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<h1 id="doc-page-title">Type System</h1>
<div id="doc-page-container">
<p>The types are defined in <a href="https://github.com/lampepfl/dotty/blob/master/src/dotty/tools/dotc/core/Types.scala">dotty/tools/dotc/core/Types.scala</a></p>
<h2><a href="#class-diagram" id="class-diagram">Class diagram</a></h2>
<ul>
<li><a href="https://github.com/samuelgruetter/dotty/blob/classdiagrampdf/dotty-types.pdf">PDF</a>, generated with <a href="https://github.com/samuelgruetter/scaladiagrams/tree/print-descendants">a fork of scaladiagrams</a></li>
</ul>
<h2><a href="#proxy-types-and-ground-types" id="proxy-types-and-ground-types">Proxy types and ground types</a></h2>
<p>A type which inherits <code>TypeProxy</code> is a proxy for another type accessible using
the <code>underlying</code> method, other types are called <em>ground</em> types and inherit
<code>CachedGroundType</code> or <code>UncachedGroundType</code>.</p>
<p>Here's a diagram, copied from <a href="https://github.com/lampepfl/dotty/blob/master/src/dotty/tools/dotc/core/Types.scala">dotty/tools/dotc/core/Types.scala</a>:</p>
<pre><code>Type -+- ProxyType --+- NamedType ----+--- TypeRef
| | \
| +- SingletonType-+-+- TermRef
| | |
| | +--- ThisType
| | +--- SuperType
| | +--- ConstantType
| | +--- MethodParam
| | +----RecThis
| | +--- SkolemType
| +- PolyParam
| +- RefinedOrRecType -+-- RefinedType
| | -+-- RecType
| +- HKApply
| +- TypeBounds
| +- ExprType
| +- AnnotatedType
| +- TypeVar
| +- PolyType
|
+- GroundType -+- AndType
+- OrType
+- MethodType -----+- ImplicitMethodType
| +- JavaMethodType
+- ClassInfo
|
+- NoType
+- NoPrefix
+- ErrorType
+- WildcardType
</code></pre>
<h2><a href="#representations-of-types" id="representations-of-types">Representations of types</a></h2>
<table>
<thead>
<tr><th>Type</th><th>Representation</th></tr>
</thead>
<tbody>
<tr><td><code>p.x.type</code></td><td><code>TermRef(p, x)</code></td></tr>
<tr><td><code>p#T</code></td><td><code>TypeRef(p, T)</code></td></tr>
<tr><td><code>p.x.T</code> == <code>p.x.type#T</code></td><td><code>TypeRef(TermRef(p, x), T)</code></td></tr>
<tr><td><code>this.type</code></td><td><code>ThisType</code></td></tr>
<tr><td><code>A & B</code></td><td><code>AndType(A, B)</code></td></tr>
<tr><td>`A</td><td>B`</td></tr>
<tr><td><code>=> T</code></td><td><code>ExprType(T)</code></td></tr>
<tr><td><code>p { refinedName }</code></td><td><code>RefinedType(p, refinedName)</code></td></tr>
<tr><td>type of the value <code>super</code></td><td><code>SuperType</code></td></tr>
<tr><td><code>type T >: A <: B</code></td><td><code>TypeRef</code> with underlying type <code>RealTypeBounds(A, B)</code></td></tr>
<tr><td><code>type T = A</code></td><td><code>TypeRef</code> with underlying type <code>TypeAlias(A)</code></td></tr>
<tr><td><code>class p.C ...</code></td><td><code>ClassInfo(p, C, ...)</code></td></tr>
</tbody>
</table>
<h3><a href="#representation-of-methods" id="representation-of-methods">Representation of methods</a></h3>
<pre><code class="language-scala">def f[A, B <: Ord[A]](x: A, y: B): Unit
</code></pre>
<p>is represented as:</p>
<pre><code class="language-scala">val p = PolyType(List("A", "B"))(
List(TypeBounds(Nothing, Any),
TypeBounds(Nothing,
RefinedType(Ordering,
scala$math$Ordering$$T, TypeAlias(PolyParam(p, 0))))),
m)
val m = MethodType(List("x", "y"),
List(PolyParam(p, 0), PolyParam(p, 1)))(Unit)
</code></pre>
<p>(This is a slightly simplified version, e.g. we write <code>Unit</code> instead of
<code>TypeRef(TermRef(ThisType(TypeRef(NoPrefix,<root>)),scala),Unit)</code>).</p>
<p>Note that a PolyParam refers to a type parameter using its index (here A is 0
and B is 1).</p>
<h2><a href="#subtyping-checks" id="subtyping-checks">Subtyping checks</a></h2>
<p><code>topLevelSubType(tp1, tp2)</code> in <a href="https://github.com/lampepfl/dotty/blob/master/src/dotty/tools/dotc/core/TypeComparer.scala">dotty/tools/dotc/core/TypeComparer.scala</a>
checks if <code>tp1</code> is a subtype of <code>tp2</code>.</p>
<h3><a href="#type-rebasing" id="type-rebasing">Type rebasing</a></h3>
<p><strong>FIXME</strong>: This section is no longer accurate because
<a href="https://github.com/lampepfl/dotty/pull/331">https://github.com/lampepfl/dotty/pull/331</a> changed the handling of refined
types.</p>
<p>Consider <a href="https://github.com/lampepfl/dotty/blob/master/tests/pos/refinedSubtyping.scala">tests/pos/refinedSubtyping.scala</a></p>
<pre><code class="language-scala">class Test {
class C { type T; type Coll }
type T1 = C { type T = Int }
type T11 = T1 { type Coll = Set[Int] }
type T2 = C { type Coll = Set[T] }
type T22 = T2 { type T = Int }
var x: T11 = _
var y: T22 = _
x = y
y = x
}
</code></pre>
<p>We want to do the subtyping checks recursively, since it would be nice if we
could check if <code>T22 <: T11</code> by first checking if <code>T2 <: T1</code>. To achieve this
recursive subtyping check, we remember that <code>T2#T</code> is really <code>T22#T</code>. This
procedure is called rebasing and is done by storing refined names in
<code>pendingRefinedBases</code> and looking them up using <code>rebase</code>.</p>
<h2><a href="#type-caching" id="type-caching">Type caching</a></h2>
<p>TODO</p>
<h2><a href="#type-inference-via-constraint-solving" id="type-inference-via-constraint-solving">Type inference via constraint solving</a></h2>
<p>TODO</p>
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