ML_Programming/polymorphic_examples.sml at master · hackath0r/ML_Programming · GitHub

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(*
  length : T1 -> T2
  xs : T1

  x : T3
  xs' : T3 list

  T1 = T3 list
  T2 = int

  T3 list -> int
  'a list -> int
*)

fun length xs =
    case xs of
	[] => 0
     | x::xs'  =>  1 + length xs'


(*
  f : T1 * T2 * T3 -> T4
  x : T1
  y : T2
  z : T3

  T4 : T1 * T2 * T3
  T4 = T2 * T1 * T3
  only way those can both be true is if T1 = T2
  put it all together: f : T1 * T1 * T3 -> T1 * T1 * T3
  'a * 'a * 'b -> 'a * 'a * 'b
*)
fun f (x,y,z) =
    if true
    then (x,y,z)
    else (y,x,z)


(*
  compose : T1 * T2 -> T3
  f : T1
  g : T2
  x : T4

  body being a function has type T3=T4->T5
  from g being passed x, T2 =T4->T6 for some T6
  from f being passed the result of g, T1=T6->T7 for some T7
  from call to f being body of anonymous function T7=T5

  put it all together: T1=T6->T5, T2=T4->T6, T3=T4->T5
  (T6->T5) * (T4->T6) -> (T4->T5)
  ('a -> 'b) * ('c -> 'a) -> ('c -> 'b)
*)

fun compose (f,g) = fn x => f(g x)