diff --git a/spec/rule_list.tex b/spec/rule_list.tex index a272e80430d7fddc4072f6824214813bf6cc0aa1..791852c36d534e3aef4f63a20c1c93d11fa0a2e2 100644 --- a/spec/rule_list.tex +++ b/spec/rule_list.tex @@ -1136,8 +1136,14 @@ The possible transformations are: \label{sec:ite-simp-rules} \begin{proof-rule}{ite_simplify}{veriT} -This rule simplifies an if-then-else term by applying equivalent -transformations as long as possible. Depending on the sort of the + This rule simplifies an if-then-else term by applying equivalent + transformations until fix point\footnote{Note however that the order of the + application is important, since the set of rules is not confluent. For + example, the term $(\operatorname{ite} \top \; t_1 \; t_2 \leftrightarrow + t_1)$ can be simplified into both $p$ and $(not (not p))$ depending on the + order of applications.} + % +Depending on the sort of the $\operatorname{ite}$-term the rule can have one of two forms. If the sort is $\mathbf{Bool}$ it has the form \begin{plContainer}