如何定义引用其定义的递归数据类型

Question

I want to write a data type to evaluate the expressions like this:

a is evaluated to a

a + b * c / d -e is evaluated to a + (b * (c / (d - e)))

So the first argument is always a number and the second one is either a number or an expression

I have tried to define a data type like this

 data Exp  = Single Int
          | Mult (Single Int) Exp

But it gives me this compilation error:

    Not in scope: type constructor or class ‘Single’
    A data constructor of that name is in scope; did you mean DataKinds?
  |         
9 |           | Mult (Single Integer ) Exp 
  |            

I can define it like this:

data Exp  = Single Integer
          | Mult Exp  Exp

But it does not give the precise definition of the Type I want. How can I define this?

Answer 1

But it does not give the precise definition of the Type I want.

Single a is not a type. Single is a data constructor . So Single a does not make much sense.

You can use Exp here as first parameter, or if you want to restrict the first operand, you can use:

data Exp a = Single a | Mult  (Exp a)

Indeed, since Single a just wraps an a , you can use an a as first parameter of Mult . The Mult data constructor context, makes it clear how to interpret that a .

If you want to allow multiplying two Exp a s, then you can define this as:

data Exp a = Single a | Mult  (Exp a)

You can use generic abstract data types (GADTs) to make finer specifications when two expressions can be multiplied.