From 555edbc61004ff4cacf36c10a7cfd7f4d1234bcd Mon Sep 17 00:00:00 2001 From: Hans-Joerg Schurr <commits@schurr.at> Date: Thu, 15 Jul 2021 14:18:59 +0200 Subject: [PATCH] Add source code for pxtp21 slides --- .gitignore | 5 + talks/pxtp21/Makefile | 8 + talks/pxtp21/alethe.png | Bin 0 -> 380898 bytes talks/pxtp21/skeleton.png | Bin 0 -> 676300 bytes talks/pxtp21/smtlib2.py | 119 +++++++++++++ talks/pxtp21/talk.tex | 348 ++++++++++++++++++++++++++++++++++++++ 6 files changed, 480 insertions(+) create mode 100644 talks/pxtp21/Makefile create mode 100644 talks/pxtp21/alethe.png create mode 100644 talks/pxtp21/skeleton.png create mode 100644 talks/pxtp21/smtlib2.py create mode 100644 talks/pxtp21/talk.tex diff --git a/.gitignore b/.gitignore index face61d..48f1eed 100644 --- a/.gitignore +++ b/.gitignore @@ -10,3 +10,8 @@ _minted-*/ *.pag *.toc *.pyg +*.vrb +*.snm +*.run.xml +*.nav +*.bcf diff --git a/talks/pxtp21/Makefile b/talks/pxtp21/Makefile new file mode 100644 index 0000000..343e826 --- /dev/null +++ b/talks/pxtp21/Makefile @@ -0,0 +1,8 @@ +.PHONY: clean pngslides all + +all: + latexmk -shell-escape -pdflatex=lualatex -pdf talk + +pngslides: + mkdir -p pngslides + pdftocairo talk.pdf pngslides/talk -png -transp -scale-to-x 1920 -scale-to-y 1080 diff --git a/talks/pxtp21/alethe.png b/talks/pxtp21/alethe.png new file mode 100644 index 0000000000000000000000000000000000000000..e912cf133a1608d90ea8a91d0bd60ee23e706569 GIT binary patch literal 380898 zcmYIvby$>J`!ygc-O_@Lbf?nYU4wvhcXvzo&<&$B14s!-gS2!@cXu~@kH2%y`~5L- z4P4L6v-chAUTf_LWko4;6k-%OI5>0}X>nCJID|>y0f+Po_#`**z8`o&c97O`hJ#~% z|Mvm!Q6S_72loz6MqEVQWA313Hj#4Hwdgu~U+y5@+iX)6tOeGcirKTf2n>N^%OVOO zcHlO{BR4r`9U+#<l5!jrPq%#fGS(TLevu#F^-*AyasojWQ94e{2#Ir47yW}*`QBXW zLTcY&-yi;kM>2t*-X<n)Z$>xb@cLSz>6udEk{&iwwovHJqH{3RnRj0(0qRM^l@|pP zwY`;#>|Ax=CdCNrJpCB((A-)%d<PL1@6j(R-Yc2O(tpjBvHa=FS~ae9*gyZ*Ypzs0 zue5{(NA!ZVTSNL%x=`dCrS=Ur>K`2#7l94UG;pQA7mOVVRj!9NQ%q~acM+}=8S`VG 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b/talks/pxtp21/smtlib2.py new file mode 100644 index 0000000..862a2a3 --- /dev/null +++ b/talks/pxtp21/smtlib2.py @@ -0,0 +1,119 @@ +# -*- coding: utf-8 -*- + +import re + +from pygments.lexer import Lexer, RegexLexer, bygroups, do_insertions, \ + default, include +from pygments.token import Text, Comment, Operator, Keyword, Name, String, \ + Number, Punctuation, Generic +from pygments import unistring as uni + +__all__ = ['Smt2Lexer'] + + +line_re = re.compile('.*?\n') + +class CustomLexer(RegexLexer): + """ + A SMT-Lib 2 parser + """ + name = 'Smt2' + aliases = ['smt2'] + filenames = ['*.smt2'] + mimetypes = ['text/x-smt2'] + + # list of known keywords and builtins taken form vim 6.4 scheme.vim + # syntax file. + keywords = ( + 'declare-const', 'declare-fun', 'declare-sort', 'define-fun', 'assert', 'check-sat', + 'get-model', 'get-proof', 'get-value', 'echo', 'exit', 'error', + 'sat', 'unsat', 'unknown', 'model', 'set-option', 'set-logic', + 'anchor', 'step', 'assume' + ) + sorts = ( + 'Int', 'Bool' + ) + builtins = ( + '*', '+', '-', '/', '<', '<=', '=', '>', '>=', 'and', 'or', 'distinct', + 'not', ':=', 'forall', 'exists', 'cl' + ) + + # valid names for identifiers + # well, names can only not consist fully of numbers + # but this should be good enough for now + valid_name = r'[\w\.!