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Fix text around least upper bound.

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R=eernst@google.com

Review-Url: https://codereview.chromium.org/2802633002 .
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Lasse R.H. Nielsen 2017-04-05 14:09:06 +02:00
parent 7c011eda26
commit 94b23d3b12
1 changed files with 14 additions and 3 deletions
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17
docs/language/dartLangSpec.tex
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@ -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