From 6b528d921eba0e1304bfb6a892d45a7d9288d041 Mon Sep 17 00:00:00 2001 From: Francesco Mecca Date: Sun, 5 Apr 2020 20:33:38 +0200 Subject: [PATCH 1/3] more latex for inf rules --- tesi/conv.py | 2 +- tesi/mathpartir.sty | 469 ++++++++++++++++++++++++++++++++++++ tesi/mumble_meeting_gabriel | 2 +- tesi/notations.sty | 36 +++ tesi/tesi.pdf | Bin 384600 -> 445438 bytes tesi/tesi_unicode.org | 265 +++++++++++++++++--- 6 files changed, 735 insertions(+), 39 deletions(-) create mode 100644 tesi/mathpartir.sty create mode 100644 tesi/notations.sty diff --git a/tesi/conv.py b/tesi/conv.py index 20477f4..1f28a56 100644 --- a/tesi/conv.py +++ b/tesi/conv.py @@ -3,7 +3,7 @@ import re from sys import argv allsymbols = json.load(open('./unicode-latex.json')) -mysymbols = ['≡', '≠', '≼', '→', '←', '⊀', '⋠', '≺', '∀', '∈', 'ε','₀', '₂', '₁', '₃', 'ₐ', 'ₖ', 'ₘ', 'ₙ', 'ᵢ', 'ⁱ', '⋮', 'ₛ', 'ₜ', '≃', '⇔', '∧', '∅', 'ℕ', 'ⱼ', 'ʲ', '⊥', 'π', 'α', 'β', '∞', 'σ', '≤', '⊈', '∧', '∨', '∃', '⇒' ] +mysymbols = ['≡', '≠', '≼', '→', '←', '⊀', '⋠', '≺', '∀', '∈', 'ε','₀', '₂', '₁', '₃', 'ₐ', 'ₖ', 'ₘ', 'ₙ', 'ᵢ', 'ⁱ', '⋮', 'ₛ', 'ₜ', '≃', '⇔', '∧', '∅', 'ℕ', 'ⱼ', 'ʲ', '⊥', 'π', 'α', 'β', '∞', 'σ', '≤', '⊈', '∧', '∨', '∃', '⇒', '∩', '∉', '⋃' ] extrasymbols = {'〚': '\llbracket', '〛': '\rrbracket'} symbols = {s: allsymbols[s] for s in mysymbols} diff --git a/tesi/mathpartir.sty b/tesi/mathpartir.sty new file mode 100644 index 0000000..bcd26a1 --- /dev/null +++ b/tesi/mathpartir.sty @@ -0,0 +1,469 @@ +%% +%% This is file `mathpartir.sty', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% mathpartir.dtx (with options: `package') +%% +%% This is a generated file. +%% +%% Copyright (C) 2015, 2020 by Didier Remy +%% +%% This file is part of mathpartir. +%% +%% mathpartir is free software: you can redistribute it and/or modify +%% it under the terms of the GNU General Public License as published by +%% the Free Software Foundation, either version 2 of the License, or +%% (at your option) any later version. +%% +%% mathpartir is distributed in the hope that it will be useful, +%% but WITHOUT ANY WARRANTY; without even the implied warranty of +%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +%% GNU General Public License for more details. +%% +%% You should have received a copy of the GNU General Public License +%% along with mathpartir. If not, see . +%% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{mathpartir} + [2020/02/15 version 1.4.0 Math Paragraph for Typesetting Inference Rules] +%% Identification +%% Preliminary declarations + +\RequirePackage {keyval} + +%% Options +%% More declarations + +%% PART I: Typesetting maths in paragraphe mode + +%% \newdimen \mpr@tmpdim +%% Dimens are a precious ressource. Uses seems to be local. +\let \mpr@tmpdim \@tempdima + +\let \mpr@hva \empty + +%% normal paragraph parametters, should rather be taken dynamically +\def \mpr@savepar {% + \edef \MathparNormalpar + {\noexpand \lineskiplimit \the\lineskiplimit + \noexpand \lineskip \the\lineskip}% + } + +\def \mpr@rulelineskip {\lineskiplimit=0.3em\lineskip=0.2em plus 0.1em} +\def \mpr@lesslineskip {\lineskiplimit=0.6em\lineskip=0.5em plus 0.2em} +\def \mpr@lineskip {\lineskiplimit=1.2em\lineskip=1.2em plus 0.2em} +\let \MathparLineskip \mpr@lineskip +\def \mpr@paroptions {\MathparLineskip} +\let \mpr@prebindings \relax + +\newskip \mpr@andskip \mpr@andskip 2em plus 0.5fil minus 0.5em + +\def \mpr@goodbreakand + {\hskip -\mpr@andskip \penalty -1000\hskip \mpr@andskip} +\def \mpr@and {\hskip \mpr@andskip} +\def \mpr@andcr {\penalty 50\mpr@and} +\def \mpr@cr {\penalty -10000\mpr@and} +\def \mpr@eqno #1{\mpr@andcr #1\hskip 0em plus -1fil \penalty 10} + +\def \mpr@bindings {% + \let \and \mpr@andcr + \let \par \mpr@andcr + \let \\\mpr@cr + \let \eqno \mpr@eqno + \let \hva \mpr@hva + } +\let \MathparBindings \mpr@bindings +\def \MathparBeginhook {} +\def \MathparEndhook {} + +\let \MathparCentering \centering +\newenvironment{mathpar}[1][] + {$$ + \MathparBeginhook + %% We save \lineskip parameters so that the user can restore them + %% inside math \MathparNormalpar + \mpr@savepar + %% We define the shape of the paragrah + \parskip 0em \hsize \linewidth \MathparCentering + \vbox \bgroup \mpr@prebindings \mpr@paroptions #1\ifmmode $\else + \noindent $\displaystyle\fi + \MathparBindings} + {\MathparEndhook \unskip \ifmmode $\fi\egroup $$\ignorespacesafterend} + +\newenvironment{mathparpagebreakable}[1][] + {\begingroup + \par + \mpr@savepar \parskip 0em \hsize \linewidth \centering + \mpr@prebindings \mpr@paroptions #1% + \vskip \abovedisplayskip \vskip -\lineskip% + \ifmmode \else $\displaystyle\fi + \MathparBindings + } + {\unskip + \ifmmode $\fi \par\endgroup + \vskip \belowdisplayskip + \noindent + \ignorespacesafterend} + + +%%% HOV BOXES + +\def \mathvbox@ #1{\hbox \bgroup \mpr@normallineskip + \vbox \bgroup \tabskip 0em \let \\ \cr + \halign \bgroup \hfil $##$\hfil\cr #1\crcr \egroup \egroup + \egroup} + +\def \mathhvbox@ #1{\setbox0 \hbox {\let \\\qquad $#1$}\ifnum \wd0 < \hsize + \box0\else \mathvbox {#1}\fi} + +%% Part II -- operations on lists + +\newtoks \mpr@lista +\newtoks \mpr@listb + +\long \def\mpr@cons #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter +{#2}\edef #2{\the \mpr@lista \the \mpr@listb}} + +\long \def\mpr@snoc #1\mpr@to#2{\mpr@lista {\\{#1}}\mpr@listb \expandafter +{#2}\edef #2{\the \mpr@listb\the\mpr@lista}} + +\long \def \mpr@concat#1=#2\mpr@to#3{\mpr@lista \expandafter {#2}\mpr@listb +\expandafter {#3}\edef #1{\the \mpr@listb\the\mpr@lista}} + +\def \mpr@head #1\mpr@to #2{\expandafter \mpr@head@ #1\mpr@head@ #1#2} +\long \def \mpr@head@ #1#2\mpr@head@ #3#4{\def #4{#1}\def#3{#2}} + +\def \mpr@flatten #1\mpr@to #2{\expandafter \mpr@flatten@ #1\mpr@flatten@ #1#2} +\long \def \mpr@flatten@ \\#1\\#2\mpr@flatten@ #3#4{\def #4{#1}\def #3{\\#2}} + +\def \mpr@makelist #1\mpr@to #2{\def \mpr@all {#1}% + \mpr@lista {\\}\mpr@listb \expandafter {\mpr@all}\edef \mpr@all {\the + \mpr@lista \the \mpr@listb \the \mpr@lista}\let #2\empty + \def \mpr@stripof ##1##2\mpr@stripend{\def \mpr@stripped{##2}}\loop + \mpr@flatten \mpr@all \mpr@to \mpr@one + \expandafter \mpr@snoc \mpr@one \mpr@to #2\expandafter \mpr@stripof + \mpr@all \mpr@stripend + \ifx \mpr@stripped \empty \let \mpr@isempty 0\else \let \mpr@isempty 1\fi + \ifx 1\mpr@isempty + \repeat +} + +\def \mpr@rev #1\mpr@to #2{\let \mpr@tmp \empty + \def \\##1{\mpr@cons ##1\mpr@to \mpr@tmp}#1\let #2\mpr@tmp} + +%% Part III -- Type inference rules + +\newif \if@premisse +\newbox \mpr@hlist +\newbox \mpr@vlist +\newif \ifmpr@center \mpr@centertrue +\def \mpr@vskip {} +\let \mpr@vbox \vbox +\def \mpr@htovlist {% + \setbox \mpr@hlist + \hbox {\strut + \ifmpr@center \hskip -0.5\wd\mpr@hlist\fi + \unhbox \mpr@hlist}% + \setbox \mpr@vlist + \mpr@vbox {\if@premisse + \box \mpr@hlist + \ifx \mpr@vskip \empty \else + \hrule height 0em depth \mpr@vskip width 0em + \fi + \unvbox \mpr@vlist + \else + \unvbox \mpr@vlist + \ifx \mpr@vskip \empty \else + \hrule height 0em depth \mpr@vskip width 0em + \fi + \box \mpr@hlist + \fi}% +} + +\def \mpr@item #1{$\displaystyle #1$} +\def \mpr@sep{2em} +\def \mpr@blank { } +\def \mpr@hovbox #1#2{\hbox + \bgroup + \ifx #1T\@premissetrue + \else \ifx #1B\@premissefalse + \else + \PackageError{mathpartir} + {Premisse orientation should either be T or B} + {Fatal error in Package}% + \fi \fi + \def \@test {#2}\ifx \@test \mpr@blank\else + \setbox \mpr@hlist \hbox {}% + \setbox \mpr@vlist \vbox {}% + \if@premisse \let \snoc \mpr@cons \else \let \snoc \mpr@snoc \fi + \let \@hvlist \empty \let \@rev \empty + \mpr@tmpdim 0em + \expandafter \mpr@makelist #2\mpr@to \mpr@flat + \if@premisse \mpr@rev \mpr@flat \mpr@to \@rev \else \let \@rev \mpr@flat \fi + \def \\##1{% + \def \@test {##1}\ifx \@test \empty + \mpr@htovlist + \mpr@tmpdim 0em %%% last bug fix not extensively checked + \else + \setbox0 \hbox{\mpr@item {##1}}\relax + \advance \mpr@tmpdim by \wd0 + %\mpr@tmpdim 1.02\mpr@tmpdim + \ifnum \mpr@tmpdim < \hsize + \ifnum \wd\mpr@hlist > 0 + \if@premisse + \setbox \mpr@hlist + \hbox {\unhbox0 \hskip \mpr@sep \unhbox \mpr@hlist}% + \else + \setbox \mpr@hlist + \hbox {\unhbox \mpr@hlist \hskip \mpr@sep \unhbox0}% + \fi + \else + \setbox \mpr@hlist \hbox {\unhbox0}% + \fi + \else + \ifnum \wd \mpr@hlist > 0 + \mpr@htovlist + \mpr@tmpdim \wd0 + \fi + \setbox \mpr@hlist \hbox {\unhbox0}% + \fi + \advance \mpr@tmpdim by \mpr@sep + \fi + }% + \@rev + \mpr@htovlist + \ifmpr@center \hskip \wd\mpr@vlist\fi \box \mpr@vlist + \fi + \egroup +} + +%%% INFERENCE RULES + +\@ifundefined{@@over}{% + \let\@@over\over % fallback if amsmath is not loaded + \let\@@overwithdelims\overwithdelims + \let\@@atop\atop \let\@@atopwithdelims\atopwithdelims + \let\@@above\above \let\@@abovewithdelims\abovewithdelims + }{} + +%% The default + +\def \mpr@@fraction #1#2{\hbox {\advance \hsize by -0.5em + $\displaystyle {#1\mpr@over #2}$}} +\def \mpr@@nofraction #1#2{\hbox {\advance \hsize by -0.5em + $\displaystyle {#1\@@atop #2}$}} + +\let \mpr@fraction \mpr@@fraction + +%% A generic solution to arrow + +\def \mpr@@fractionaboveskip {0ex} +\def \mpr@@fractionbelowskip {0.22ex} + +\def \mpr@make@fraction #1#2#3#4#5{\hbox {% + \def \mpr@tail{#1}% + \def \mpr@body{#2}% + \def \mpr@head{#3}% + \setbox1=\hbox{$#4$}\setbox2=\hbox{$#5$}% + \setbox3=\hbox{$\mkern -3mu\mpr@body\mkern -3mu$}% + \dimen0\ht3\advance\dimen0 by \dp3\relax + \dimen0 0.5\dimen0\relax + \advance \dimen0 by \mpr@@fractionaboveskip + \setbox1=\hbox {\raise \dimen0 \box1}\relax + \dimen0 -\dimen0\advance \dimen0 \mpr@@fractionaboveskip\dimen0 -\dimen0 + \advance \dimen0 by \mpr@@fractionbelowskip + \setbox2=\hbox {\lower \dimen0 \box2}\relax + \setbox0=\hbox {$\displaystyle {\box1 \atop \box2}$}% + \dimen0=\wd0\box0 + \box0 \hskip -\dimen0\relax + \hbox to \dimen0 {$%\color{blue} + \mathrel{\mpr@tail}\joinrel + \xleaders\hbox{\copy3}\hfil\joinrel\mathrel{\mpr@head}% + $}}} + +%% Old stuff should be removed in next version +\def \mpr@@nothing #1#2 + {$\lower 0.01pt \mpr@@nofraction {#1}{#2}$} +\def \mpr@@reduce #1#2{\hbox + {$\lower 0.01pt \mpr@@fraction {#1}{#2}\mkern -15mu\rightarrow$}} +\def \mpr@@rewrite #1#2#3{\hbox + {$\lower 0.01pt \mpr@@fraction {#2}{#3}\mkern -8mu#1$}} +\def \mpr@infercenter #1{\vcenter {\mpr@hovbox{T}{#1}}} + +\def \mpr@empty {} +\def \mpr@inferrule + {\bgroup + \ifnum \linewidth<\hsize \hsize \linewidth\fi + \mpr@rulelineskip + \let \and \qquad + \let \hva \mpr@hva + \let \@rulename \mpr@empty + \let \@rule@options \mpr@empty + \let \mpr@over \@@over + \mpr@inferrule@} +\newcommand {\mpr@inferrule@}[3][] + {\everymath={\displaystyle}% + \def \@test {#2}\ifx \empty \@test + \def \@test {#3}\ifx \empty \@test + \PackageWarning {mathpartir} + {\string\inferrule\space empty arguments substituted}{}% + \setbox0 \mpr@fraction {?