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It is known as a binary search tree: # let rec insert ( k, v ) = function | Leaf -> Node ( Leaf, ( k, v ), Leaf ) | Node ( l, ( k', v' ), r ) -> if k k' then Node ( l, ( k', v' ), insert ( k, v ) r ) else Node ( l, ( k, v ), r ) val insert : 'a * 'b -> ( 'a * 'b ) tree -> ( 'a * 'b ) tree = Larger key, we have a data structure for dictionaries which performs better Insist that the keys are unique and that a smaller key is always left of a Instead of integers, we could build a tree of key-value pairs. Let's try our new functions out: # let all = total t val all : int = 10 # let flipped = flip t val flipped : int tree = Node ( Node ( Leaf, 4, Node ( Leaf, 3, Leaf ) ), 2, Node ( Leaf, 1, Leaf ) ) # t = flip flipped - : bool = true Here, flip is polymorphic while total operates only on trees of type int tree. Pattern matching on our new constructors: # let rec total = function | Leaf -> 0 | Node ( l, x, r ) -> total l + x + total r val total : int tree -> int = # let rec flip = function | Leaf -> Leaf | Node ( l, x, r ) -> Node ( flip r, x, flip l ) val flip : 'a tree -> 'a tree = Now we can write recursive and polymorphic functions over these trees by In our example, we built an integer tree, but any type can be A Node holds a left tree, a value of type 'a,Īnd a right tree. Notice that we give the type parameter 'a before the type name (if there is Here is an OCaml data typeįor a binary tree carrying any kind of data: # type 'a tree = | Leaf | Node of 'a tree * 'a * 'a tree type 'a tree = Leaf | Node of 'a tree * 'a * 'a tree # let t = Node ( Node ( Leaf, 1, Leaf ), 2, Node ( Node ( Leaf, 3, Leaf ), 4, Leaf ) ) val t : int tree = Node ( Node ( Leaf, 1, Leaf ), 2, Node ( Node ( Leaf, 3, Leaf ), 4, Leaf ) ) Therefore, a record definition is a set of field name and type: # type point = Example: Treesĭata types may be polymorphic as well as recursive. In records, a field has a name order is no longer relevant. In tuples, a field sits at some place: first, second, third, etc. We have records, which are like labeled tuples. Next, we have tuples, which collect a fixed number of elements together: # ( 5.0, 6.5 ) - : float * float = ( 5. 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