# Parsing and Printing LTL Formulas

## Table of Contents

Our first task is to read formulas and print them in another syntax.

## Shell command

Using `ltlfilt`

, you can easily read an LTL formula in one syntax, and
output it in another syntax. By default, the parser will accept a
formula in any infix syntax, but if the input is in the prefix syntax
of LBT, you should use `--lbt-input`

. The output syntax is controlled
using different options such as (`--spin`

, `--lbt`

, `--latex`

, etc.).
Full parentheses can also be requested using `-p`

.

ltlfilt -f '[]<>p0 || <>[]p1' formula='& & G p0 p1 p2' ltlfilt --lbt-input -f "$formula" --latex ltlfilt --lbt-input -f "$formula" --lbt ltlfilt --lbt-input -f "$formula" --spin -p

GFp0 | FGp1 p_{1} \land p_{2} \land \G p_{0} & & p1 p2 G p0 (p1) && (p2) && ([](p0))

The reason the LBT parser has to be explicitly enabled is because of
some corner cases that have different meanings in the two syntaxes.
(For instance `t`

and `f`

are the true and false constants in LBT's
syntax, but they are considered as atomic propositions in all the
other syntaxes.)

## Python bindings

Here are the same operations in Python

import spot print(spot.formula('[]<>p0 || <>[]p1')) f = spot.formula('& & G p0 p1 p2') print(f.to_str('latex')) print(f.to_str('lbt')) print(f.to_str('spin', parenth=True))

GFp0 | FGp1 p_{1} \land p_{2} \land \G p_{0} & & p1 p2 G p0 (p1) && (p2) && ([](p0))

The `spot.formula`

function wraps the calls to the two formula parsers
of Spot. It first tries to parse the formula using infix syntaxes,
and if it fails, it tries to parse it with the prefix parser. (So
this might fail to correctly interpret `t`

or `f`

if you are
processing a list of LBT formulas.) Using `spot.formula`

, parse
errors are returned as an exception.

## C++

### Simple wrapper for the two parsers

We first start with the easy parser interface, similar to the one used above in the python bindings. Here parse errors would be returned as exceptions.

#include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> int main() { std::cout << spot::parse_formula("[]<>p0 || <>[]p1") << '\n'; spot::formula f = spot::parse_formula("& & G p0 p1 p2"); print_latex_psl(std::cout, f) << '\n'; print_lbt_ltl(std::cout, f) << '\n'; print_spin_ltl(std::cout, f, true) << '\n'; return 0; }

After compiling and executing we get:

GFp0 | FGp1 p_{1} \land p_{2} \land \G p_{0} & & p1 p2 G p0 (p1) && (p2) && ([](p0))

Notice that, except for the `<<`

operator, the different output
routines specify in their name the syntax to use for output, and the
type of formula they can output. Here we are only using LTL formulas
for demonstration, and PSL is a superset of LTL, so those three output
functions are all OK with that. The routine used by `<<`

is
`print_psl()`

, the default syntax used by Spot.

We do not recommend using the `parse_formula()`

interface because of
the potential formulas (like `f`

or `t`

) that have different meanings
in the two parsers that are tried.

Instead, depending on whether you want to parse formulas with infix syntax, or formulas with prefix syntax, you should call the appropriate parser. Additionally, this give you control over how to print errors.

### Calling the infix parser explicitly

Here is how to call the infix parser explicitly:

#include <string> #include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> int main() { std::string input = "[]<>p0 || <>[]p1"; spot::parsed_formula pf = spot::parse_infix_psl(input); if (pf.format_errors(std::cerr)) return 1; std::cout << pf.f << '\n'; return 0; }

GFp0 | FGp1

Note that as its name implies, this parser can read more than LTL formulas: the fragment of PSL we support is basically LTL extended with regular expressions. (Refer to the temporal logic specifications for the syntax and semantics.)

The `parse_infix_psl()`

function processes `input`

, and returns a
`spot::parsed_formula`

object. In addition to the `spot::formula`

we
desire (stored as the `spot::parsed_formula::f`

attribute), the
`spot::parsed_formula`

also stores any diagnostic collected during the
parsing. Those diagnostics are stored in the
`spot::parsed_formula::errors`

attribute, but they can conveniently be
printed by calling the `spot::parsed_formula::format_errors()`

method:
this method returns `true`

if and only if a diagnostic was output, so
this is usually used to abort the program with an error status as
above.

