166 lines
4.4 KiB
TeX
Vendored
166 lines
4.4 KiB
TeX
Vendored
\newcommand{\Haskell}{{\sc Haskell}}
|
|
|
|
\newcommand{\eg}{{e.g.}}
|
|
\newcommand{\ie}{{i.e.}}
|
|
\newcommand{\cf}{{cf.}}
|
|
|
|
\newcommand{\sect}[1]{Section~\ref{#1}}
|
|
\newcommand{\fig}[1]{Figure~\ref{#1}}
|
|
|
|
\renewcommand{\|}{{~\mid~}}
|
|
\renewcommand{\:}{{\; : \;}}
|
|
\renewcommand{\=}{{~~ = ~~}}
|
|
|
|
\newcommand{\der}{\vdash}
|
|
\newcommand{\emptyctxt}{()}
|
|
\newcommand{\inctxt}[2]{#1\der#2}
|
|
\newcommand{\inctxtT}[3]{#1\der#2~:#3}
|
|
|
|
\newcommand{\set}[1]{\{ #1 \}}
|
|
|
|
% the subst and mod macros
|
|
\newcommand{\subst}[2]{(#1/#2)}
|
|
%\newcommand{\subst}[2]{(#1=#2)}
|
|
\renewcommand{\mod}[1]{\; ({\sf mod.} \; #1)}
|
|
\newcommand{\hmapsto}{~}
|
|
|
|
% generic name for an equivalence (used to be \sigma, now f)
|
|
\newcommand\myeq{f}
|
|
|
|
% path abstraction: <i>
|
|
\newcommand{\pabs}[1]{{\langle}#1{\rangle} \; }
|
|
|
|
% refl
|
|
\newcommand{\refl}[1]{{1_{#1}}} % {{\sf refl_{#1}}}
|
|
\DeclareMathOperator{\transport}{\mathsf{transp}} % transport as special case of comp
|
|
%\DeclareMathOperator{\J}{\mathsf{J}}
|
|
\newcommand{\J}{\mathsf{J}}
|
|
\DeclareMathOperator{\idrefl}{\mathsf{r}}
|
|
|
|
\newcommand{\dM}{{\sf dM}}
|
|
\newcommand{\II}{\mathbb{I}}
|
|
\newcommand{\FF}{\mathbb{F}}
|
|
|
|
|
|
% nat
|
|
\newcommand{\NN}{{\sf N}}
|
|
\newcommand{\natrec}{{\sf natrec}}
|
|
\newcommand{\s}{{\sf s}}
|
|
\newcommand{\suc}[1]{\s \; #1}
|
|
\newcommand{\0}{{\sf 0}}
|
|
|
|
\newcommand{\Id}{{\sf Id}}
|
|
\newcommand{\ident}{{\sf id}}
|
|
\newcommand{\Path}{{\sf Path}}
|
|
\newcommand{\Equiv}{{\sf Equiv}}
|
|
\newcommand{\isEquiv}{{\sf isEquiv}}
|
|
\newcommand{\ext}{{\sf contr}}
|
|
\newcommand{\isContr}{{\sf isContr}}
|
|
|
|
\DeclareMathOperator{\dom}{dom}
|
|
\DeclareMathOperator{\cod}{cod}
|
|
|
|
\def\NN{\hbox{\sf N}}
|
|
\def\Type{\hbox{\sf Type}}
|
|
\def\Box{\hbox{\sf B}}
|
|
\def\PER{\hbox{\sf PER}}
|
|
\def\FUN{\Pi}
|
|
\def\ELEM{\hbox{\sf El}}
|
|
\def\GG{\hbox{\sf G}}
|
|
\def\TP{\hbox{\sf TP}}
|
|
\def\N0{\hbox{\sf N}_0}
|
|
\def\ZERO{\hbox{\sf zero}}
|
|
\def\SUCC{\hbox{s}}
|
|
|
|
%% \newcommand{\app}{\mathsf{app}}
|
|
\newcommand{\lam}[2]{{\langle}#1{\rangle}#2}
|
|
%\newcommand{\id}{{1}}
|
|
\newcommand{\id}{\mathrm{id}}
|
|
\newcommand{\pp}{{\sf p}}
|
|
\newcommand{\qq}{{\sf q}}
|
|
\newcommand{\comp}{{\sf comp}}
|
|
\newcommand{\hcomp}{{\sf hcomp}}
|
|
\newcommand{\pres}[1]{{\sf pres}^{#1}}
|
|
\newcommand{\extend}{{\sf extend}}
|
|
\newcommand{\eq}{{\sf equiv}}
|
|
|
|
\newcommand{\Comp}{{\sf fill}}
|
|
|
|
