format.fs

module Format
open System
open Type
open Exp

let rec formatType t =
  match t with
  | Num -> "num"
  | Bool -> "bool"
  | TypeError -> "TypeError"
  | Func(t1, t2) ->
    match t1 with
    | Func(_) -> String.Format("({0})->{1}", formatType t1, formatType t2)
    | _ -> String.Format("{0}->{1}", formatType t1, formatType t2)

let rec formatNumber exp =
  match exp with
  | Zero -> Some 0
  | Succ(n) -> 
    match (formatNumber n) with
    | Some(n') -> Some (n'+1)
    | _ -> None
  | _ -> None

let format exp =
  let rec format exp flg: string =
    let s =
      match exp with
      | NumericValue(e) -> 
        match formatNumber(e) with
          | Some(n) -> n.ToString()
          | _ -> "error" // unreachable
      | True -> "true"
      | False -> "false"
      | Var(s) -> s
      | Succ(e) -> String.Format ("succ {0}", format e (isApply e))
      | Pred(e) -> String.Format ("pred {0}", format e (isApply e))
      | IsZero(e) -> String.Format ("iszero {0}", format e (isApply e))
      | If(e1, e2, e3) -> String.Format ("if {0} then {1} else {2}", format e1 false, format e2 false, format e3 false)
      | App(e1, e2) -> String.Format("{0} {1}", format e1 (isAbstraction e1), format e2 (isApply e2))
      | Lambda((name, t), e) -> String.Format ("λ{0}:{1}.{2}", name, formatType t, format e false)
      | Fix((name, t), e) -> String.Format ("μ{0}:{1}.{2}", name, formatType t, format e false)
      | Error(e) ->
        match e with
        | Some(s) -> String.Format ("error({0})", s)
        | _ -> "error"
      | _ -> "error" // unreachable
    in if (flg) then "("+s+")" else s
  in format exp false