All numerals for computations are stored in a stack of arbitrary size

Starts the main recursion with empty stack

Gets command and updates stack according to user input.

The command "show" will print the stack. All other inputs will be passed to parsing. At the end calc is called with the updated stack.

Returns string representation of the first item on the stack. If the stack is empty, the string Nothing is returned.

Safely updates the stack by checking first if Maybe Stack is Nothing the user will be informed and the old stack is returned. Otherwise the stack is extracted and returned.

Takes a list of commands and applys them sequencially to the stack.

If a computation fails, Nothing is returned.

Examples:

>>> parsing [] $ words "3 2 ^ 4 2 ^ + sqrt"
Just [5.0]
>>> parsing [2.0] ["/"] -- Too few arguments on stack!
Nothing

Parses command and applys the corresponding function to the first elements of the stack.

If the command is not recognised or there are too few numbers on the stack, Nothing is returned.

Examples:

>>> let stack = [-6.0, 2.0] :: Stack
>>> pars stack "*"
Just [-12.0]
>>> pars stack "abs"
Just [6.0,2.0]
>>> pars stack ".."
Just [-6.0,-5.0,-4.0,-3.0,-2.0,-1.0,0.0,1.0,2.0]
>>> pars stack "katze" -- I can't imagine such a command exists
Nothing
>>> pars stack "4.3"
Just [4.3,-6.0,2.0]
>>> pars stack "4,3" -- Damn you German decimal separator
Nothing

Checks whether a string contains a numeral

A Double implementation for the factorial

Note:

Doubles will be truncated.

Example:

>>> fac 4.2
24.0

A Double implementation for "n choose r"

Note:

Doubles will be truncated.

The backbone of nCr

Safely retrieves (l - i - 1)-th value of a list

Note:

The function retrieves this value because it is the i-th value that was pushed to the stack

Example

>>> let xs = [1..5]
>>> getMaybe xs 0
Just 5
>>> getMaybe xs 1
Just 4
>>> getMaybe xs 5 -- Index to large
Nothing
>>> getMaybe xs (-2)
Nothing