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8194 lines (5210 loc) · 112 KB
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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\begin_document
\begin_header
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% or ...
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% or whatever (possibly just delete it)
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% or whatever (possibly just delete it)
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\end_header
\begin_body
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
This file is a solution template for:
\end_layout
\begin_layout Itemize
Talk at a conference/colloquium.
\end_layout
\begin_layout Itemize
Talk length is about 20min.
\end_layout
\begin_layout Itemize
Style is ornate.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status collapsed
\begin_layout Plain Layout
Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
\end_layout
\begin_layout Plain Layout
In principle, this file can be redistributed and/or modified under the terms
of the GNU Public License, version 2.
However, this file is supposed to be a template to be modified for your
own needs.
For this reason, if you use this file as a template and not specifically
distribute it as part of a another package/program, the author grants the
extra permission to freely copy and modify this file as you see fit and
even to delete this copyright notice.
\end_layout
\end_inset
\end_layout
\begin_layout Title
Generic pattern unification
\end_layout
\begin_layout Author
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Ambroise
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Lafont
\bar default
\begin_inset ERT
status collapsed
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\backslash
and
\end_layout
\end_inset
Neel
\begin_inset space ~
\end_inset
Krishnaswami
\begin_inset Note Note
status collapsed
\begin_layout Itemize
Give the names in the same order as the appear in the paper.
\end_layout
\begin_layout Itemize
Use the
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Institute mark
\begin_inset Quotes erd
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inset (
\family sans
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\bar under
A.
Lafont
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, N.
Krishnaswami
\begin_inset Note Note
status collapsed
\begin_layout Plain Layout
- optional, use only with lots of authors
\end_layout
\begin_layout Plain Layout
- if there are really lots of authors, use
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Author et al.
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University of Cambridge
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status collapsed
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\begin_inset Quotes erd
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Insert\SpecialChar menuseparator
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Keep it simple, no one is interested in your street address.
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University of Cambridge
\begin_inset Note Note
status collapsed
\begin_layout Plain Layout
optional, but mostly needed
\end_layout
\end_inset
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\end_layout
\begin_layout Date
\begin_inset Note Note
status open
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Conference on Fabulous Presentations, 2003
\begin_inset Note Note
status collapsed
\begin_layout Itemize
Either use conference name or its abbreviation.
\end_layout
\begin_layout Itemize
Not really informative to the audience, more for people (including yourself)
who are reading the slides online
\end_layout
\end_inset
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CFP 2003
\begin_inset Note Note
status collapsed
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\begin_layout Standard
\begin_inset FormulaMacro
\newcommand{\pruningstepwise}[1]{\dfrac{\Gamma\prune{\veciflyx{}{t_{1}}}{\veciflyx{}{M_{1}}(\vec{x})}{\sigma_{1}}{\veciflyx{}{u_{1}}}\dashv\Delta_{1}\quad\Delta_{1}\prune{\veciflyx{#1}{t_{2}}[\sigma_{1}]}{\veciflyx{#1}{M_{2}}}{\sigma_{2}\dashv\Delta_{2}}{\veciflyx{#1}{u_{2}}}}{\Gamma\prune{\veciflyx{}{t_{1}},\veciflyx{#1}{t_{2}}}{\veciflyx{}{M_{1}}(\vec{x}),\veciflyx{#1}{M_{2}}}{\sigma_{1}[\sigma_{2}]}{\veciflyx{}{u_{1}}[\sigma_{2}],\veciflyx{#1}{u_{2}}}\dashv\Delta_{2}}}
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
If you have a file called "institution-logo-filename.xxx", where xxx is a
graphic format that can be processed by latex or pdflatex, resp., then you
can add a logo by uncommenting the following:
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset ERT
status open
\begin_layout Plain Layout
%
\backslash
pgfdeclareimage[height=0.5cm]{institution-logo}{institution-logo-filename}
\end_layout
\begin_layout Plain Layout
%
\backslash
logo{
\backslash
pgfuseimage{institution-logo}}
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
The following causes the table of contents to be shown at the beginning
of every subsection.
