simplifier: new LTL simplifications

if e is pure eventuality and g => e, then e U g = Fg
if u is purely universal and u => g, then u R g = Gg

Fixes #93.

* doc/tl/tl.tex, NEWS: Document the rules.
* spot/tl/simplify.cc: Implement them.
* tests/core/reduccmp.test: Test them.
 ... ... @@ -1720,7 +1720,9 @@ In the following rewritings rules, $f\simp g$ means that $g$ was proved to be implied by $f$ using either of the above two methods. Additionally, implications denoted by $f\Simp g$ are only checked if the \verb|tl_simplifier_options::containment_checks_stronger|'' option is set (otherwise the rewriting rule is not applied). option is set (otherwise the rewriting rule is not applied). As in the previous section, formulas $e$ and $u$ represent respectively pure eventualities and purely universal formulas. \begin{equation*} \begin{array}{cccr@{\,}l} ... ... @@ -1731,6 +1733,7 @@ option is set (otherwise the rewriting rule is not applied). \text{if}& f\simp g &\text{then}& f\U g &\equiv g \\ \text{if}& (f\U g)\Simp g &\text{then}& f\U g &\equiv g \\ \text{if}& (\NOT f)\simp g &\text{then}& f\U g &\equiv \F g \\ \text{if}& g\simp e &\text{then}& e\U g &\equiv \F g \\ \text{if}& f\simp g &\text{then}& f\U (g \U h) &\equiv g \U h \\ \text{if}& f\simp g &\text{then}& f\U (g \W h) &\equiv g \W h \\ \text{if}& g\simp f &\text{then}& f\U (g \U h) &\equiv f \U h \\ ... ... @@ -1753,6 +1756,7 @@ option is set (otherwise the rewriting rule is not applied). \text{if}& g\simp h &\text{then}& (f\U g) \W h &\equiv (f \U g) \OR h \\ \text{if}& g\simp f &\text{then}& f\R g &\equiv g \\ \text{if}& g\simp \NOT f &\text{then}& f\R g &\equiv \G g \\ \text{if}& u\simp g &\text{then}& u\R g &\equiv \G g \\ \text{if}& g\simp f &\text{then}& f\R (g \R h) &\equiv g \R h \\ \text{if}& g\simp f &\text{then}& f\R (g \M h) &\equiv g \M h \\ \text{if}& f\simp g &\text{then}& f\R (g \R h) &\equiv f \R h \\ ... ... @@ -1771,8 +1775,8 @@ option is set (otherwise the rewriting rule is not applied). \end{array} \end{equation*} The above rules were collected from various sources~\cite{somenzi.00.cav,tauriainen.03.a83,babiak.12.tacas} and Many of the above rules were collected from the literature~\cite{somenzi.00.cav,tauriainen.03.a83,babiak.12.tacas} and sometimes generalized to support operators such as $\M$ and $\W$. \appendix ... ...