# Relabeling Formulas

The task is to read an LTL formula, relabel all (possibly double-quoted) atomic propositions, and provide `#define` statements for each of these renamings, writing everything in Spin's syntax.

## Shell

```ltlfilt -ps --relabel=pnn --define -f '"Proc@Here" U ("var > 10" | "var < 4")'
```
```#define p0 (Proc@Here)
#define p1 (var < 4)
#define p2 (var > 10)
(p0) U ((p1) || (p2))

```

When is this output interesting, you may ask? It is useful for instance if you want to call `ltl2ba` (or any other LTL-to-Büchi translator) using a formula with complex atomic propositions it cannot parse. Then you can pass the rewritten formula to `ltl2ba`, and prepend all those `#define` to its output. For instance:

```ltlfilt -ps --relabel=pnn --define=tmp.defs -f '"Proc@Here" U ("var > 10" | "var < 4")' >tmp.ltl
cat tmp.defs; ltl2ba -F tmp.ltl
rm tmp.defs tmp.ltl
```
```#define p0 (Proc@Here)
#define p1 (var < 4)
#define p2 (var > 10)
never { /* (p0) U ((p1) || (p2))
*/
T0_init:
if
:: (p0) -> goto T0_init
:: (p1) || (p2) -> goto accept_all
fi;
accept_all:
skip
}
```

Aside: another way to work around syntax limitations of tools is to use `ltldo`. On the above example, ```ltldo ltl2ba -f '"Proc@Here" U ("var > 10" | "var < 4")' -s``` would produce a never claim with the correct atomic propositions, even though `ltl2ba` cannot parse them.

## Python

The `spot.relabel` function takes an optional third parameter that should be a `relabeling_map`. If supplied, this map is filled with pairs of atomic propositions of the form (new-name, old-name).

```import spot
m = spot.relabeling_map()
g = spot.relabel('"Proc@Here" U ("var > 10" | "var < 4")', spot.Pnn, m)
for newname, oldname in m.items():
print("#define {} ({})".format(newname.to_str(), oldname.to_str('spin', True)))
print(g.to_str('spin', True))
```
```#define p0 (Proc@Here)
(p0) U ((p1) || (p2))
#define p1 (var < 4)
(p0) U ((p1) || (p2))
#define p2 (var > 10)
(p0) U ((p1) || (p2))

```

## C++

The `spot::relabeling_map` is just implemented as a `std::map`.

```#include <string>
#include <iostream>
#include <spot/tl/parse.hh>
#include <spot/tl/print.hh>
#include <spot/tl/relabel.hh>

int main()
{
std::string input = "\"Proc@Here\" U (\"var > 10\" | \"var < 4\")";
spot::parsed_formula pf = spot::parse_infix_psl(input);
if (pf.format_errors(std::cerr))
return 1;
spot::formula f = pf.f;
spot::relabeling_map m;
f = spot::relabel(f, spot::Pnn, &m);
for (auto& i: m)
{
std::cout << "#define " << i.first << " (";
print_spin_ltl(std::cout, i.second, true) << ")\n";
}
print_spin_ltl(std::cout, f, true) << '\n';
return 0;
}
```
```#define p0 (Proc@Here)
#define p1 (var < 4)
#define p2 (var > 10)
(p0) U ((p1) || (p2))

```

### Two ways to name atomic propositions

Instead of `--relabel=pnn` (or `spot.Pnn`, or `spot::Pnn`), you can actually use `--relabel=abc` (or `spot.Abc`, or `spot::Abc`) to have the atomic propositions named `a`, `b`, `c`, etc.

### Relabeling Boolean sub-expressions

Instead of relabeling each atomic proposition, you could decide to relabel each Boolean sub-expression:

```ltlfilt -ps --relabel-bool=pnn --define -f '"Proc@Here" U ("var > 10" | "var < 4")'
```
```#define p0 (Proc@Here)
#define p1 ((var < 4) || (var > 10))
(p0) U (p1)

```

The relabeling routine is smart enough to not give different names to Boolean expressions that have some sub-expression in common.

For instance `a U (a & b)` will not be relabeled into `(p0) U (p1)` because that would hide the fact that both `p0` and `p1` check for `a`. Instead we get this:

```ltlfilt -ps --relabel-bool=pnn --define -f 'a U (a & b)'
```
```#define p0 (a)
#define p1 (b)
(p0) U ((p0) && (p1))

```

This "Boolean sub-expression" relabeling is available in Python and C++ via the `relabel_bse` function. The interface is identical to `relabel`.