Delete this, if you do not want it.
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
AtBeginSubsection[]{%
\end_layout
\begin_layout Plain Layout
\backslash
frame<beamer>{
\end_layout
\begin_layout Plain Layout
\backslash
frametitle{Outline}
\end_layout
\begin_layout Plain Layout
\backslash
tableofcontents[currentsection,currentsubsection]
\end_layout
\begin_layout Plain Layout
}
\end_layout
\begin_layout Plain Layout
}
\end_layout
\begin_layout Plain Layout
\backslash
AtBeginSection[]{%
\end_layout
\begin_layout Plain Layout
\backslash
frame<beamer>{
\end_layout
\begin_layout Plain Layout
\backslash
frametitle{Outline}
\end_layout
\begin_layout Plain Layout
\backslash
tableofcontents[currentsection]
\end_layout
\begin_layout Plain Layout
}
\end_layout
\begin_layout Plain Layout
}
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
If you wish to uncover everything in a step-wise fashion, uncomment the
following command:
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset ERT
status open
\begin_layout Plain Layout
%
\backslash
beamerdefaultoverlayspecification{<+->}
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Note Note
status open
\begin_layout Plain Layout
Structuring a talk is a difficult task and the following structure may not
be suitable.
Here are some rules that apply for this solution:
\end_layout
\begin_layout Itemize
Exactly two or three sections (other than the summary).
\end_layout
\begin_layout Itemize
At *most* three subsections per section.
\end_layout
\begin_layout Itemize
Talk about 30s to 2min per frame.
So there should be between about 15 and 30 frames, all told.
\end_layout
\begin_layout Itemize
A conference audience is likely to know very little of what you are going
to talk about.
So *simplify*!
\end_layout
\begin_layout Itemize
In a 20min talk, getting the main ideas across is hard enough.
Leave out details, even if it means being less precise than you think necessary.
\end_layout
\begin_layout Itemize
If you omit details that are vital to the proof/implementation, just say
so once.
Everybody will be happy with that.
\end_layout
\end_inset
\end_layout
\begin_layout Frame
\begin_inset Argument 4
status open
\begin_layout Plain Layout
A quick introduction to unification
\end_layout
\end_inset
\begin_inset Formula
\[
\underbrace{t}\stackrel{?}{=}\underbrace{u}
\]
\end_inset
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
vspace{-1.5em}
\end_layout
\end_inset
\begin_inset Formula
\[
\text{terms with metavariables \ensuremath{M,N,\dots}}
\]
\end_inset
\end_layout
\begin_layout Frame
\end_layout
\begin_deeper
\begin_layout Standard
\series bold
Unifier
\series default
=
\series bold
\series default
metavariable substitution
\begin_inset Formula $\sigma$
\end_inset
s.t.
\begin_inset Formula
\[
t[\sigma]=u[\sigma]
\]
\end_inset
\end_layout
\begin_layout Pause
\end_layout
\begin_layout Standard
\series bold
Most general unifier
\series default
=
\series bold
\series default
unifier
\begin_inset Formula $\sigma$
\end_inset
that uniquely factors any other
\begin_inset Formula
\[
\forall\delta,\qquad t[\delta]=u[\delta]\quad\Leftrightarrow\quad\exists!\delta'.\ \ \delta=\delta'\circ\sigma
\]
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Separator plain
\end_inset
\end_layout
\begin_layout Standard
\align left
\series bold
Goal of unification
\series default
= find the most general unifier
\end_layout
\end_deeper
\begin_layout Standard
\begin_inset Separator plain
\end_inset
\end_layout
\begin_layout Frame
\begin_inset Argument 4
status open
\begin_layout Plain Layout
Where is unification used?
\end_layout
\end_inset