
|
||||
|
||||
% Now define a bunch of theorem-type environments.
|
||||
\newtheorem{thm}{Theorem}[section]
|
||||
\crefname{thm}{Theorem}{Theorems}
|
||||
\defthm{propn}{Proposition}{Propositions} % Probably we shouldn't use "Proposition" in this way
|
||||
\defthm{cor}{Corollary}{Corollaries}
|
||||
\defthm{lem}{Lemma}{Lemmas}
|
||||
\defthm{ax}{Axiom}{Axioms}
|
||||
\defthm{conj}{Conjecture}{Conjectures}
|
||||
% Since definitions and theorems in type theory are synonymous, should
|
||||
% we actually use the same theoremstyle for them?
|
||||
\theoremstyle{definition}
|
||||
\defthm{defn}{Definition}{Definitions}
|
||||
\theoremstyle{remark}
|
||||
\defthm{rmk}{Remark}{Remarks}
|
||||
\defthm{ex}{Example}{Examples}
|
||||
\defthm{exs}{Examples}{Examples}
|
||||
\defthm{notes}{Notes}{Notes}
|
||||
% Number exercises within chapters, with their own counter.
|
||||
%\newtheorem{ex}{Exercise}[chapter]
|
||||
%\crefname{ex}{Exercise}{Exercises}
|
||||
|
||||
% Display format for sections
|
||||
\crefformat{section}{\S#2#1#3}
|
||||
\Crefformat{section}{Section~#2#1#3}
|
||||
\crefrangeformat{section}{\S\S#3#1#4--#5#2#6}
|
||||
\Crefrangeformat{section}{Sections~#3#1#4--#5#2#6}
|
||||
\crefmultiformat{section}{\S\S#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
|
||||
\Crefmultiformat{section}{Sections~#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
|
||||
\crefrangemultiformat{section}{\S\S#3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}{, #3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}
|
||||
\Crefrangemultiformat{section}{Sections~#3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}{, #3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}
|
||||
|
||||
% Display format for appendices
|
||||
\crefformat{appendix}{Appendix~#2#1#3}
|
||||
\Crefformat{appendix}{Appendix~#2#1#3}
|
||||
\crefrangeformat{appendix}{Appendices~#3#1#4--#5#2#6}
|
||||
\Crefrangeformat{appendix}{Appendices~#3#1#4--#5#2#6}
|
||||
\crefmultiformat{appendix}{Appendices~#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
|
||||
\Crefmultiformat{appendix}{Appendices~#2#1#3}{ and~#2#1#3}{, #2#1#3}{ and~#2#1#3}
|
||||
\crefrangemultiformat{appendix}{Appendices~#3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}{, #3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}
|
||||
\Crefrangemultiformat{appendix}{Appendices~#3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}{, #3#1#4--#5#2#6}{ and~#3#1#4--#5#2#6}
|
||||
|
||||
\crefname{part}{Part}{Parts}
|
||||
|
||||
% Number subsubsections
|
||||
\setcounter{secnumdepth}{5}
|
||||
|
||||
% Display format for figures
|
||||
\crefname{figure}{Figure}{Figures}
|
||||
|
||||
% Use cleveref instead of hyperref's \autoref
|
||||
\let\autoref\cref
|
||||
|
||||
|
||||
%%%% EQUATION NUMBERING %%%%
|
||||
|
||||
% The following hack uses the single theorem counter to number
|
||||
% equations as well, so that we don't have both Theorem 1.1 and
|
||||
% equation (1.1).
|
||||
\let\c@equation\c@thm
|
||||
\numberwithin{equation}{section}
|
||||
|
||||
|
||||
%%%% ENUMERATE NUMBERING %%%%
|
||||
|
||||
% Number the first level of enumerates as (i), (ii), ...
|
||||
\renewcommand{\theenumi}{(\roman{enumi})}
|
||||
\renewcommand{\labelenumi}{\theenumi}
|
||||
|
||||
|
||||
%%%% MARGINS %%%%
|
||||
|
||||
% This is a matter of personal preference, but I think the left
|
||||
% margins on enumerates and itemizes are too wide.
|
||||
% \setitemize[1]{leftmargin=2em}
|
||||
% \setenumerate[1]{leftmargin=*}
|
||||
|
||||
% Likewise that they are too spaced out.
|
||||
% \setitemize[1]{itemsep=-0.2em}
|
||||
% \setenumerate[1]{itemsep=-0.2em}
|
||||
|
||||
%%% Notes %%%
|
||||
\def\noteson{%
|
||||
\gdef\note##1{\mbox{}\marginpar{\color{blue}\textasteriskcentered\ ##1}}}
|
||||
\gdef\notesoff{\gdef\note##1{\null}}
|
||||
\noteson
|
||||
|
||||
\newcommand{\Coq}{\textsc{Coq}\xspace}
|
||||
\newcommand{\Agda}{\textsc{Agda}\xspace}
|
||||
\newcommand{\NuPRL}{\textsc{NuPRL}\xspace}
|
||||
|
||||
%%%% CITATIONS %%%%
|
||||
|
||||
% \let \cite \citep
|
||||
|
||||
%%%% INDEX %%%%
|
||||
|
||||
\newcommand{\footstyle}[1]{{\hyperpage{#1}}n} % If you index something that is in a footnote
|
||||
\newcommand{\defstyle}[1]{\textbf{\hyperpage{#1}}} % Style for pageref to a definition
|
||||
|
||||
\newcommand{\indexdef}[1]{\index{#1|defstyle}} % Index a definition
|
||||
\newcommand{\indexfoot}[1]{\index{#1|footstyle}} % Index a term in a footnote
|
||||
\newcommand{\indexsee}[2]{\index{#1|see{#2}}} % Index "see also"
|
||||
|
||||
|
||||
%%%% Standard phrasing or spelling of common phrases %%%%
|
||||
|
||||
\newcommand{\ZF}{Zermelo--Fraenkel}
|
||||
\newcommand{\CZF}{Constructive \ZF{} Set Theory}
|
||||
|
||||
\newcommand{\LEM}[1]{\ensuremath{\mathsf{LEM}_{#1}}\xspace}
|
||||
\newcommand{\choice}[1]{\ensuremath{\mathsf{AC}_{#1}}\xspace}
|
||||
|
||||
%%%% MISC %%%%
|
||||
|
||||
\newcommand{\mentalpause}{\medskip} % Use for "mental" pause, instead of \smallskip or \medskip
|
||||
|
||||
%% Use \symlabel instead of \label to mark a pageref that you need in the index of symbols
|
||||
\newcounter{symindex}
|
||||
\newcommand{\symlabel}[1]{\refstepcounter{symindex}\label{#1}}
|
||||
|
||||
% Local Variables:
|
||||
% mode: latex
|
||||
% TeX-master: "hott-online"
|
||||
% End:
|
||||
Loading…
Reference in a new issue