$%&*+,/:<=>?@^~|-]+' + + tokens = { + 'root': [ + # the comments + # and going to the end of the line + (r';.*$', Comment.Single), + # multi-line comment + (r'#\|', Comment.Multiline, 'multiline-comment'), + # commented form (entire sexpr folliwng) + (r'#;\s*\(', Comment, 'commented-form'), + # signifies that the program text that follows is written with the + # lexical and datum syntax described in r6rs + (r'#!r6rs', Comment), + + # whitespaces - usually not relevant + (r'\s+', Text), + + # numbers + (r'-?\d+\.\d+', Number.Float), + (r'-?\d+', Number.Integer), + # support for uncommon kinds of numbers - + # have to figure out what the characters mean + # (r'(#e|#i|#b|#o|#d|#x)[\d.]+', Number), + + # strings, symbols and characters + (r'"(\\\\|\\"|[^"])*"', String), + (r"'" + valid_name, String.Symbol), + (r"#\\([()/'\"._!§$%& ?=+-]|[a-zA-Z0-9]+)", String.Char), + + # constants + (r'(true|false)', Name.Constant), + + # special operators + (r"('|#|`|,@|,)", Operator), + + # highlight the keywords + ('(%s)' % '|'.join(re.escape(entry) for entry in keywords), + Keyword.Reserved), + + # highlight the sorts + ('(%s)' % '|'.join(re.escape(entry) for entry in sorts), + Keyword.Type), + + # first variable in a quoted string like + # '(this is syntactic sugar) + (r"(?<='\()" + valid_name, Name.Variable), + (r"(?<=#\()" + valid_name, Name.Variable), + + # highlight the builtins + ("(?<=\()(%s)" % '|'.join(re.escape(entry) + '\s+' for entry in builtins), + Name.Builtin), + + (r':' + valid_name, Name.Function), + + # the remaining functions + #(r'(?<=\()' + valid_name, Name.Function), + # find the remaining variables + (valid_name, Name.Variable), + + # the famous parentheses! + (r'(\(|\))', Punctuation), + (r'(\[|\])', Punctuation), + ], + 'multiline-comment': [ + (r'#\|', Comment.Multiline, '#push'), + (r'\|#', Comment.Multiline, '#pop'), + (r'[^|#]+', Comment.Multiline), + (r'[|#]', Comment.Multiline), + ], + 'commented-form': [ + (r'\(', Comment, '#push'), + (r'\)', Comment, '#pop'), + (r'[^()]+', Comment), + ], + } diff --git a/talks/pxtp21/talk.tex b/talks/pxtp21/talk.tex new file mode 100644 index 0000000..1739efd --- /dev/null +++ b/talks/pxtp21/talk.tex @@ -0,0 +1,348 @@ +\documentclass[aspectratio=169,compress]{beamer} + +\usepackage[utf8]{inputenc} +\usepackage{listings} +\usepackage{minted} +\usepackage{microtype} +\usepackage{amssymb} +\usepackage{tikz} +\usepackage{textcomp} +\usepackage[makeroom]{cancel} +\usepackage[most]{tcolorbox} +\usepackage{emoji} +\usepackage{booktabs} + +\usepackage{bussproofs} +\EnableBpAbbreviations +\def\ScoreOverhang{1.5pt} +\def\proofSkipAmount{\vskip 0pt} +\def\defaultHypSeparation{\hskip0.75em} + +% == Bibtex Setup == +\usepackage[backend=biber,style=authoryear,maxcitenames=1,sorting=none]{biblatex} +\addbibresource{bib.bib} + +% == Minted Setup == +\usemintedstyle{trac} + +% == Beamer Setup == +\usecolortheme{rose} +\usefonttheme{metropolis} +\beamertemplatenavigationsymbolsempty +\setbeamertemplate{footline}[frame number] +\setbeamercovered{transparent} +\usebackgroundtemplate{} + +% == Commands Setup == +\newcommand\Refl{\textsc{Refl}} +\newcommand\Taut{\textsc{Taut}} +\newcommand\Tautof[1]{\Taut\smash{\ensuremath{_{#1}}}} +\newcommand\TautT{\Tautof{\T}} +\newcommand\Trans{\textsc{Trans}} +\newcommand\Cong{\textsc{Cong}} +\newcommand\Bind{\textsc{Bind}} +\newcommand\Sko{\textsc{Sko}} +\newcommand\SkoEx{\Sko\smash{\ensuremath{_{\,\exists}}}} +\newcommand\SkoAll{\Sko\smash{\ensuremath{_{\,\forall}}}} +\newcommand\Let{\textsc{Let}} +\newcommand\OnePoint{\textsc{1Pt}} +\newcommand\OnePointEx{\OnePoint\smash{\ensuremath{_{\,\exists}}}} +\newcommand\OnePointAll{\OnePoint\smash{\ensuremath{_{\,\forall}}}} + +\newcommand\vvthinspace{\kern+0.041667em} +\newcommand\vthinspace{\kern+0.083333em} +\newcommand\negvthinspace{\kern-0.083333em} +\newcommand\negvvthinspace{\kern-0.041667em} + +\newcommand\All[2]{\forall #1.\;#2} +\newcommand\Ex[2]{\exists #1.\;#2} +\newcommand\Choicename{\varepsilon} +\newcommand\Choice[2]{\Choicename #1.\>#2} +\newcommand\judgei[1]{{\vartriangleright}\;#1} +\newcommand\judge[2]{#1\;\vthinspace{\vartriangleright}\;#2} +\newcommand\judgealti[1]{{\blacktriangleright}\;#1} +\newcommand\judgealt[2]{#1\;\vthinspace{\blacktriangleright}\;#2} +\newcommand\Not{{\lnot}\,} +\newcommand\limp{\rightarrow} + +\newcommand\axiomstrut{\vrule height 1.25ex depth 0pt width 0pt} %% TYPESETTING + +% Common Abbreviations +\newcommand\smtlib{SMT-LIB} + +\title{Alethe: Towards a Generic SMT Proof Format} +\subtitle{PxTP 2021} +\author{ +\textbf{Hans-Jörg Schurr}\inst{1}, +Mathias Fleury\inst{2}, +Haniel Barbosa\inst{3}, +Pascal Fontaine\inst{4} +} + +\institute{ + \inst{1}University of Lorraine, CNRS, Inria, and LORIA\and + \inst{2}Johannes Kepler University Linz, Austria\and + \inst{3}Universidade Federal de Minas Gerais, Belo Horizonte, Brazil\and + \inst{4}Universit\'{e} de Liège +} + +\tcbset{on line, + boxsep=0pt, left=0pt,right=0pt,top=0pt,bottom=0pt, + colframe=white,colback=orange!30, + highlight math style={enhanced} +} + +\date{July 11, 2021} + +\begin{document} + +\frame{\titlepage} + +\note[itemize]{ + \item Say this is an effort that emerged over the last few month + \item Mention other people are also involved + \item Clarify for SMT! +} + +\begin{frame}{Some History} +\begin{columns} + \begin{column}{0.5\textwidth} + \begin{block}{Within \raisebox{-0.21\height}{\includegraphics[scale=.12]{veritlogo}}} + \begin{itemize} + \item First: Ad-hoc (\emoji{scroll} TACAS 2006) + \item Later: Redesigned (\emoji{scroll} PxTP 2011) + \item Syntax changed over time + \end{itemize} + \end{block} + \pause + \begin{block}{SMTCoq} + \begin{itemize} + \item One of the first users + \item Verified checker (\emoji{scroll} CPP 2011) + \item Base for automation in Coq\\ (\emoji{scroll} CAV 2017, PxTP -3h20) + \end{itemize} + \end{block} + \end{column} + \begin{column}{0.5\textwidth} + \pause + \begin{block}{Fine-Grained Proofs and Isabelle} + \begin{itemize} + \item Support for reasoning with bound variables (\emoji{scroll} CADE 2017, JAR 2020) + \item Typical for pre-processing in SMT + \item Isabelle/HOL integration\\ (\emoji{scroll} CADE +49h40) + \end{itemize} + \end{block} + \pause + \begin{block}{Now!} + \begin{itemize} + \item[\emoji{skull}] Proofonomicon + \item[\emoji{angel}] Speculative Specification + \item[\emoji{feather}] It's now Alethe! (\emoji{scroll} PxTP -0h05) + \end{itemize} + \end{block} + + \end{column} + +\end{columns} +\end{frame} + +\note[itemize]{ + \item Say that it's not very scientific and that I probably miss some things + \item Mention other people are also involved: + \begin{itemize} + \item Frédéric Besson and Laurent Théry, + \item David Déharbe and Bruno Woltzenlogel Paleo + \end{itemize} + \item Clarify for SMT! +} + +\begin{frame}[label=bird,plain] + \begin{center} + \includegraphics[scale=1.6]{alethe} + \end{center} +\end{frame} + +\begin{frame}[plain] + \begin{center} + \includegraphics[scale=0.25]{skeleton} + \end{center} +\end{frame} + +\begin{frame}[fragile]{Basic Structur} + \begin{columns} + \begin{column}{0.4\textwidth} +{\Large +\[ + \AXC{$t_1$} + \AXC{$t_2$} + \UIC{$t_3$} + \noLine + \UIC{$\vdots$} + \noLine + \UIC{$\neg t_1$} + \RightLabel{\normalsize\texttt{resolution}} + \BIC{ + $\bot$ + } + \DP +\] +} + \end{column} + \begin{column}{0.6\textwidth} + \begin{center} +\begin{minted}[fontsize=\footnotesize]{smtlib2.py -x} +(assume a0 t1) +(assume a1 t2) +(step s1 (cl t3) + :premises (a1) :rule rule1) + ... +(step s20 (cl (not t1)) + :premises (s19) :rule rule2) +(step s21 (cl ) + :premises (a0 s20) :rule resolution) + +\end{minted} + + \end{center} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}[fragile]{Subproofs With Assumptions} + \begin{columns} + \begin{column}{0.4\textwidth} +{\Large +\[ + \AXC{$t_1$} + \UIC{$t_2$} + \AXC{$[t_2]$} + \noLine + \UIC{$\vdots$} + \noLine + \UIC{$t_3$} + \RightLabel{\normalsize\texttt{subproof}} + \UIC{$\neg t_2, t_3$} + \RightLabel{\normalsize\texttt{resolution}} + \BIC{ + $t_3$ + } + \DP +\] +} + \end{column} + \begin{column}{0.6\textwidth} + \begin{center} +\begin{minted}[fontsize=\footnotesize]{smtlib2.py -x} +(assume a0 t1) +(step s1 (cl t2) + :premises (a0) :rule rule1) +(anchor :step s2) + (assume s2.a1 t2) + ... + (step s2.s10 (cl