The parser usually tries to do some error recovery, so the `f`

attribute can be non-null even if some parsing errors were returned.
For instance if you have input `(a U b))`

the parser will complain
about the extra parenthesis, but it will still return a formula that
is equivalent to `a U b`

. You could decide to continue with the
"fixed" formula if you wish. Here is an example:

#include <string> #include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> int main() { std::string input = "(a U b))"; spot::parsed_formula pf = spot::parse_infix_psl(input); // Use std::cout instead of std::cerr because we can only // show the output of std::cout in this documentation. (void) pf.format_errors(std::cout); if (pf.f == nullptr) return 1; std::cout << "Parsed formula: " << pf.f << '\n'; return 0; }

>>> (a U b)) ^ syntax error, unexpected closing parenthesis >>> (a U b)) ^ ignoring trailing garbage Parsed formula: a U b

The formula `pf.f`

would only be returned as null when the parser
really cannot recover anything.

### Calling the prefix parser explicitly

The only difference here is the call to `parse_prefix_ltl()`

instead
of `parse_infix_psl()`

.

#include <string> #include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> int main() { std::string input = "& & G p0 p1 p2"; spot::parsed_formula pf = spot::parse_prefix_ltl(input); if (pf.format_errors(std::cerr)) return 1; spot::formula f = pf.f; print_latex_psl(std::cout, f) << '\n'; print_lbt_ltl(std::cout, f) << '\n'; print_spin_ltl(std::cout, f, true) << '\n'; return 0; }

p_{1} \land p_{2} \land \G p_{0} & & p1 p2 G p0 (p1) && (p2) && ([](p0))

## Additional Comments

### PSL vs LTL

LTL is a subset of PSL as far as Spot is concerned, so you can parse
an LTL formula with `parse_infix_psl()`

, and later print it with for
instance `print_spin_ltl()`

(which, as its name implies, can only
print LTL formulas). There is no `parse_infix_ltl()`

function because
you can simply use `parse_infix_psl()`

to parse LTL formulas.

There is a potential problem if you design a tool that only works with
LTL formulas, but call `parse_infix_psl()`

to parse user input. In
that case, the user might input a PSL formula and cause problem
down the line.

For instance, let's see what happens if a PSL formulas is passed to
`print_spin_ltl`

:

#include <string> #include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> int main() { std::string input = "{a*;b}<>->(a U (b & GF c))"; spot::parsed_formula pf = spot::parse_infix_psl(input); if (pf.format_errors(std::cerr)) return 1; print_spin_ltl(std::cout, pf.f) << '\n'; return 0; }

{a[*];b}<>-> (a U (b && []<>c))

The output is a 'best effort' output. The LTL subformulas have been
rewritten, but the PSL-specific part (the SERE and `<>->`

operator)
are output in the only syntax Spot knows, definitively not
Spin-compatible.

If that is unwanted, here are two possible solutions.

The first is to simply diagnose non-LTL formulas.

#include <string> #include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> int main() { std::string input = "{a*;b}<>->(a U (b & GF c))"; spot::parsed_formula pf = spot::parse_infix_psl(input); if (pf.format_errors(std::cerr)) return 1; spot::formula f = pf.f; if (!f.is_ltl_formula()) { std::cerr << "Only LTL formulas are supported.\n"; return 1; } print_spin_ltl(std::cout, f) << '\n'; return 0; }

A second (but slightly weird) idea would be to try to simplify the PSL formula, and hope that the simplifier is able to come up with an equivalent LTL formula. This does not always work, so you need to be prepared to reject the formula anyway. In our example, we are lucky (maybe because it was carefully chosen…):

