open Format
open Syntax
open Support.Error
open Support.Pervasive

(* ------------------------   EVALUATION  ------------------------ *)

let rec isval ctx t = match t with
    TmAbs(_,_,_,_) -> true
  | _ -> false

exception NoRuleApplies

let rec eval1 ctx t = match t with
    TmApp(fi,TmAbs(_,x,tyT11,t12),v2) when isval ctx v2 ->
      termSubstTop v2 t12
  | TmApp(fi,v1,t2) when isval ctx v1 ->
      let t2' = eval1 ctx t2 in
      TmApp(fi, v1, t2')
  | TmApp(fi,t1,t2) ->
      let t1' = eval1 ctx t1 in
      TmApp(fi, t1', t2)
  | _ -> 
      raise NoRuleApplies

let rec eval ctx t =
  try let t' = eval1 ctx t
      in eval ctx t'
  with NoRuleApplies -> t

(* ------------------------   SUBTYPING  ------------------------ *)

let rec subtype tyS tyT =
   (=) tyS tyT ||
   match (tyS,tyT) with
     (_,TyTop) -> 
       true
   | (TyBot,_) -> 
       true
   | (TyArr(tyS1,tyS2),TyArr(tyT1,tyT2)) ->
       (subtype tyT1 tyS1) && (subtype tyS2 tyT2)
   | (_,_) -> 
       false

(* ------------------------   TYPING  ------------------------ *)

let rec typeof ctx t =
  match t with
    TmVar(fi,i,_) -> getTypeFromContext fi ctx i
  | TmAbs(fi,x,tyT1,t2) ->
      let ctx' = addbinding ctx x (VarBind(tyT1)) in
      let tyT2 = typeof ctx' t2 in
      TyArr(tyT1, tyT2)
  | TmApp(fi,t1,t2) ->
      let tyT1 = typeof ctx t1 in
      let tyT2 = typeof ctx t2 in
      (match tyT1 with
          TyArr(tyT11,tyT12) ->
            if subtype tyT2 tyT11 then tyT12
            else error fi "parameter type mismatch" 
        | TyBot -> TyBot
        | _ -> error fi "arrow type expected")