/** md
Title: Running a Strategy, continued

## Disjunctive Normal Form

The next Stratego example, in {! ../docrefs/sec4.2.md !}, extends
`prop-eval-rules` to convert SPL propositions into disjunctive normal form (DNF).
As the manual notes, another way to see what the `dnf` strategy does to a given
AST is to add a Spoofax Test Language test that claims it transforms to
something that it definitely does **not** parse to, e.g.
```SPT
{! ../test/manual-suite.spt extract:
  start: '\*\*[/]'
terminate: '(.*run dnf.*)$' !}
```

The difficulty is that in a standard Spoofax language project, the error popup
showing what the transformation actually does is nearly unreadable due to
a tremendous amount of annotation produced by the default static analysis process.

Since in this repository we are not actually doing any (meaningful) static
analysis, it includes a hack which makes the editor popup much more readable.
Namely, it strips the annotation, by modifying the
`editor-analyze` rule in `trans/analysis.str` like so:
```Stratego
{! ../trans/analysis.str terminate: Debugging!}  [rest of file omitted]
```

**/

module prop-dnf-rules
imports prop-eval-rules
rules
  E : Impl(x, y) -> Or(Not(x), y)
  E : Eq(x, y)   -> And(Impl(x, y), Impl(y, x))

  E : Not(Not(x)) -> x

  E : Not(And(x, y)) -> Or(Not(x), Not(y))
  E : Not(Or(x, y))  -> And(Not(x), Not(y))

  E : And(Or(x, y), z) -> Or(And(x, z), And(y, z))
  E : And(z, Or(x, y)) -> Or(And(z, x), And(z, y))