Verifying program correctness using phantom types in Haskell -

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suppose i'm working code of stack machine, can simple operations (push constant, add, mul, dup, swap, pop, convert types) on ints , doubles.

now program i'm writing takes description in other language , translates code stack machine. need calculate maximum size of stack.

i suspect it's possible use haskell type checker eliminate bugs, e.g.:

  • popping empty stack
  • multiplying doubles using int multiplication

i thought declare, example: 

dup :: stack (a :%: b) -> stack (a :%: b :%: b) int2double :: stack (a :%: sint) -> stack (a :%: sdouble)

and on. don't know how generate code , calculate stack size.

is possible this? , simple/convenient/worth it?

see chris okasaki's "techniques embedding postfix languages in haskell": http://www.eecs.usma.edu/webs/people/okasaki/pubs.html#hw02

also, this:

{-# language typeoperators #-} module stacks  data :* b = :* b deriving show data nilstack = nilstack deriving show  infixr 1 :*  class stack     stacksize :: -> int  instance stack b => stack (a :* b)     stacksize (_ :* x) = 1 + stacksize x  instance stack nilstack     stacksize _ = 0  push :: stack b => -> b -> :* b push = (:*)  pop :: stack b => :* b -> (a,b) pop (x :* y) = (x,y)  dup :: stack b => :* b -> :* :* b dup (x :* y) = x :* x :* y  liftbiop :: stack rest => (a -> b -> c) -> :* b :* rest -> c :* rest liftbiop f (x :* y :* rest) = push (f x y) rest  add :: (stack rest, num a) => :* :* rest -> :* rest add = liftbiop (+)  {- demo:   *stacks> stacksize  $ dup (1 :* nilstack) 2  *stacks> add $ dup (1 :* nilstack) 2 :* nilstack  -}

since stack varies in type, can't pack regular state monad (although can pack parameterized monad, that's different story) other that, should straightforward, pleasant, , statically checked.


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