5bfd0267e7
Fixes #105. * src/bin/common_trans.cc (quote_shell_string): Move ... * src/misc/escape.cc, src/misc/escape.hh (quote_shell_string): ... here. * wrap/python/spot_impl.i: Wrap escape.hh. * wrap/python/spot.py: Implement formula.__format__. * wrap/python/tests/ltlsimple.py: Test it. * NEWS, doc/org/tut01.org, wrap/python/tests/formulas.ipynb: Document it.
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24 KiB
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723 lines
No EOL
24 KiB
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{
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.4.3+"
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},
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"name": ""
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},
|
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"nbformat": 3,
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"nbformat_minor": 0,
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"worksheets": [
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Handling LTL and PSL formulas\n",
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"============================="
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"import spot"
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],
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 1
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"For interactive use, formulas can be entered as text strings and passed to the `spot.formula` constructor."
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"f = spot.formula('p1 U p2 R (p3 & !p4)')\n",
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"f"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"latex": [
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"$p_{1} \\mathbin{\\mathsf{U}} (p_{2} \\mathbin{\\mathsf{R}} (p_{3} \\land \\lnot p_{4}))$"
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],
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 2,
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"text": [
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"p1 U (p2 R (p3 & !p4))"
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]
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}
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],
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"prompt_number": 2
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"g = spot.formula('{a;b*;c[+]}<>->GFb'); g"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"latex": [
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"$\\{a \\mathbin{\\mathsf{;}} b^{\\star} \\mathbin{\\mathsf{;}} c^+\\}\\mathrel{\\Diamond\\kern-1.7pt\\raise.4pt\\hbox{$\\mathord{\\rightarrow}$}} \\mathsf{G} \\mathsf{F} b$"
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],
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 3,
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"text": [
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"{a;b[*];c[+]}<>-> GFb"
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]
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}
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],
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"prompt_number": 3
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"By default the parser recognizes an infix syntax, but when this fails, it tries to read the formula with the [LBT](http://www.tcs.hut.fi/Software/maria/tools/lbt/) syntax:"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
|
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"h = spot.formula('& | a b c'); h"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"latex": [
|
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"$c \\land (a \\lor b)$"
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],
|
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 4,
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"text": [
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"c & (a | b)"
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]
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}
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],
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"prompt_number": 4
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"By default, a formula object is presented using mathjax as above.\n",
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"When a formula is converted to string you get Spot's syntax by default:"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"str(f)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
|
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 5,
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"text": [
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"'p1 U (p2 R (p3 & !p4))'"
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]
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}
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],
|
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"prompt_number": 5
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"If you prefer to print the string in another syntax, you may use the `to_str()` method, with an argument that indicates the output format to use. The `latex` format assumes that you will the define macros such as `\\U`, `\\R` to render all operators as you wish. On the otherhand, the `sclatex` (with `sc` for self-contained) format hard-codes the rendering of each of those operators: this is typically the output that is used to render formulas using MathJax in a notebook. "
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"for i in ['spot', 'spin', 'lbt', 'wring', 'utf8', 'latex', 'sclatex']:\n",
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" print(\"%-10s%s\" % (i, f.to_str(i)))"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"spot p1 U (p2 R (p3 & !p4))\n",
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"spin p1 U (p2 V (p3 && !p4))\n",
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"lbt U p1 V p2 & p3 ! p4\n",
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"wring (p1=1) U ((p2=1) R ((p3=1) * (p4=0)))\n",
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"utf8 p1 U (p2 R (p3\u2227\u00acp4))\n",
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"latex p_{1} \\U (p_{2} \\R (p_{3} \\land \\lnot p_{4}))\n",
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"sclatex p_{1} \\mathbin{\\mathsf{U}} (p_{2} \\mathbin{\\mathsf{R}} (p_{3} \\land \\lnot p_{4}))\n"
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]
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}
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],
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"prompt_number": 6
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Formulas output via `format()` can also use some convenient shorthand to select the syntax:"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"print(\"\"\"\\\n",
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"Spin: {0:s}\n",
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"Spin+parentheses: {0:sp}\n",
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"Spot (default): {0}\n",
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"Spot+shell quotes: {0:q}\n",
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"LBT, right aligned: {0:l:~>40}\"\"\".format(f))"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"Spin: p1 U (p2 V (p3 && !p4))\n",
