As previously mentioned, I am learning haskell. In that endeavor, I am trying to cross the chasm from “tutorial following” to actual real projects (albeit, very small projects). My latest project is a simple simulator for my prosper.com account. For those who don’t know, prosper.com allows people to make smallish loans to each other with terms of three year repayment. Money amounts range from $50 to $25,000, and interest rates are negotiated in an auction. As a lender, I want to know what return on investment I am likely to receive given various scenarios.

Now on to the show

My first stab at the simulator was done in ruby. This gives me a working model, and the ability to compare and contrast some of the design requirements that functional programming, and specifically haskell will impose.

Ruby

First I needed a function to generate random rates, simulating the auction style rate negotiation.
def get_new_rate
   return MIN_RATE + rand(RATE_WINDOW)
end


where MIN_RATE is defined as the minimum rate I am willing to lend at (8.0%), and RATE_WINDOW is defined as the spread between my minimum rate, and the highest rate I am interested in lending at (20.0%).

Second off, I needed a function to generate a number of loans given a certain account balance.
def add_loans(loans, account_balance)
  new_loan_count = account_balance / INITIAL_PRINCIPLE
  new_loan_count.to_i.times do
    rate = get_new_rate
    loans << {:principle => INITIAL_PRINCIPLE, :rate => rate, :min_payment => calc_minimum_payment(INITIAL_PRINCIPLE,rate)}
    account_balance -= INITIAL_PRINCIPLE
  end
  account_balance
end


where INITIAL_PRINCIPLE is set to the amount that I am willing to lend ($50) in each loan. (Read this for an explanation of why I only lend $50.)
This function calculates how many loans I can generate from the given account balance, then creates each one. The new loans are appended to the collection of loans that was passed in as an argument. The calc_minimum_payment function simply determines what the minimum payment will be each month.

I then needed a function that would calculate the payment on the loan – particularly at the end of the loan when the payment may be less than the minimum payment.
def calc_payment(loan, months=1)
  if loan[:principle] < loan[:min_payment]
    payment = loan[:principle]
  loan[:principle] = 0
  return payment
  end
  
  interest = loan[:principle] * loan[:rate] / 100.0 / 12
  loan[:principle] -= loan[:min_payment] - interest
  return loan[:min_payment]
end


Given these functions, I can now create the simulation
account_balance = ARGV[0].to_f if ARGV[0]
account_balance ||= 0.0
  
monthly_deposit = ARGV[1].to_f if ARGV[1]
monthly_deposit ||= 100.0
  
number_of_years = ARGV[2].to_i if ARGV[2]
number_of_years ||= 1

First grab the scenario parameters from the cmdline. monthly_deposit is how much money to add to the account balance each month (in addition to the payments from the outstanding loans)

loans = []
for i in (1..number_of_years*12)
  old_loans = loans.size
  account_balance = add_loans loans, account_balance
  print "Month #{i}\n"
  print "Number of loans: #{loans.size} (#{loans.size - old_loans})\n"
  print "Average Rate: #{calc_average(loans.collect {|i| i[:rate]})}\n"
  income= loans.inject(0) {|bal, i| bal + calc_payment(i)}
  print "Account balance: #{account_balance}\n"
  print "Income: #{income}\n"
  account_balance += income + monthly_deposit
  print "Account value: #{loans.collect {|i| i[:principle]}.inject(account_balance) {|sum, i| sum + i}}\n"
  print "\n"
  loans.delete_if {|item| item[:principle] == 0}
end

Then run the simulation, and print out various statistics for each month of the simulation.

So that’s the simulator in ruby. It is not “perfectly optimized” for ruby, because I wanted to keep it somewhat close to the structure that I would use for haskell. See the link below for full source.

Haskell

I tried to keep the architecture of the haskell version as close to the ruby approach as was possible. As a consequence, many haskell people may look at this and balk. My apologies in advance.
First I needed some constants and a struct to keep the relevant loan data in
minRate = 8.0
maxRate = 20.0
initialPrinciple = 50.0
periods = 36
  
data Loan = Loan {principle :: Double, rate :: Double, minPayment :: Double}


Then comes the function used to simulate the rate auctions
-- Generate a random rate within the "rate window"
getNewRate :: IO Double
getNewRate = do randomRIO (minRate, maxRate)


Where I calculate some random number between the minRate and maxRate. Note the type – IO Double. For all you non-haskellites, that means that the function will be using a monad inside of itself. In this case, the monad is randomRIO. The monad allows you to call randomRIO multiple times, and get different numbers each time. Useful that!

