How to translate logical notation to Haskell syntax

Question

I\'ve recently picked up Haskell at uni and I\'m working my way through a set of exercises, here\'s a snippet of one that I can\'t make sense of:

\"Consider the followin

Answer 1

How do I declare type or data(not a variable) for fixed values, namely 0-9?

You can define a type, like

data Digit = Zero | One | Two | Three | Four | Five | Six | Seven | Eight | Nine deriving (Eq, Show)

This represents the num in your problem. Obviously we cannot use 0, 1, 2, 3, ... since they are already interpreted as numbers in Haskell.

Then, you can define

data Number = Single Digit | Many Digit Number deriving (Eq, Show)

which is equivalent to int in your problem. This type represents one (Single ...) or more (Many ...) digits, which together make a one decimal number. For example, with these data types a number 361 would be Many Three (Many Six (Single One)).

Also, how can I put symbols like - or + in a declaration?

There is no way to put those symbols in type or data declarations. You can use, however, names for the operations, like Sum, Sub and Mul. Then the expr of the grammar of your problem would translate to

data Expr   = Lit Number
            | Sub Expr Expr
            | Sum Expr Expr
            | Mul Expr Expr
            deriving (Eq, Show)

If we would have a string "+ (- (2 5) (1 3)) 3", which represents an expression in the prefix calculator language of your problem , it would be parsed to Sum (Sub (Lit (Many Two (Single Five))) (Lit (Many One (Single Three)))) (Single Three).