t3) + :premises (s2.s9) :rule rule2) +(step s2 (cl (not t2) t3) :rule subproof) +(step s3 (cl t3) + :premises (s1 s2) :rule resolution) +\end{minted} + \end{center} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}[fragile]{Reasoning With Binders} + \begin{columns} + \begin{column}{0.4\textwidth} +%\newcommand\judge[2]{#1\;\vthinspace{\vartriangleright}\;#2} +{\Large +\[ + \AX$\fCenter$ + \RightLabel{\normalsize\texttt{refl}} + \UI$x\mapsto y\;\vthinspace{\vartriangleright}\;\fCenter x=y$ + \RightLabel{\normalsize\texttt{cong}} + \UI$x\mapsto y\;\vthinspace{\vartriangleright}\;\fCenter f(x)=f(y)$ + \RightLabel{\normalsize\texttt{bind}} + \UI$\All{x}{f(x)}\fCenter\;=\All{y}{f(y)}$ + \DP +\] +} + \end{column} + \begin{column}{0.6\textwidth} + \begin{center} +\begin{minted}[fontsize=\footnotesize]{smtlib2.py -x} +(anchor :step s2 :args ((:= (x S) y))) + (step s2.s1 (cl (= x y)) :rule refl) + (step s2.s2 (cl (= (f x) (f y))) + :rule cong) +(step s2 (cl (= (forall ((x S)) (f x)) + (forall ((y S)) (f y))) + :rule bind) +\end{minted} + \end{center} + \end{column} + \end{columns} +\end{frame} + +\againframe{bird} + +\begin{frame}{Rules} + \begin{block}{Current State} + \begin{itemize} + \item Overall 90 rules, mostly simple tautologies + \item Seven categories -- with overlaps + \item Some historic overhead + \item[\emoji{building-construction}] Cleanup and normalization + \end{itemize} + \end{block} + \pause + \begin{block}{How can we accommodate different solvers?} + \begin{itemize} + \item Some solvers might be able to use rules more strictly. + \item Example: + \begin{itemize} + \item $a = b \land b = c\limp a = c$ + \item $c = b \land a = b\limp a = c$ + \end{itemize} + \item[\emoji{light-bulb}] Have an optional annotation to mark restricted usage. + \end{itemize} + \end{block} +\end{frame} + +\begin{frame}{Tools} + \begin{block}{A Checker and Elaborator} + \begin{itemize} + \item ``A second pair of eyes". + \item Small, independent codebase -- in Rust. + \item Long term: rewrite steps to their stricter form, framework + to replace non-standard rules by standard rules. + \item[\emoji{man}] Bruno Andreotti + \end{itemize} + \end{block} + \pause + \begin{block}{Support in \emph{cvc5}} + \begin{itemize} + \item Part of a wider effort to overhaul the proof module of \emph{cvc5}. + \item Will add more theories to Alethe. + \item[\emoji{woman}] Hanna Lachnitt and the wider \emph{cvc5} team. + \end{itemize} + \end{block} +\end{frame} + +\begin{frame}[plain] + \begin{columns} + \begin{column}{0.28\textwidth} + \end{column} + \begin{column}{0.64\textwidth} + \begin{block}{Speculative Specification} + \texttt{http://www.verit-solver.org/alethe.pdf} + \end{block} + \begin{block}{Feedback} + \texttt{https://gitlab.uliege.be/verit/alethe} + \end{block} + \end{column} + \begin{column}{0.28\textwidth} + \end{column} + \end{columns} +\end{frame} + +\end{document} -- GitLab