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here's a full code example:

    import Data.String

    -- takes two integers, and a proof that x < y, and yields an integer
    add : 
      (x : Integer) -> 
      (y : Integer) -> 
      (prf : x < y = True) ->     -- require a proof that that x < y
      Integer
    add x y prf = x + y

    main : IO ()
    main = do
      sx <- getLine -- read string from input
      sy <- getLine -- read string from input
      let Just x = parseInteger sx -- assuming int parse is ok, else error
      let Just y = parseInteger sy -- assuming int parse is ok, else error
      case decEq (x < y) True of   -- decEq constructs a proof if x < y is True
        Yes prf => print (add x y prf)
        No => putStrLn "no prf, x is not less than y"
lets say I mess up the sign of the comparison on the case line and write decEq (x > y) instead... then I'd get a type error

    When checking argument prf to function Main.add:
    Type mismatch between
                x > y = True (Type of prf)
        and
                x < y = True (Expected type)
there's no way to construct the prf value artificially, or sneak in different parameters that are unrelated to the prf value.

it's either a compile error or it's valid.




that is pretty awesome




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