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"Spin+parentheses: (p1) U ((p2) V ((p3) && (!(p4))))\n",
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"Spot (default): p1 U (p2 R (p3 & !p4))\n",
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"Spot+shell quotes: 'p1 U (p2 R (p3 & !p4))'\n",
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"LBT, right aligned: ~~~~~~~~~~~~~~~~~~~~~U p1 V p2 & p3 ! p4\n"
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]
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}
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],
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"prompt_number": 7
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},
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{
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"cell_type": "markdown",
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|
"metadata": {},
|
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"source": [
|
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"The specifiers that can be used with `format` are documented as follows:"
|
|
]
|
|
},
|
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
|
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"help(spot.formula.__format__)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"Help on function _formula_format in module spot:\n",
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"\n",
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"_formula_format(self, spec)\n",
|
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" Format the formula according to spec.\n",
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" \n",
|
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" 'spec' should be a list of letters that select\n",
|
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" how the formula should be formatted.\n",
|
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" \n",
|
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" Use one of the following letters to select the syntax:\n",
|
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" \n",
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" - 'f': use Spot's syntax (default)\n",
|
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" - '8': use Spot's syntax in UTF-8 mode\n",
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" - 's': use Spin's syntax\n",
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" - 'l': use LBT's syntax\n",
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" - 'w': use Wring's syntax\n",
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" - 'x': use LaTeX output\n",
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" - 'X': use self-contained LaTeX output\n",
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" \n",
|
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" Add some of those letters for additional options:\n",
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" \n",
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" - 'p': use full parentheses\n",
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" - 'c': escape the formula for CSV output (this will\n",
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" enclose the formula in double quotes, and escape\n",
|
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" any included double quotes)\n",
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" - 'h': escape the formula for HTML output\n",
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" - 'd': escape double quotes and backslash,\n",
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" for use in C-strings (the outermost double\n",
|
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" quotes are *not* added)\n",
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" - 'q': quote and escape for shell output, using single\n",
|
|
" quotes or double quotes depending on the contents.\n",
|
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" \n",
|
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" - ':spec': pass the remaining specification to the\n",
|
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" formating function for strings.\n",
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"\n"
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]
|
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}
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],
|
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"prompt_number": 8
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},
|
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{
|
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"cell_type": "markdown",
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|
"metadata": {},
|
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"source": [
|
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"A `spot.formula` object has a number of built-in predicates whose value have been computed when the formula was constructed. For instance you can check whether a formula is in negative normal form using `is_in_nenoform()`, and you can make sure it is an LTL formula (i.e. not a PSL formula) using `is_ltl_formula()`:"
|
|
]
|
|
},
|
|
{
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"cell_type": "code",
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|
"collapsed": false,
|
|
"input": [
|
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"f.is_in_nenoform() and f.is_ltl_formula()"
|
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],
|
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"language": "python",
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"metadata": {},
|
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"outputs": [
|
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{
|
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"metadata": {},
|
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"output_type": "pyout",
|
|
"prompt_number": 9,
|
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"text": [
|
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"True"
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]
|
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}
|
|
],
|
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"prompt_number": 9
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},
|
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{
|
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"cell_type": "code",
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"collapsed": false,
|
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"input": [
|
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"g.is_ltl_formula()"
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],
|
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"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
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{
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 10,
|
|
"text": [
|
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"False"
|
|
]
|
|
}
|
|
],
|
|
"prompt_number": 10
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"Similarly, `is_syntactic_stutter_invariant()` tells wether the structure of the formula guarranties it to be stutter invariant. For LTL formula, this means the `X` operator should not be used. For PSL formula, this function capture all formulas built using the [siPSL grammar](http://www.daxc.de/eth/paper/09atva.pdf)."
