I recently got fed up trying to understand my mortgage using excel. After twenty minutes guddling with cells and individual values, I felt the need to create higher-level abstractions such as “mortgage” and “payment strategy”. I also wanted to create a list of possible repayment strategies and easily compare them to see how it affects the loan duration and total interest payed. This is possible in excel, but no fun.<\/p>\n
So, fast-forward to the end of an evening’s hacking with Haskell. I now have hmortgage<\/a>, a EDSL for expressing payment strategies and code which will expand out a mortgage into monthly steps, like this:<\/p>\n ie. if you overpay by \u00a32 each month, and pay an initial lump sum of \u00a3200, you’ll save about \u00a3140 overall and will repay the mortgage nearly 4 years early.<\/p>\n There’s a few points of haskelly interest in this code, mostly inspired by stuff I read a few years ago – behaviors in FRP, and SPJ’s “composing contracts” paper.<\/p>\n I have a few primitive payment strategies, which can be combined into more complex strategies:<\/p>\n The dsl is a shallow embedding; it represents the monthly payment plan as a function from month-number to the payment amount, ie. Integer -> Currency. There’s a problem with this approach – the only thing you can do with a function is apply it to some arguments. This is fine for finding the payment for a particular month, but I would also like to derive a textual description of the payment plan – which isn’t possible with functions.<\/p>\n From stuff I’ve read previously, I think my two options are:<\/p>\n Initially, the only way I had to create a ‘Currency’ value was via the ‘pounds’ function. In haskell, the function precedes the argument, hence it looks like “pounds 20”. The source code would read nicer if I could write this as “20 pounds” like we do in english. I didn’t think this was possible in Haskell.<\/p>\n Then I remembered seeing Lennart Augustsson’s crazy embedding of BASIC into Haskell<\/a>. In particular, he had code which looked like this:<\/p>\n How the heck does that parse? It’s using ‘do’ notation, so “20 END” must have a type in the Monad class. But, as I understood things, “x y” means “apply the (function) value x to value y”. And “20” doesn’t look much like a function to me.<\/p>\n Digging into the source, I found this:<\/p>\n\r\nWe are looking at loan of \u00a31000.00 at 5.0% over 10y, which has required monthly payment of \u00a310.58\r\nBaseline:\r\n Total interest: \u00a3272.97 Total payments: \u00a31272.97 Duration=10y 1m\r\nOverpayment scenario \"2 pm, 200 initial\":\r\n Total interest: \u00a3132.09 Total payments: \u00a31132.09 Duration=6y 3m\r\n Compared to baseline: interest=\u00a3-140.88, payments=\u00a3-140.88, duration=-3y 10m\r\nFor month 1, balance: \u00a31000.00 -> \u00a3791.58 (interest: \u00a34.16, payment: \u00a3212.58)\r\nFor month 2, balance: \u00a3791.58 -> \u00a3782.29 (interest: \u00a33.29, payment: \u00a312.58)\r\nFor month 3, balance: \u00a3782.29 -> \u00a3772.96 (interest: \u00a33.25, payment: \u00a312.58)\r\nFor month 4, balance: \u00a3772.96 -> \u00a3763.60 (interest: \u00a33.22, payment: \u00a312.58)\r\n<\/pre>\n
Combinators for payment strategies<\/h3>\n
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Shallow embedding of DSL<\/h3>\n
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Crazy Lennart-inspired postfix operators<\/h3>\n
\r\nrunBasic $ do\r\n 10 PRINT \"HELLO\"\r\n 20 END\r\n<\/pre>\n
\r\n-- 10 END\r\ninstance Num (END -> Expr a) where\r\n fromInteger i c = ...\r\n<\/pre>\n