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mirror of https://github.com/dhil/phd-dissertation synced 2026-03-13 02:58:26 +00:00
This commit is contained in:
2021-05-04 23:00:40 +01:00
parent fc0c6a98bb
commit d6b67950b2
3 changed files with 3568 additions and 49 deletions

View File

@@ -235,6 +235,7 @@
\newcommand{\concat}{\mathbin{+\!\!+}}
\newcommand{\revconcat}{\mathbin{\widehat{\concat}}}
\newcommand{\snoc}[2]{\ensuremath{#1 \concat [#2]}}
%%
%% CPS notation
@@ -540,4 +541,96 @@
edge from parent node[above right] {$\res{\False}$}
}
;
\end{tikzpicture}}
\end{tikzpicture}}
%%
%% Asymptotic improvement macros
%%
\newcommand{\naive}{naïve\xspace}
\newcommand{\naively}{naïvely\xspace}
\newcommand{\Naive}{Naïve\xspace}
\newcommand{\sem}[1]{\ensuremath{\pi_{#1}}}
\newcommand{\Iff}{\Leftrightarrow}
\newcommand{\Implies}{\Rightarrow}
\newcommand{\BCalcS}{\ensuremath{\lambda_{\textrm{\normalfont s}}\xspace}}
\newcommand{\BCalcE}{\ensuremath{\lambda_{\textrm{\normalfont e}}\xspace}}
\newcommand{\BCalcSE}{\ensuremath{\lambda_{\textrm{\normalfont se}}\xspace}}
\newcommand{\IfZero}{\keyw{ifzero}}
\newcommand{\Superpoint}{\lambda\_.\Do\;\Branch~\Unit}
\newcommand{\ECount}{\dec{effcount}}
\newcommand{\Countprog}{K}
\newcommand{\Plus}{\mathsf{Plus}}
\newcommand{\Minus}{\mathsf{Minus}}
\newcommand{\Eq}{\mathsf{Eq}}
\newcommand{\BList}{\mathbb{B}^\ast}
\newcommand{\CtxCat}{\CatName{Ctx}}
\newcommand{\PureCont}{\mathsf{PureCont}}
\newcommand{\Addr}{\mathsf{Addr}}
\newcommand{\Lab}{\mathsf{Lab}}
\newcommand{\Env}{\mathsf{Env}}
\newcommand{\Time}{\dec{DTIME}}
\newcommand{\query}{\mathord{?}}
\newcommand{\ans}{\mathord{!}}
\newcommand{\labs}{\mathsf{labs}}
\newcommand{\steps}{\mathsf{steps}}
\newcommand{\tree}{\tau}
\newcommand{\tl}{\labs(\tree)}
\newcommand{\ts}{\steps(\tree)}
\newcommand{\T}[1]{\ensuremath{\mathcal{T}_{#1}}}
\newcommand{\Config}{\dec{Config}}
\newcommand{\cekl}{\langle}
\newcommand{\cekr}{\rangle}
\newcommand{\const}[1]{\ulcorner #1 \urcorner}
\newcommand{\HC}{\ensuremath{\mathcal{H}}}
\newcommand{\tr}{\mathcal{T}}
\newcommand{\tru}{\mathcal{U}}
\newcommand{\Tree}{\dec{Tree}}
\newcommand{\TimedTree}{\dec{TimedTree}}
\newcommand{\denotep}[1]{\ensuremath{\mathbb{P}\llbracket #1 \rrbracket}}
\newcommand\ttTwoTree{
\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 4cm/##1,
level distance = 2.0cm}]
\node (root) [opnode] {Branch}
child { node [opnode] {Branch}
child { node [leaf] {$\True$}
edge from parent node[above left] {$\True$}
}
child { node [leaf] {$\True$}
edge from parent node[above right] {$\False$}
}
edge from parent node[above left] {$\True$}
}
child { node [opnode] {Branch}
child { node [leaf] {$\True$}
edge from parent node[above left] {$\True$}
}
child { node [leaf] {$\True$}
edge from parent node[above right] {$\False$}
}
edge from parent node[above right] {$\False$}
}
;
\end{tikzpicture}}
\newcommand{\tossTree}{
\begin{tikzpicture}[->,>=stealth',level/.style={sibling distance = 2.5cm/##1,
level distance = 1.0cm}]
\node (root) [opnode] {$\dec{Branch}$}
child { node [leaf] {$\dec{Heads}$}
edge from parent node[above left] {$\True$}
}
child { node [leaf] {$\dec{Tails}$}
edge from parent node[above right] {$\False$}
}
;
\end{tikzpicture}}
\newenvironment{twoeqs}{\ba[t]{@{}r@{~}c@{~}l@{~}c@{~}r@{~}c@{~}l@{}}}{\ea}