|
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]
|
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},
|
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{
|
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"cell_type": "code",
|
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"collapsed": false,
|
|
"input": [
|
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"f.is_syntactic_stutter_invariant()"
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|
],
|
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"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 11,
|
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"text": [
|
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"True"
|
|
]
|
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}
|
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],
|
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"prompt_number": 11
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},
|
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{
|
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"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
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"spot.formula('{a[*];b}<>->c').is_syntactic_stutter_invariant()"
|
|
],
|
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"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 12,
|
|
"text": [
|
|
"False"
|
|
]
|
|
}
|
|
],
|
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"prompt_number": 12
|
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},
|
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{
|
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"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
|
"spot.formula('{a[+];b[*]}<>->d').is_syntactic_stutter_invariant()"
|
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],
|
|
"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 13,
|
|
"text": [
|
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"True"
|
|
]
|
|
}
|
|
],
|
|
"prompt_number": 13
|
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},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"`spot.relabel` renames the atomic propositions that occur in a formula, using either letters, or numbered propositions:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
|
"gf = spot.formula('(GF_foo_) && \"a > b\" && \"proc[2]@init\"'); gf"
|
|
],
|
|
"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"latex": [
|
|
"$``\\mathit{a > b}\\textrm{''} \\land ``\\mathit{proc[2]@init}\\textrm{''} \\land \\mathsf{G} \\mathsf{F} \\mathit{\\_foo\\_}$"
|
|
],
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 14,
|
|
"text": [
|
|
"\"a > b\" & \"proc[2]@init\" & GF_foo_"
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|
]
|
|
}
|
|
],
|
|
"prompt_number": 14
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
|
"spot.relabel(gf, spot.Abc)"
|
|
],
|
|
"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"latex": [
|
|
"$a \\land b \\land \\mathsf{G} \\mathsf{F} c$"
|
|
],
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 15,
|
|
"text": [
|
|
"a & b & GFc"
|
|
]
|
|
}
|
|
],
|
|
"prompt_number": 15
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
|
"spot.relabel(gf, spot.Pnn)"
|
|
],
|
|
"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"latex": [
|
|
"$p_{0} \\land p_{1} \\land \\mathsf{G} \\mathsf{F} p_{2}$"
|
|
],
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 16,
|
|
"text": [
|
|
"p0 & p1 & GFp2"
|
|
]
|
|
}
|
|
],
|
|
"prompt_number": 16
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"The AST of any formula can be displayed with `show_ast()`. Despite the name, this is not a tree but a DAG, because identical subtrees are merged. Binary operators have their left and right operands denoted with `L` and `R`, while non-commutative n-ary operators have their operands numbered."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"collapsed": false,
|
|
"input": [
|
|
"print(g); g.show_ast()"
|
|
],
|
|
"language": "python",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"output_type": "stream",
|
|
"stream": "stdout",
|
|
"text": [
|
|
"{a;b[*];c[+]}<>-> GFb\n"
|
|
]
|
|
},
|
|
{
|
|
"metadata": {},
|
|
"output_type": "pyout",
|
|
"prompt_number": 17,
|
|
"svg": [
|
|
"<svg height=\"260pt\" viewBox=\"0.00 0.00 269.00 260.00\" width=\"269pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
|
|
"<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 256)\">\n",
|
|
"<title>G</title>\n",
|
|
"<polygon fill=\"white\" points=\"-4,4 -4,-256 265,-256 265,4 -4,4\" stroke=\"none\"/>\n",
|
|
"<!-- 0 -->\n",
|
|
"<g class=\"node\" id=\"node1\"><title>0</title>\n",
|
|
"<ellipse cx=\"106\" cy=\"-234\" fill=\"none\" rx=\"40.8928\" ry=\"18\" stroke=\"black\"/>\n",
|
|
"<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"106\" y=\"-230.3\">EConcat</text>\n",
|
|
"</g>\n",
|
|
"<!-- 1 -->\n",
|
|
"<g class=\"node\" id=\"node2\"><title>1</title>\n",
|
|
"<ellipse cx=\"155\" cy=\"-162\" fill=\"none\" rx=\"35.9954\" ry=\"18\" stroke=\"black\"/>\n",
|
|
"<text font-family=\"Times,serif\" font-size=\"14.00\" text-anchor=\"middle\" x=\"155\" y=\"-158.3\">Concat</text>\n",
|
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"</g>\n",
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"<g class=\"node\" id=\"node9\"><title>8</title>\n",
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"</svg>"
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],
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"text": [
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"<IPython.core.display.SVG object>"
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]
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}
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],
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"f = spot.formula('F(a & X(!a & b))'); f"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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|
