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    <p>Just to make things more explicit, this data type:</p> <pre><code>data List a = Cons a (List a) | Nil </code></pre> <p>...has the same structure as the built-in list type, but without the (nicer, but potentially confusing) special syntax. Here's what some correspondences look like:</p> <ul> <li><code>List</code> = <code>[]</code>, type constructors with kind <code>* -&gt; *</code></li> <li><code>List a</code> = <code>[a]</code>, types with kind <code>*</code></li> <li><code>Nil</code> = <code>[]</code>, values with polymorphic types <code>List a</code> and <code>[a]</code> respectively</li> <li><code>Cons</code> = <code>:</code>, data constructors with types <code>a -&gt; List a -&gt; List a</code> and <code>a -&gt; [a] -&gt; [a]</code> respectively</li> <li><code>Cons 5 Nil</code> = <code>[5]</code> or <code>5:[]</code>, single element lists</li> <li><code>f Nil = ...</code> = <code>f [] = ...</code>, pattern matching empty lists</li> <li><code>f (Cons x Nil) = ...</code> = f [x] = ...`, pattern matching single-element lists</li> <li><code>f (Cons x xs) = ...</code> = <code>f (x:xs) = ...</code>, pattern matching non-empty lists</li> </ul> <p>In fact, if you ask ghci about <code>[]</code>, it tells you pretty much the same definition:</p> <pre><code>&gt; :i [] data [] a = [] | a : [a] -- Defined in GHC.Types </code></pre> <p>But you can't write such a definition yourself because the list syntax and its "outfix" type constructor is a special case, defined in the language spec.</p>
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    1. POWhat is [] (list constructor) in Haskell?
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    1. COCould you explain more about the last part `a:[a]` rather than `a:[]` is the empty list `[]` typed `[a]`, the first part of the definition `data [] = [] | a : [a]`, would leave me to believe it is `[]`. Does `[]`, also suffice the requirement for `[a]`?
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      1. USEvan Carroll
    2. COI'm not sure what you're asking. In `a:[a]`, `:` is defining the data constructor (like `Cons`), and `[a]` is specifying the type of an argument to the constructor (like `List a`). In the first part of the definition, `[]` is a data constructor with no arguments, like `Nil`. Both parts produce values of type `[a]`, because that's exactly what is being defined!
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    3. COPerhaps what's tripping you up is that *data constructors* don't have to take parameters representing all (or any) of the parameters to the *type constructor*? In `data Either a b = Left a | Right b`, the data constructor `Left a` still creates a value of type `Either a b`, even though there's no `b` to be had. Same goes for `Nothing` and `[]`. You could even have something like `data NoValue a b c d e f = Lonely`. Even though it holds no values, `Lonely` is still haunted by the specter of all those type parameters, keeping it distinct from any `Lonely`s with different types.
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