#include <string> #include <iostream> #include <spot/tl/parse.hh> #include <spot/tl/print.hh> #include <spot/tl/simplify.hh> int main() { std::string input = "{a*;b}<>->(a U (b & GF c))"; spot::parsed_formula pf = spot::parse_infix_psl(input); if (pf.format_errors(std::cerr)) return 1; spot::formula f = pf.f; if (!f.is_ltl_formula()) { spot::tl_simplifier simp; f = simp.simplify(f); } if (!f.is_ltl_formula()) { std::cerr << "Only LTL formulas are supported.\n"; return 1; } print_spin_ltl(std::cout, f) << '\n'; return 0; }

a U (b && (a U (b && []<>c)))

### Lenient parsing

In version 6, Spin extended its command-line LTL parser to accept
arbitrary atomic propositions to be specified. For instance ```
(a > 4)
U (b < 5)
```

would be correct input, with `a > 4`

and `b < 5`

considered
as two atomic propositions. Of course the atomic proposition could be
arbitrarily complex, and there is no way we can teach Spot about the
syntax for atomic propositions supported by any tool. The usual
workaround in Spot is to double-quote any arbitrary atomic
proposition:

echo compare ltlfilt -f '"a > 4" U "b < 5"' echo and ltlfilt -f '"a > 4" U "b < 5"' --spin

compare "a > 4" U "b < 5" and (a > 4) U (b < 5)

When the Spin output is requested, these atomic propositions are atomically output in a way that Spin can parse.

This Spin syntax is not accepted by default by the infix parser, but
it has an option for that. This is called *lenient parsing*: when the
parser finds a parenthetical block it does not understand, it simply
assumes that this block represents an atomic proposition.

```
ltlfilt --lenient -f '(a > 4) U (b < 5)'
```

"a > 4" U "b < 5"

Lenient parsing is risky, because any parenthesized sub-formula that is a syntax-error will be treated as an atomic proposition:

```
ltlfilt --lenient -f '(a U ) U c'
```

"a U" U c

In C++ you can enable lenient using one of the Boolean arguments of
`parse_infix_psl()`

.

### Python formatting

Formulas have a custom format specification language that allows you
to easily change the way a formula should be output when using the
`format()`

method of strings, or using formatted string litterals.

import spot formula = spot.formula('a U b U "$strange[0]=name"') print("""\ Default output: {f} Spin syntax: {f:s} (Spin syntax): {f:sp} Default for shell: echo {f:q} | ... LBT for shell: echo {f:lq} | ... Default for CSV: ...,{f:c},... Wring, centered: {f:w:~^50}""".format(f = formula))

Default output: a U (b U "$strange[0]=name") Spin syntax: a U (b U ($strange[0]=name)) (Spin syntax): (a) U ((b) U ($strange[0]=name)) Default for shell: echo 'a U (b U "$strange[0]=name")' | ... LBT for shell: echo 'U "a" U "b" "$strange[0]=name"' | ... Default for CSV: ...,"a U (b U ""$strange[0]=name"")",... Wring, centered: ~~~~~(a=1) U ((b=1) U ("$strange[0]=name"=1))~~~~~

The specifiers after the first `:`

are specific to formulas. The
specifiers after the second `:`

(if any) are the usual format
specifiers (typically alignment choices) and are applied on the string
produced from the formula.

The complete list of specifier that apply to formulas can always be
printed with `help(spot.formula.__format__)`

:

Help on function __format__ in module spot: __format__(self, spec) Format the formula according to `spec`. Parameters ---------- spec : str, optional a list of letters that specify how the formula should be formatted. Supported specifiers -------------------- - 'f': use Spot's syntax (default) - '8': use Spot's syntax in UTF-8 mode - 's': use Spin's syntax - 'l': use LBT's syntax - 'w': use Wring's syntax - 'x': use LaTeX output - 'X': use self-contained LaTeX output - 'j': use self-contained LaTeX output, adjusted for MathJax Add some of those letters for additional options: - 'p': use full parentheses - 'c': escape the formula for CSV output (this will enclose the formula in double quotes, and escape any included double quotes) - 'h': escape the formula for HTML output - 'd': escape double quotes and backslash, for use in C-strings (the outermost double quotes are *not* added) - 'q': quote and escape for shell output, using single quotes or double quotes depending on the contents. - '[...]': rewrite away all the operators specified in brackets, using spot.unabbreviate(). - ':spec': pass the remaining specification to the formating function for strings.