"latex": [
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"$\\mathsf{F} (a \\land \\mathsf{X} (\\lnot a \\land b))$"
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],
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 18,
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"text": [
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"F(a & X(!a & b))"
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]
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}
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],
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"prompt_number": 18
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Etessami's rule for removing X (valid only in stutter-invariant formulas)"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"spot.remove_x(f)"
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],
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"language": "python",
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"metadata": {},
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"outputs": [
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{
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"latex": [
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"$\\mathsf{F} (a \\land ((a \\land (a \\mathbin{\\mathsf{U}} (\\lnot a \\land b)) \\land ((\\lnot b \\mathbin{\\mathsf{U}} \\lnot a) \\lor (b \\mathbin{\\mathsf{U}} \\lnot a))) \\lor (\\lnot a \\land (\\lnot a \\mathbin{\\mathsf{U}} (a \\land \\lnot a \\land b)) \\land ((\\lnot b \\mathbin{\\mathsf{U}} a) \\lor (b \\mathbin{\\mathsf{U}} a))) \\lor (b \\land (b \\mathbin{\\mathsf{U}} (\\lnot a \\land b \\land \\lnot b)) \\land ((\\lnot a \\mathbin{\\mathsf{U}} \\lnot b) \\lor (a \\mathbin{\\mathsf{U}} \\lnot b))) \\lor (\\lnot b \\land (\\lnot b \\mathbin{\\mathsf{U}} (\\lnot a \\land b)) \\land ((\\lnot a \\mathbin{\\mathsf{U}} b) \\lor (a \\mathbin{\\mathsf{U}} b))) \\lor (\\lnot a \\land b \\land (\\mathsf{G} \\lnot a \\lor \\mathsf{G} a) \\land (\\mathsf{G} \\lnot b \\lor \\mathsf{G} b))))$"
|
|
],
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 19,
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"text": [
|
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"F(a & ((a & (a U (!a & b)) & ((!b U !a) | (b U !a))) | (!a & (!a U (a & !a & b)) & ((!b U a) | (b U a))) | (b & (b U (!a & b & !b)) & ((!a U !b) | (a U !b))) | (!b & (!b U (!a & b)) & ((!a U b) | (a U b))) | (!a & b & (G!a | Ga) & (G!b | Gb))))"
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]
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}
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],
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Removing abbreviated operators"
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]
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
|
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"f = spot.formula(\"G(a xor b) -> F(a <-> b)\")\n",
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"spot.unabbreviate(f, \"GF^\")"
|
|
],
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"language": "python",
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"metadata": {},
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"outputs": [
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|
{
|
|
"latex": [
|
|
"$(\\bot \\mathbin{\\mathsf{R}} \\lnot (a \\leftrightarrow b)) \\rightarrow (\\top \\mathbin{\\mathsf{U}} (a \\leftrightarrow b))$"
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|
],
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 20,
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"text": [
|
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"(0 R !(a <-> b)) -> (1 U (a <-> b))"
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]
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}
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],
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"prompt_number": 20
|
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},
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{
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"cell_type": "code",
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"collapsed": false,
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"input": [
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"spot.unabbreviate(f, \"GF^ei\")"
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],
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"language": "python",
|
|
"metadata": {},
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"outputs": [
|
|
{
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"latex": [
|
|
"$(\\top \\mathbin{\\mathsf{U}} ((a \\land b) \\lor (\\lnot a \\land \\lnot b))) \\lor \\lnot (\\bot \\mathbin{\\mathsf{R}} ((\\lnot a \\land b) \\lor (a \\land \\lnot b)))$"
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],
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"metadata": {},
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"output_type": "pyout",
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"prompt_number": 21,
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"text": [
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"(1 U ((a & b) | (!a & !b))) | !(0 R ((!a & b) | (a & !b)))"
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]
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}
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],
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"prompt_number": 21
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}
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],
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"metadata": {}
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}
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]
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} |