Then I have the loan creation functions

-- figure out what the minimum payment will be on a given loan
calcMinimumPayment :: Double -> Double -> Double
calcMinimumPayment p i = (r * p *(1+r)^periods) / ((1+r)^periods - 1)
                         where r = i / 12.0 / 100
 
-- create a new loan
newLoan :: Double -> IO Loan
newLoan p = do
          i <- getNewRate
          let m = calcMinimumPayment p i
          return (Loan p i m)

As in the ruby version, create a new loan, then populate the structure with the rate and minimum payment. Note the type for calcMinimumPayment doesn’t specify IO… that means this is a “clean function” and can be called anywhere. newLoan however is a monad function – because it calls getNewRate. Since newLoan uses a monad function, it has to return a monad itself.

Here’s where things had to deviate from how I did them in ruby. Since haskell has immutable values, I couldn’t modify the loans. I had to create new loans, and collect them into a new structure. Here is where the new loan is created, given the state of the provided loan.
-- Given a loan, make a payment and create a new loan with the remaining principle
calcPayment :: Loan -> Loan
calcPayment l = if principle l > minPayment l
      then Loan (principle l - p) (rate l) (minPayment l)
      else Loan 0 (rate l) (principle l) -- mark this as the last payment
      where
        i = (principle l) * (rate l / 100 / 12)
        p = minPayment l - i

Again, here’s a “pure function”. It can be called anywhere, and any time.

Now, given an account balance, create as many loans as I can, and return them as a collection of Loans.
-- Take the current account balance, and make as many loans as possible from it
makeLoans :: Double -> IO [Loan]
makeLoans bal = if bal >= initialPrinciple
      then do
        l <- newLoan initialPrinciple
        ls <- makeLoans (bal - initialPrinciple)
        return ([l] ++ ls)
      else
        return []

Note the recursive call to continue building the list. I am finding that functional programming relies on recursion a lot more than OOP.

This is another portion of code where I had to deviate. Here is where I actually parse the passed in loans, and return a new array of updated loans, and a new account balance. This is probably the most un-haskellish function of the group, and definitely needs some work.
-- make payments on the given loans, and return the updated loans, and resulting total payments
collectPayments :: [Loan] -> ([Loan], Double)
collectPayments loans = (filteredLoans, payments)
      where
        clearStaleLoans = filter (\x -> minPayment x > 0) -- remove any loans that have been fully paid back
        filteredLoans = clearStaleLoans (map calcPayment loans= sum (map minPayment filteredLoans)


Then a function that runs through each iteration of the simulation – i.e. each month. This has to be its own function so that it can recursively call itself to continue the simulation.
-- run through a loan scenario, reinvesting returns for 'term' months. Print out various statistics on the account
run :: Double -> [Loan] -> Int -> Double -> IO Double
run startingBalance loans term monthlyDeposit = if term <= 0
        then return startingBalance
      else do
        l <- makeLoans startingBalance
                              let (newLoans, newPayments) = collectPayments (loans ++ l)
        let newPrinciple = (initialPrinciple * fromIntegral (length l))
        let newBalance = (startingBalance - newPrinciple + newPayments)
        let loanValue = sum (map principle newLoans)
        let averageRate = (sum (map rate newLoans)) / fromIntegral (length newLoans)
        putStr $ unlines ["Term: " ++ show term, "Loan count: " ++ show (length newLoans), "Average Rate: " ++ show averageRate, "Loan Value: " ++ show loanValue, "New balance: " ++ show newBalance, "New Principle: " ++ show newPrinciple, "New Payments: " ++ show newPayments,"---------"]
        bal <- (run (newBalance + monthlyDeposit) newLoans (term-1) monthlyDeposit)
        return bal

Note how, although run is a monad function, a majority of its processing is non-monadic. In theory each of those ‘let’ statements could run in parallel.

Finally a “main” function to get the works rolling
main :: IO ()
main = do
        args <- getArgs
        let accountBalance = if(length args > 0) then read (args !! 0) :: Double else 300.0
        let monthlyDeposit = if(length args > 1) then read (args !! 1) :: Double else 100.0
        let term = if(length args > 2) then read (args !! 2) :: Int else 1
        putStr $ unlines ["Starting balance: " ++ show accountBalance, "Starting run", "----------"]
        endingBalance <- run accountBalance [] (term * 12) monthlyDeposit
        putStr $ unlines ["Ending Balance: " ++ show endingBalance]


Summing it up

Well, comparing and contrasting these two scripts is giving me a new appreciation for both languages. Each script could be refined to better match its underlying language, but the goal was to keep the code as close as possible to maximize comparability. If enough people ask, perhaps I’ll refine each script.
Hopefully some comparison of the two scripts will help another budding haskell developer wrap their head around this powerful, but oh so different language.

Here is the full ruby source code – prosper.rb (right click – “Save As”)
Here is the full haskell source code – prosper.hs (right click – “Save As”)

-Joe

This entry was posted on Wednesday, March 26th, 2008 at 9:52 am and is filed under Ramblings, Software Development. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.