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KataBankOCR checksum at the type level
/**
* We can use the Scala type system (with help from Miles Sabin's Shapeless
* library) to solve the bank account number validation problem in the second
* user story of the KataBankOCR kata on Coding Dojo:
*
* http://codingdojo.org/cgi-bin/wiki.pl?KataBankOCR
*
* By Travis Brown in response to a question by Paul Snively on the Shapeless
* Dev mailing list:
*
* https://groups.google.com/d/msg/shapeless-dev/Q0VezBW2bhQ/RKF6uGljwroJ
*
* Tested with Scala 2.9.2 and Shapeless 1.2.3.
*/
import shapeless._, Nat._
// Evidence that the sum of (each item in L multiplied by (its distance from
// the end of the list plus one)) modulo eleven is S.
trait HasChecksum[L <: HList, S <: Nat]
implicit object hnilHasChecksum extends HasChecksum[HNil, _0]
implicit def hlistHasChecksum[
H <: Nat, T <: HList, S <: Nat,
TL <: Nat, TS <: Nat,
HL <: Nat, HS <: Nat
](implicit
tl: LengthAux[T, TL],
ts: HasChecksum[T, TS],
hl: ProdAux[H, Succ[TL], HL],
hs: SumAux[HL, TS, HS],
sm: ModAux[HS, _11, S]
) = new HasChecksum[H :: T, S] {}
// Check that the list has nine elements and a checksum of zero.
def isValid[L <: HList](l: L)(implicit
len: LengthAux[L, _9],
hcs: HasChecksum[L, _0]
) {}
// Now the following valid sequence (an example from the kata) compiles:
isValid(_3 :: _4 :: _5 :: _8 :: _8 :: _2 :: _8 :: _6 :: _5 :: HNil)
// But these invalid sequences don't:
// isValid(_3 :: _1 :: _5 :: _8 :: _8 :: _2 :: _8 :: _6 :: _5 :: HNil)
// isValid(_3 :: _4 :: _5 :: _8 :: _8 :: _2 :: _8 :: _6 :: HNil)
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