docs: reference Lars' metric space paper

docs/algebra.tex

@@ -2,7 +2,9 @@
 
 \subsection{COFE}
 
+The model of Iris lives in the category of \emph{Complete Ordered Families of Equivalences} (COFEs).
 This definition varies slightly from the original one in~\cite{catlogic}.
+
 \begin{defn}[Chain]
   Given some set $\cofe$ and an indexed family $({\nequiv{n}} \subseteq \cofe \times \cofe)_{n \in \mathbb{N}}$ of equivalence relations, a \emph{chain} is a function $c : \mathbb{N} \to \cofe$ such that $\All n, m. n \leq m \Ra c (m) \nequiv{n} c (n)$.
 \end{defn}

docs/bib.bib

@@ -3577,3 +3577,118 @@ year = {2013}
 	note       = {Available at \url{http://users-cs.au.dk/birke/modures/tutorial/categorical-logic-tutorial-notes.pdf}}
 }
 
+@article{dodds:higher-order-sync,
+  author    = {Mike Dodds and
+               Suresh Jagannathan and
+               Matthew J. Parkinson and
+               Kasper Svendsen and
+               Lars Birkedal},
+  title     = {Verifying Custom Synchronization Constructs Using Higher-Order Separation
+               Logic},
+  journal   = {{ACM} Trans. Program. Lang. Syst.},
+  volume    = {38},
+  number    = {2},
+  pages     = {4},
+  year      = {2016},
+  url       = {http://doi.acm.org/10.1145/2818638},
+  doi       = {10.1145/2818638},
+  timestamp = {Fri, 29 Jan 2016 12:43:32 +0100},
+  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/toplas/DoddsJPSB16},
+  bibsource = {dblp computer science bibliography, http://dblp.org}
+}
+
+@inproceedings{iris,
+  author    = {Ralf Jung and
+               David Swasey and
+               Filip Sieczkowski and
+               Kasper Svendsen and
+               Aaron Turon and
+               Lars Birkedal and
+               Derek Dreyer},
+  title     = {Iris: Monoids and Invariants as an Orthogonal Basis for Concurrent
+               Reasoning},
+  booktitle = {POPL},
+  pages     = {637--650},
+  year      = {2015},
+}
+
+@phdthesis{krebbers:phd,
+  author      = {Robbert Krebbers},
+  title       = "{The C standard formalized in Coq}",
+  year        = {2015},
+  school      = {Radboud University},
+}
+
+@inproceedings{garillot:gonthier:mahboubi:rideau:09,
+  author    = {Fran{\c{c}}ois Garillot and
+               Georges Gonthier and
+               Assia Mahboubi and
+               Laurence Rideau},
+  title     = "{Packaging Mathematical Structures}",
+  booktitle = {TPHOLs},
+  pages     = {327--342},
+  series    = {LNCS},
+  volume    = {5674},
+  year      = {2009},
+}
+
+@article{spitters:weegen:11,
+  author    = {Bas Spitters and Eelis van der Weegen},
+  title     = "{Type classes for mathematics in type theory}",
+  journal   = {MSCS},
+  volume    = {21},
+  number    = {4},
+  pages     = {795--825},
+  year      = {2011},
+}
+
+@article{sozeau:09,
+  author    = {Matthieu Sozeau},
+  title     = "{A New Look at Generalized Rewriting in Type Theory}",
+  journal   = {Journal of Formalized Reasoning},
+  volume    = {2},
+  number    = {1},
+  pages     = {41--62},
+  year      = {2009},
+}
+
+@InProceedings{malecha:esop2016,
+  author = 	 {Gregory Malecha and Jesper Bengtson},
+  title =     {Easy and efficient automation through reflective tactics},
+  booktitle =	 {ESOP},
+  year =	 2016,
+}
+
+@inproceedings{gps,
+  author    = {Aaron Turon and
+               Viktor Vafeiadis and
+               Derek Dreyer},
+  title     = {{GPS:} navigating weak memory with ghosts, protocols, and separation},
+  booktitle = {Proceedings of the 2014 {ACM} International Conference on Object Oriented
+               Programming Systems Languages {\&} Applications, {OOPSLA} 2014,
+               part of {SPLASH} 2014, Portland, OR, USA, October 20-24, 2014},
+  pages     = {691--707},
+  year      = {2014},
+  url       = {http://doi.acm.org/10.1145/2660193.2660243},
+  doi       = {10.1145/2660193.2660243},
+  timestamp = {Thu, 16 Oct 2014 09:16:18 +0200},
+  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/oopsla/TuronVD14},
+  bibsource = {dblp computer science bibliography, http://dblp.org}
+}
+
+@article{birkedal:metric-space,
+  author    = {Lars Birkedal and
+               Kristian St{\o}vring and
+               Jacob Thamsborg},
+  title     = {The category-theoretic solution of recursive metric-space equations},
+  journal   = {Theor. Comput. Sci.},
+  volume    = {411},
+  number    = {47},
+  pages     = {4102--4122},
+  year      = {2010},
+  url       = {http://dx.doi.org/10.1016/j.tcs.2010.07.010},
+  doi       = {10.1016/j.tcs.2010.07.010},
+  timestamp = {Tue, 07 Dec 2010 16:23:22 +0100},
+  biburl    = {http://dblp.uni-trier.de/rec/bib/journals/tcs/BirkedalST10},
+  bibsource = {dblp computer science bibliography, http://dblp.org}
+}

docs/iris.sty

@@ -36,7 +36,7 @@
 \newcommand{\upclose}{\mathord{\uparrow}}
 \newcommand{\ALT}{\ |\ }
 
-\newcommand{\spac}{\;} % a space
+\newcommand{\spac}{\,} % a space
 
 \def\All #1.{\forall #1.\spac}%
 \def\Exists #1.{\exists #1.\spac}%
@@ -292,6 +292,7 @@
 
 %% Some commonly used identifiers
 \newcommand{\timeless}[1]{\textlog{timeless}(#1)}
+\newcommand{\persistent}[1]{\textlog{persistent}(#1)}
 \newcommand{\physatomic}[1]{\textlog{atomic}($#1$)}
 \newcommand{\infinite}{\textlog{infinite}}
 
@@ -362,7 +363,7 @@
 \tikzstyle{sts_arrows} = [arrows={->[scale=1.5]},every node/.style={font=\sffamily\small}]
 
 %% Stored Propositions
-\newcommand{\mapstoprop}{\mathrel{\mapstochar\Ra}}
+\newcommand{\mapstoprop}{\mathrel{\kern-0.5ex\tikz[baseline=(m)]{\node at (0,0) (m){}; \draw[line cap=round] (0,0.16) -- (0,-0.004);}\kern-1.5ex\Ra}}
 
 
 \endinput

docs/model.tex

@@ -60,7 +60,7 @@ Furthermore, if $F$ is locally contractive, then so is $\textdom{ResF}(-)$.
 
 Now we can write down the recursive domain equation:
 \[ \iPreProp \cong \UPred(\textdom{ResF}(\iPreProp)) \]
-$\iPreProp$ is a COFE, which exists by America and Rutten's theorem~\cite{America-Rutten:JCSS89}.
+$\iPreProp$ is a COFE, which exists by America and Rutten's theorem~\cite{America-Rutten:JCSS89,birkedal:metric-space}.
 We do not need to consider how the object is constructed. 
 We only need the isomorphism, given by
 \begin{align*}