%{
open Expr
open Types
%}

%token PLUS TIMES
%token TOP BOTTOM EXFALSO
%token LPAREN RPAREN
%token FUN ARR COLON
%token <string> VARID
%token <string> TYID

%token EOL

%right ARR

%start main
%type <Expr.expr> main
                                                         
%%
main:
e=expression EOL { e }

ty_annot:
  | id=VARID COLON t=ty     { (id, t) }

ty:
  | id=TYID                 { TVar(id) }
  | LPAREN t=ty RPAREN      { t }
  | t1=ty ARR t2=ty         { Arr(t1, t2) }

expression:
  | FUN LPAREN annot=ty_annot RPAREN ARR e=expression 
                            { Fun (annot, e) }
  | e=app_expr              { e }

app_expr:
  | e=app_expr a=atomic     { App (e, a) }
  | a=atomic                { a }

atomic:
  | id=VARID                { Var id }
  | LPAREN e=expression RPAREN
                            { e }