Can someone explain this function and how to type it in Haskell (infix, :-:)

Question

infixr 5 :-:  
data List a = Empty | a :-: (List a) deriving (Show, Read, Eq, Ord)  

we just wrote a:-: (List a) instead of Cons a (List a). Now, we can write out lists in our list type like so:

ghci> 3 :-: 4 :-: 5 :-: Empty  
(:-:) 3 ((:-:) 4 ((:-:) 5 Empty))  
ghci> let a = 3 :-: 4 :-: 5 :-: Empty  
ghci> 100 :-: a  
(:-:) 100 ((:-:) 3 ((:-:) 4 ((:-:) 5 Empty)))  

I get that:-: is supposed to work like Cons but I don't really get why we are allowed to do that and how to actually type infixr 5:-: .

Answer 1

I get that :-: is supposed to work like Cons but I don't really get why we are allowed to do that …

Because the Haskell report says so. In the grammar the constr is a data constructor. The constr can be a con followed by zero, one or more types, a con followed by record syntax, or a type, an operator conop followed by another type. This is defined as :

 constr → con [!] atype 1 … [!] atype k |  (btype | ! atype) conop (btype | ! atype) |  con { fielddecl 1 , …, fielddecl n } 

The conop can be an operator consym , or an infix variant of an identifier between backticks, like `foo` , which is written in the grammar section as:

 conop → consym |  ` conid ` 

The grammar specifies that a consym is defined as:

 consym → (: {symbol })〈reservedop〉 

so a colon followed by a sequence of symbols and such symbol should not be a reserved operator like : , :: , etc.

This thus means that except for the reserved operators, you can use operators that start with a colon ( : ) as a data constructor.

… and how to actually type infixr 5:-: .

You can write multiline statements by surrounding these with :{ and :} :

ghci> :{
| infixr 5 :-:  
| data List a = Empty | a :-: (List a) deriving (Show, Read, Eq, Ord)
| :}