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| author | Adriaan Moors <adriaan.moors@typesafe.com> | 2014-03-12 17:47:43 -0700 |
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| committer | Adriaan Moors <adriaan.moors@typesafe.com> | 2014-03-12 17:47:43 -0700 |
| commit | 78d96eafe9c7404b43da38892134ba380dd77db5 (patch) | |
| tree | 0543532be3babed081af3f169f2400ca833ab067 /10-pattern-matching.md | |
| parent | 3c0d964c350b5a2eaa3fdc53e4f24a6b86d27eba (diff) | |
| download | scala-78d96eafe9c7404b43da38892134ba380dd77db5.tar.gz scala-78d96eafe9c7404b43da38892134ba380dd77db5.tar.bz2 scala-78d96eafe9c7404b43da38892134ba380dd77db5.zip | |
formatting: tables and headings
Diffstat (limited to '10-pattern-matching.md')
| -rw-r--r-- | 10-pattern-matching.md | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/10-pattern-matching.md b/10-pattern-matching.md index fd63d3fbc9..8349c52994 100644 --- a/10-pattern-matching.md +++ b/10-pattern-matching.md @@ -376,7 +376,7 @@ pattern. Inference takes into account the expected type of the pattern. -Type parameter inference for typed patterns. \ +### Type parameter inference for typed patterns. Assume a typed pattern $p: T'$. Let $T$ result from $T'$ where all wildcards in $T'$ are renamed to fresh variable names. Let $a_1 , \ldots , a_n$ be @@ -387,14 +387,14 @@ Type parameter inference constructs first a set of subtype constraints over the type variables $a_i$. The initial constraints set $\mathcal{C}_0$ reflects just the bounds of these type variables. That is, assuming $T$ has bound type variables $a_1 , \ldots , a_n$ which correspond to class -type parameters $a'_1 , \ldots , a'_n$ with lower bounds $L_1 -, \ldots , L_n$ and upper bounds $U_1 , \ldots , U_n$, $\mathcal{C}_0$ -contains the constraints +type parameters $a'_1 , \ldots , a'_n$ with lower bounds $L_1, \ldots , L_n$ +and upper bounds $U_1 , \ldots , U_n$, $\mathcal{C}_0$ contains the constraints + +| | | | | +|-------------|------|---------------|------------------------| +|$a_i$ | $<:$ | $\sigma U_i$ | $(i = 1, \ldots , n)$ | +|$\sigma L_i$ | $<:$ | $a_i$ | $(i = 1 , \ldots , n)$ | -------------- ------ -------------- ------------------------ -$a_i$ $<:$ $\sigma U_i$ $(i = 1, \ldots , n)$ -$\sigma L_i$ $<:$ $a_i$ $(i = 1 , \ldots , n)$ -------------- ------ -------------- ------------------------ where $\sigma$ is the substitution $[a'_1 := a_1 , \ldots , a'_n := a_n]$. @@ -402,14 +402,14 @@ a_n]$. The set $\mathcal{C}_0$ is then augmented by further subtype constraints. There are two cases. -Case 1: \ +###### Case 1 If there exists a substitution $\sigma$ over the type variables $a_i , \ldots , a_n$ such that $\sigma T$ conforms to $\mathit{pt}$, one determines the weakest subtype constraints $\mathcal{C}_1$ over the type variables $a_1 , \ldots , a_n$ such that $\mathcal{C}_0 \wedge \mathcal{C}_1$ implies that $T$ conforms to $\mathit{pt}$. -Case 2: \ +###### Case 2 Otherwise, if $T$ can not be made to conform to $\mathit{pt}$ by instantiating its type variables, one determines all type variables in $\mathit{pt}$ which are defined as type parameters of a method enclosing @@ -430,12 +430,12 @@ The final step consists in choosing type bounds for the type variables which imply the established constraint system. The process is different for the two cases above. -Case 1: \ +###### Case 1 We take $a_i >: L_i <: U_i$ where each $L_i$ is minimal and each $U_i$ is maximal wrt $<:$ such that $a_i >: L_i <: U_i$ for $i = 1 , \ldots , n$ implies $\mathcal{C}_0 \wedge \mathcal{C}_1$. -Case 2: \ +###### Case 2 We take $a_i >: L_i <: U_i$ and $b_i >: L'_i <: U'_i$ where each $L_i$ and $L'_j$ is minimal and each $U_i$ and $U'_j$ is maximal such that $a_i >: L_i <: U_i$ for $i = 1 , \ldots , n$ and |