# Reverse Polish Notation (RPN) Calculator in Ruby and Haskell

2014-09-05*

A friend of mine is in DevBootCamp, an intensive coding school program designed to get students ready for real world job placement. Anyway, he was telling me how he was given an extra credit assignment: implement a RPN calculator which supports 3 functions — add, subtract, and multiply — on integer numbers. I.e., write a function evaluate() that when given a string such as "3 4 + 8 *" gives the result 56. He gave me his Ruby solution; in response, I wrote my own Ruby version and decided soon thereafter to write an equivalent Haskell version, because, why not?

## Ruby

First, the Ruby version:

def evaluate(equation_str)
stack = []
equation_str.split.each do |term|
case term
when /^\d+?$/ stack.push(term.to_i) when "+", "-", "*" if stack.size < 2 raise "stack too small for operator application" else b = stack.pop a = stack.pop op = term.to_sym c = b.send(op, a) stack.push(c) end else raise "invalid input #{term}'" end end stack end Pretty straightforward, yes? The terms variable holds an array of numbers and operators. We use a calculator stack (aptly named, stack) to untangle the RPN in a stack-based way. In the each loop, the actions depend on what term looks like. If term is a number in string form, we convert it into a real number with String#to_i, and push it into stack. If term is one of the 3 recognized operators, we remove 2 terms a and b from stack and apply the necessary operation on it with Ruby’s magic Object#send method, and push the new term c back into stack for further operations (if any, in later iterations of the while loop). Otherwise, we reject the input as an invalid term. ## Haskell Here is the Haskell version: import Data.Char (isDigit) data Term = TermInt Integer | TermOp (Integer -> Integer -> Integer) evaluate :: String -> [Integer] evaluate = evalTerms . map mkTerm . words mkTerm :: String -> Term mkTerm termStr = case termStr of "+" -> TermOp (+) "-" -> TermOp (-) "*" -> TermOp (*) _ | all isDigit termStr -> TermInt$ read termStr
| otherwise -> error \$ "invalid input " ++ termStr ++ "'"

evalTerms :: [Term] -> [Integer]
evalTerms = foldl modifyStack []
where
modifyStack stack term = case term of
TermInt n -> n : stack
TermOp op -> case stack of
(a:b:_) -> op a b : drop 2 stack
_ -> error "stack too small for operator application"

Probably the first thing to note is that we define a robust data type, Term, to encapsulate the values held in a given RPN string. We take advantage of Haskell’s functions-as-first-class-values ability, and define the TermOp constructor with it (i.e., it needs an arithmetic function (Integer -> Integer -> Integer) as an argument).

The next thing to notice is that the evaluate function is composed of smaller helper functions, mkTerm and evalTerms. mkTerm simply converts a String type into an appropriate Term type. evalTerms takes a list of Term values, and reduces it as much as possible by applying the modifyStack function over it with foldl (Haskell’s version of a single-pass loop).

When modifyStack encounters a TermInt, it pushes the number into the stack. When it encounters a TermOp, it applies that operator to the first 2 items in stack, and pushes this result back into stack. We use pattern matching with (a:b:_) to pull out the a and b values from the stack — the expression (a:b:_) means a value that matches either $[x_1, x_2]$, or $[x_1, x_2, ... , x_n]$, because the _ operator matches anything, including the empty list [] used to finalize list creation. The drop 2 stack is necessary because Haskell’s types by default are immutable.

## Thoughts

I much prefer the Haskell version.

The separation of concerns is a big win — we can easily create helper functions like mkTerm and evalTerms because of Haskell’s purity1. Haskell embraces the use of algebraic data types (i.e., Term here), and perhaps this preference lends itself to the use of helper functions that convert things from one type to another. Ruby does not have types, at least in the sense of Haskell types, so to artificially create such concepts and to implement them would be difficult.2 I mean, I really want to write equivalent mkTerm and evalTerms methods in Ruby, but my beginner skills prevent me from doing it in a simple, straightforward way. I know enough about coding to abandon “solutions” that require circuitous, complex design.

I also like how all the functions are pure and thus easy to reason about with the type signatures. Refactoring code like this is a dream.

In short, algebraic data types, the clean delegation of subtasks to helper functions, and purity make the Haskell version easier to reason about and maintain in the long run.

1. Haskell’s purity is a term of art. Look it up!

2. The closest thing to Haskell types in Ruby, in my mind, are Ruby objects. Certainly, Ruby knows the difference between two objects belonging to different classes, but to do that here would make the code much longer and offer little benefit.