Haskell pattern matching with guards

Question

Suppose I want to model a tree structure in Haskell with

data Tree = Null | Node Tree Integer Tree deriving Show

and I'd like to test if every entry is, say, less than 10. I thought I would use pattern matching and write

isSmall :: Tree -> Bool
isSmall _ 
  | Null = True
  | (Node a b c) = if b >= 10
                   then False
                   else isSmall a && isSmall c

However it gives errors about a, b, and c being out of scope. I would have thought putting them in the guards would basically put them in the scope. Is this not how you're supposed to do pattern matching in Haskell? I've looked around for examples that would guide me but I haven't found any examples of pattern matching in guards that uses a data structure composed of several other data structures.

The error:

test.hs:24:6: Not in scope: data constructor ‘Node’

test.hs:24:11: Not in scope: ‘a’

test.hs:24:13: Not in scope: ‘b’

test.hs:24:15: Not in scope: ‘c’

test.hs:24:27: Not in scope: ‘b’

test.hs:26:38: Not in scope: ‘a’

test.hs:26:57: Not in scope: ‘c’

Answer 1

Is this not how you're supposed to do pattern matching in Haskell?

No. Guards are boolean expressions, not patterns.

You can do pattern matching like this:

isSmall :: Tree -> Bool
isSmall Null = True
isSmall (Node a b c) = b < 10 && isSmall a && isSmall c

... or like this:

isSmall :: Tree -> Bool
isSmall x = case x of
  Null -> True
  Node a b c -> b < 10 && isSmall a && isSmall c

... or even like this:

{-# LANGUAGE LambdaCase #-}

isSmall :: Tree -> Bool
isSmall = \case
  Null -> True
  Node a b c -> b < 10 && isSmall a && isSmall c

(using the LambdaCase language extension). This is perhaps closest to your original attempt.

That said, it is possible to embed patterns in guards by using <-. This is known as "pattern guards":

isSmall :: Tree -> Bool
isSmall x 
  | Null <- x = True
  | Node a b c <- x = b < 10 && isSmall a && isSmall c

However, this syntax doesn't buy you much here. You still have to give the argument a name (x in this case) and you have to explicitly say <- x everywhere. It would be clearer to use pattern matching directly (using case or multiple function equations).

Answer 2

As indicated in the comments, this is incorrect pattern matching. Here is one way to achieve what you seem to be looking for:

isSmall :: Tree -> Bool
isSmall Null         = True
isSmall (Node a b c) = if b >= 10
                       then False
                       else isSmall a && isSmall c

You also get another error by doing it the way you posted in the question:

* Couldn't match expected type `Bool' with actual type `Tree'
* In the expression: (Node a b c)
  In a stmt of a pattern guard for
                 an equation for `isSmall':
    (Node a b c)
  In an equation for `isSmall':
      isSmall _
        | Null = True
        | (Node a b c) = if b >= 10 then False else isSmall a && isSmall c

This indicates that the expression inside the guard statements must be of type Bool but you are providing a Tree (either Null or Node).