diff options
| -rw-r--r-- | 05-types.md | 11 | ||||
| -rw-r--r-- | 10-pattern-matching.md | 24 | ||||
| -rw-r--r-- | 12-xml-expressions-and-patterns.md | 7 |
3 files changed, 20 insertions, 22 deletions
diff --git a/05-types.md b/05-types.md index 22998b11f5..7f701c6cf0 100644 --- a/05-types.md +++ b/05-types.md @@ -791,10 +791,10 @@ These notions are defined mutually recursively as follows. We define two relations between types. ------------------ ---------------- ------------------------------------------------- -Type equivalence $T \equiv U$ $T$ and $U$ are interchangeable in all contexts. -Conformance $T <: U$ Type $T$ conforms to type $U$. ------------------ ---------------- ------------------------------------------------- +| | | | +|-----------------|----------------|-------------------------------------------------| +|Type equivalence |$T \equiv U$ |$T$ and $U$ are interchangeable in all contexts. | +|Conformance |$T <: U$ |Type $T$ conforms to type $U$. | ### Type Equivalence @@ -913,8 +913,7 @@ _subsumes_ another declaration of the same name in some compound type or class type $C'$, if one of the following holds. - A value declaration or definition that defines a name $x$ with type $T$ - subsumes - a value or method declaration that defines $x$ with type $T'$, provided + subsumes a value or method declaration that defines $x$ with type $T'$, provided $T <: T'$. - A method declaration or definition that defines a name $x$ with type $T$ subsumes a method declaration that defines $x$ with type $T'$, provided 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 diff --git a/12-xml-expressions-and-patterns.md b/12-xml-expressions-and-patterns.md index 5d4a60c33d..d1a1e33b81 100644 --- a/12-xml-expressions-and-patterns.md +++ b/12-xml-expressions-and-patterns.md @@ -23,10 +23,9 @@ related to entity resolution. The following productions describe Scala's extensible markup language, designed as close as possible to the W3C extensible markup language -standard. Only the productions for attribute values and character data -are changed. Scala does not support declarations, CDATA -sections or processing instructions. Entity references are not -resolved at runtime. +standard. Only the productions for attribute values and character data are changed. +Scala does not support declarations, CDATA sections or processing instructions. +Entity references are not resolved at runtime. ``` Element ::= EmptyElemTag |