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    <p>This is a well-known gotcha about contexts for data declaration. If you define <code>data Ord a =&gt; Tree a = ...</code> all it does is force any function that mentions <code>Tree a</code> to have an <code>Ord a</code> context. This doesn't save you any typing, but on the plus side an explicit context is clear about what's needed.</p> <h1>GADTs to the rescue!</h1> <p>The workaround is to use <a href="https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/glasgow_exts.html#generalised-algebraic-data-types-gadts" rel="nofollow noreferrer">Generalised Abstract Data Types</a> (<code>GADTs</code>). </p> <pre><code>{-# Language GADTs, GADTSyntax #-} </code></pre> <p>We can put the context on the constructor directly, by providing an explict type signature:</p> <pre><code>data Tree a where EmptyTree :: (Ord a,Eq a) =&gt; Tree a Node :: (Ord a,Eq a) =&gt; a -&gt; Tree a -&gt; Tree a -&gt; Tree a </code></pre> <p>and then whenever we pattern match with <code>Node a left right</code> we get an implicit <code>(Ord a,Eq a)</code> context, just like you want, so we can start to define <code>treeInsert</code> like this:</p> <pre><code>treeInsert :: a -&gt; Tree a -&gt; Tree a treeInsert a EmptyTree = Node a EmptyTree EmptyTree treeInsert a (Node top left right) | a &lt; top = Node top (treeInsert a left) right | otherwise = Node top left (treeInsert a right) </code></pre> <h2>Deriving stuff</h2> <p>If you just add <code>deriving Show</code> there, you get an error:</p> <pre><code>Can't make a derived instance of `Show (Tree a)': Constructor `EmptyTree' must have a Haskell-98 type Constructor `Node' must have a Haskell-98 type Possible fix: use a standalone deriving declaration instead In the data type declaration for `Tree' </code></pre> <p>That's a pain, but like it says, if we add the <code>StandaloneDeriving</code> extension (<code>{-# Language GADTs, GADTSyntax, StandaloneDeriving #-}</code>) we can then do stuff like</p> <pre><code>deriving instance Show a =&gt; Show (Tree a) deriving instance Eq (Tree a) -- wow </code></pre> <p>and everything works out ok. The wow was because the implicit <code>Eq a</code> context means we don't need an explicit <code>Eq a</code> on the instance.</p> <h2>The context only comes from contstructors</h2> <p>Bear in mind that you only get the implicit context from using one of the constructors. (Remember that's where the context was defined.)</p> <p>This is actually why we needed the context on the <code>EmptyTree</code> constructor. If we'd just put <code>EmptyTree::Tree a</code>, the line</p> <pre><code>treeInsert a EmptyTree = Node a EmptyTree EmptyTree </code></pre> <p>wouldn't have an <code>(Ord a,Eq a)</code> context from the left hand side of the equation, so the instances would be missing from the right hand side, where they're needed for the <code>Node</code> constructor. That would be an error, so it's helpful in this case to keep the contexts consistent.</p> <p>This also means that you can't have</p> <pre><code>treeMake :: [a] -&gt; Tree a treeMake xs = foldr treeInsert EmptyTree xs </code></pre> <p>you'll get a <code>no instance for (Ord a)</code> error, because <em>there's no constructor on the left hand side to give you the <code>(Ord a,Eq a)</code> context</em>.</p> <p>That means you still need </p> <pre><code>treeMake :: Ord a =&gt; [a] -&gt; Tree a </code></pre> <p>There's no way round it this time, sorry, but on the plus side, this may well be the only tree function you'll want to write with no tree argument. <em>Most</em> tree functions will take a tree on the left hand side of the definition and do somthing to it, so you'll have the implicit context most of the time.</p>
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    1. CO@Satvik It won't work on `mkTree` because there's no `Tree a` constructor on the left hand side, so you don't get the implicit context, which only arises from the constructor. It's a good point, though, so I'll edit something in about it, thanks.
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    2. CO@Satvik Done - does the last section explain OK?
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    3. COYeah. It explains it fine.
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