}{?}% + \else + \setbox0 \hbox {$\vcenter {\mpr@hovbox{B}{#3}}$}% + \fi + \else + \def \@test {#3}\ifx \empty \@test + \setbox0 \hbox {$\vcenter {\mpr@hovbox{T}{#2}}$}% + \else + \setbox0 \mpr@fraction {\mpr@hovbox{T}{#2}}{\mpr@hovbox{B}{#3}}% + \fi \fi + \def \@test {#1}\ifx \@test\empty \box0 + \else \vbox +%%% Suggestion de Francois pour les etiquettes longues +%%% {\hbox to \wd0 {\RefTirName {#1}\hfil}\box0}\fi + {\hbox {\DefTirName {#1}}\box0}\fi + \egroup} + +\def \mpr@vdotfil #1{\vbox to #1{\leaders \hbox{$\cdot$} \vfil}} + + +%% Version for Hoare triples + +\def \triple@hlinebox{\noalign{\setbox0\hbox {}\dp0 0.1ex\ht0 0.1ex\box0}} +\def \triple@hline {\triple@hlinebox\hline\triple@hlinebox} + +\newcommand{\triplerule}[4][] + {\bgroup + \ifnum \linewidth<\hsize \hsize \linewidth\fi + \mpr@rulelineskip + \let \and \qquad + \let \hva \mpr@hva + \setbox0 \hbox {\begin{array}[b]{@{}c@{}} + \mpr@hovbox{T}{#2}\cr\triple@hline + \mpr@hovbox{T}{#3}\cr\triple@hline + \let \mpr@vbox \vtop \ht0 0em + \setbox0 \strut \@tempdima \ht0 + \setbox0 \mpr@hovbox{B}{#4}\advance \@tempdima by -\ht0 + \setbox0 \hbox{\raise \@tempdima \box0}\box0 + \end{array}}% + \def \@test {#1}\ifx \@test\empty \box0 + \else \vbox + %%% Suggestion de Francois pour les etiquettes longues + %%% {\hbox to \wd0 {\RefTirName {#1}\hfil}\box0}\fi + {\hbox {\DefTirName {#1}}\box0}\fi + \egroup} + + +%% Keys that make sence in all kinds of rules +\def \mprset #1{\setkeys{mprset}{#1}} +\define@key {mprset}{andskip}[]{\mpr@andskip=#1} +\define@key {mprset}{lineskip}[]{\lineskip=#1} +\define@key {mprset}{lessskip}[]{\lineskip=0.5\lineskip} +\define@key {mprset}{flushleft}[]{\mpr@centerfalse} +\define@key {mprset}{center}[]{\mpr@centertrue} +\define@key {mprset}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite} +\define@key {mprset}{atop}[]{\let \mpr@fraction \mpr@@nofraction} +\define@key {mprset}{myfraction}[]{\let \mpr@fraction #1} +\define@key {mprset}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}} +\define@key {mprset}{defaultfraction}[]{\let \mpr@fraction \mpr@@fraction} +\define@key {mprset}{sep}{\def\mpr@sep{#1}} +\define@key {mprset}{fractionaboveskip}{\def\mpr@@fractionaboveskip{#1}} +\define@key {mprset}{fractionbelowskip}{\def\mpr@@fractionbelowskip{#1}} +\define@key {mprset}{style}[1]{\def\TirNameStyle{#1}def} +\define@key {mprset}{rightstyle}[1]{\def\RightTirNameStyle{#1}} +\define@key {mprset}{leftstyle}[1]{\def\LeftTirNameStyle{#1}} +\define@key {mprset}{vskip}[1]{\def \mpr@vskip{#1}} + +\newbox \mpr@right +\define@key {mpr}{flushleft}[]{\mpr@centerfalse} +\define@key {mpr}{center}[]{\mpr@centertrue} +\define@key {mpr}{rewrite}[]{\let \mpr@fraction \mpr@@rewrite} +\define@key {mpr}{myfraction}[]{\let \mpr@fraction #1} +\define@key {mpr}{fraction}[]{\def \mpr@fraction {\mpr@make@fraction #1}} +\define@key {mpr}{width}{\hsize #1} +\define@key {mpr}{sep}{\def\mpr@sep{#1}} +\define@key {mpr}{before}{#1} +\define@key {mpr}{lab}{\let \DefTirName \LabTirName \def \mpr@rulename {#1}} +\define@key {mpr}{Lab}{\let \DefTirName \LabTirName \def \mpr@rulename {#1}} +\define@key {mpr}{style}[1]{\def\TirNameStyle{#1}def} +\define@key {mpr}{rightstyle}[1]{\def\RightTirNameStyle{#1}} +\define@key {mpr}{leftstyle}[1]{\def\LeftTirNameStyle{#1}} +\define@key {mpr}{vskip}[1]{\def \mpr@vskip{#1}} +\define@key {mpr}{narrower}{\hsize #1\hsize} +\define@key {mpr}{leftskip}{\hskip -#1} +\define@key {mpr}{reduce}[]{\let \mpr@fraction \mpr@@reduce} +\define@key {mpr}{rightskip} + {\setbox \mpr@right \hbox {\unhbox \mpr@right \hskip -#1}} +\define@key {mpr}{LEFT}{\setbox0 \hbox {$#1$}\relax + \advance \hsize by -\wd0\box0} + +\define@key {mpr}{left}{\setbox0 \hbox {$\LeftTirName {#1}\;$}\relax + \advance \hsize by -\wd0\box0} +\define@key {mpr}{Left}{\llap{$\LeftTirName {#1}\;$}} +\define@key {mpr}{right} + {\setbox0 \hbox {$\;\RightTirName {#1}$}\relax \advance \hsize by -\wd0 + \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}} +\define@key {mpr}{RIGHT} + {\setbox0 \hbox {$#1$}\relax \advance \hsize by -\wd0 + \setbox \mpr@right \hbox {\unhbox \mpr@right \unhbox0}} +\define@key {mpr}{Right} + {\setbox \mpr@right \hbox {\unhbox \mpr@right \rlap {$\;\RightTirName {#1}$}}} +\define@key {mpr}{vdots}{\def \mpr@vdots {\@@atop \mpr@vdotfil{#1}}} +\define@key {mpr}{after}{\edef \mpr@after {\mpr@after #1}} +\define@key {mpr}{vcenter}[]{\mpr@vcentertrue} + +\newif \ifmpr@vcenter \mpr@vcenterfalse +\newcommand \mpr@inferstar@ [3][]{\begingroup + \setbox0 \hbox + {\let \mpr@rulename \mpr@empty \let \mpr@vdots \relax + \setbox \mpr@right \hbox{}% + \setkeys{mpr}{#1}% + $\ifx \mpr@rulename \mpr@empty \mpr@inferrule {#2}{#3}\else + \mpr@inferrule [{\mpr@rulename}]{#2}{#3}\fi + \box \mpr@right \mpr@vdots$ + \ifmpr@vcenter \aftergroup \mpr@vcentertrue \fi} + \ifmpr@vcenter + \box0 + \else + \setbox1 \hbox {\strut} + \@tempdima \dp0 \advance \@tempdima by -\dp1 + \raise \@tempdima \box0 + \fi + \endgroup} + +\def \mpr@infer {\@ifnextchar *{\mpr@inferstar}{\mpr@inferrule}} +\newcommand \mpr@err@skipargs[3][]{} +\def \mpr@inferstar*{\ifmmode + \let \@do \mpr@inferstar@ + \else + \let \@do \mpr@err@skipargs + \PackageError {mathpartir} + {\string\inferrule* can only be used in math mode}{}% + \fi \@do} + +%%% Exports + + +\let \inferrule \mpr@infer + +\@ifundefined {infer}{\let \infer \mpr@infer}{} + +\def \TirNameStyle #1{\small \textsc{#1}} +\def \LeftTirNameStyle #1{\TirNameStyle {#1}} +\def \RightTirNameStyle #1{\TirNameStyle {#1}} + +\def \lefttir@name #1{\hbox {\small \LeftTirNameStyle{#1}}} +\def \righttir@name #1{\hbox {\small \RightTirNameStyle{#1}}} +\let \TirName \lefttir@name +\let \LeftTirName \lefttir@name +\let \DefTirName \lefttir@name +\let \LabTirName \lefttir@name +\let \RightTirName \righttir@name + +%%% Other Exports + +\endinput +%% +%% End of file `mathpartir.sty'. diff --git a/tesi/mumble_meeting_gabriel b/tesi/mumble_meeting_gabriel index 3436c00..d299e58 100644 --- a/tesi/mumble_meeting_gabriel +++ b/tesi/mumble_meeting_gabriel @@ -12,7 +12,7 @@ Test(S,true) = Yes ------------------------------- -equiv \emptyset Cs Ct gs ~> Yes +equiv \emptyset Cs Ct gs \to Yes ----------------------------------------- equiv S Failure (Leaf BBt) gs ~>No(vs, vt) diff --git a/tesi/notations.sty b/tesi/notations.sty new file mode 100644 index 0000000..a7c051c --- /dev/null +++ b/tesi/notations.sty @@ -0,0 +1,36 @@ +\newcommand{\bnfeq}{\mathrel{::=}\;} +\newcommand{\bnfor}{\mathrel{\vert}} + +\newcommand{\paramrel}[3]{#2 \mathrel{\approx_{#1}} #3} +\newcommand{\vrel}[2]{\paramrel{\mathsf{val}}{#1}{#2}} +\newcommand{\trel}[2]{\paramrel{\mathsf{term}}{#1}{#2}} + +\newcommand{\sem}[1]{{\llbracket{#1}\rrbracket}} + +\newcommand{\Fam}[2]{{(#2)}^{#1}} + +\newcommand{\match}[2]{\mathtt{match}(#1,#2)} + +\newcommand{\var}[1]{\mathtt{#1}} +\newcommand{\pK}{\mathtt{K}} +\newcommand{\any}{\mathtt{\_}} + +% \equiv is already taken +\newcommand{\Equiv}[4]{\mathsf{equiv}(#1, #2, #3, #4)} +\newcommand{\Equivrel}[4]{#1 \vdash_{#4} #2 \approx #3} + +\newcommand{\covers}[2]{#1 \mathrel{\mathsf{covers}} #2} + +\newcommand{\Yes}{\mathsf{Yes}} +\newcommand{\No}[2]{\mathsf{No}(#1, #2)} + +\newcommand{\Leaf}[1]{\mathsf{Leaf}(#1)} +\newcommand{\Failure}{\mathsf{Failure}} +\newcommand{\Switch}[3]{\mathsf{Switch}(#1, #2, #3)} +\newcommand{\Guard}[3]{\mathsf{Guard}(#1, #2, #3)} + +\newcommand{\emptyqueue}{\mathord{[]}} + +\newcommand{\Cfb}{C_{\mathsf{fb}}} + +\newcommand{\trim}[2]{\mathsf{trim}(#1, #2)} \ No newline at end of file diff --git a/tesi/tesi.pdf b/tesi/tesi.pdf index 7089d0d15c5445f1bd7446f06e6846d6b64e429b..cc26d50541b0ed2c59d2955ccf660b04dde5b811 100644 GIT binary patch delta 305185 zcmZU(Q=29Vu%uhIZQHhO+qUhmY}@RzZQE9tZJRx7@0qJ}t}_2XWV}yCZ1iCMX5c20 zg0OOD0AqmA05oM2wm6Xb&NR=dfE#6^eY7BS3hA>8#R((WeWXLeG>Yv>lFyTu>M$n~ 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