diff --git a/docs/language/dartLangSpec.tex b/docs/language/dartLangSpec.tex index 62dba698369..3d43547c24b 100644 --- a/docs/language/dartLangSpec.tex +++ b/docs/language/dartLangSpec.tex @@ -7791,8 +7791,18 @@ Let $T$ be the declared type of a declaration $d$, as it appears in the program \LMHash{} % does this diverge in some cases? -Given two interfaces $I$ and $J$, let $S_I$ be the set of superinterfaces of $I$, let $S_J$ be the set of superinterfaces of $J$ and let $S = (I \cup S_I) \cap (J \cup S_J)$. Furthermore, we define $S_n = \{T | T \in S \wedge depth(T) =n\}$ for any finite $n$ %, and $k=max(depth(T_1), \ldots, depth(T_m)), T_i \in S, i \in 1..m$, -where $depth(T)$ is the number of steps in the longest inheritance path from $T$ to \code{Object}. Let $q$ be the largest number such that $S_q$ has cardinality one. The least upper bound of $I$ and $J$ is the sole element of $S_q$. +Given two interfaces $I$ and $J$, +let $S_I$ be the set of superinterfaces of $I$, +let $S_J$ be the set of superinterfaces of $J$ +and let $S = (\{I\} \cup S_I) \cap (\{J\} \cup S_J)$. +Furthermore, +we define $S_n = \{T | T \in S \wedge depth(T) = n\}$ for any finite $n$ +where $depth(T)$ is the number of steps in the longest inheritance path +from $T$ to \code{Object}. +%TODO(lrn): Specify that "inheritance path" is a path in the superinterface graph. +Let $q$ be the largest number such that $S_q$ has cardinality one, +which must exist because $S_0$ is $\{\code{Object}\}$. +The least upper bound of $I$ and $J$ is the sole element of $S_q$. \LMHash{} The least upper bound of \DYNAMIC{} and any type $T$ is \DYNAMIC{}. @@ -7801,7 +7811,8 @@ The least upper bound of $\bot$ and any type $T$ is $T$. Let $U$ be a type variable with upper bound $B$. The least upper bound of $U$ and a type $T \ne \bot$ is the least upper bound of $B$ and $T$. \LMHash{} -The least upper bound relation is symmetric and reflexive. +The least upper bound operation is commutative and idempotent, +but it is not associative. % Function types