% HIT
|
|
\newcommand{\base}{{\sf base}}
|
|
\newcommand{\inc}{{\sf inc}}
|
|
\newcommand{\inh}{\mathsf{inh}}
|
|
\newcommand{\squash}{{\sf squash}}
|
|
\newcommand{\transp}{{\sf transp}} % defined operation on HITs
|
|
\newcommand{\squeeze}{{\sf squeeze}}
|
|
\newcommand{\LOOP}{{\sf loop}}
|
|
\newcommand{\Sp}{{\sf S}}
|
|
|
|
% Universe
|
|
\newcommand{\Glue}{{\sf Glue}}
|
|
\newcommand{\glue}{{\sf glue}}
|
|
\newcommand{\ugl}{{\sf unglue}}
|
|
\newcommand{\U}{\mathsf{U}}
|
|
\DeclareMathOperator{\eqToPath}{\mathsf{eqToPath}}
|
|
\newcommand{\can}{\mathsf{pathToEq}} % "the" canonical map for ua
|
|
|
|
% Semantics
|
|
\newcommand{\Set}{\mathbf{Set}}
|
|
\newcommand{\Top}{\mathbf{Top}}
|
|
\DeclareMathOperator{\sing}{\mathrm{S}}
|
|
\newcommand{\CC}{\mathcal{C}}
|
|
\renewcommand{\deg}{\mathrm{s}}
|
|
\newcommand{\op}{\mathrm{op}}
|
|
% \newcommand{\CdM}{\CC_\dM}
|
|
\DeclareMathOperator{\Hom}{Hom}
|
|
\newcommand{\cwf}{CwF}
|
|
\DeclareMathOperator{\Ty}{Ty}
|
|
\DeclareMathOperator{\FTy}{FTy} % for "fibrant" types
|
|
\DeclareMathOperator{\Ter}{Ter}
|
|
\newcommand{\den}[1]{[\![#1]\!]} % denotation
|
|
\DeclareMathOperator{\yoneda}{\mathbf{y}}
|
|
%\DeclareMathOperator{\scomp}{\mathbf{c}} % semantic composition
|
|
\DeclareMathOperator{\scomp}{\mathtt{comp}} % semantic composition
|
|
\DeclareMathOperator{\sGlue}{\mathtt{Glue}} % semantic Glue
|
|
\DeclareMathOperator{\sglue}{\mathtt{glue}} % semantic glue
|
|
\DeclareMathOperator{\sugl}{\mathtt{unglue}} % semantic unglue
|
|
\newcommand{\sNN}{\mathtt{N}}
|
|
|
|
%\DeclareMathOperator{\sequiv}{\mathbf{e}} % equivalence structure
|
|
\DeclareMathOperator{\sequiv}{\mathtt{e}} % equivalence structure
|
|
|
|
%\newcommand{\sPath}{\Path}
|
|
\newcommand{\sPath}{\mathtt{Path}}
|
|
\newcommand{\spabs}{\langle \, \rangle}
|
|
|
|
\newcommand{\NAT}{\mathbb{N}} % {0,1,2,..}
|
|
\newcommand{\UU}{\mathtt{U}} % semantic universe
|
|
|
|
|
|
\DeclareMathOperator{\app}{\mathtt{app}}
|
|
|
|
|
|
\DeclareMathOperator{\El}{\mathsf{El}}
|
|
\newcommand{\code}[1]{\ulcorner #1 \urcorner}
|
|
|
|
\tikzset{
|
|
comp line/.style={thick,draw=black,decorate, decoration={snake},
|
|
->, >=stealth'},
|
|
path line/.style={thick,draw=black},
|
|
fun line/.style={thick,draw=black, ->, >=stealth'}
|
|
}
|
|
|
|
|
|
\tikzset{
|
|
comp line/.style={thick,draw=black,decorate, decoration={snake},
|
|
->, >=stealth'},
|
|
path line/.style={thick,draw=black},
|
|
fun line/.style={thick,draw=black, ->, >=stealth'}
|
|
}
|
|
|
|
|
|
|
|
%%% Local Variables:
|
|
%%% mode: latex
|
|
%%% TeX-master: "main"
|
|
%%% End:
|