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 rpn.rb [GitHub] [Download]
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" rpn.hs [GitHub] [Download]
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.
