parse.mly

%{
open Infer

let rec expr_app e = function
  | [e'] -> App (e, e')
  | h :: ((_ :: _) as t) -> expr_app (App (e, h)) t
  | _ -> failwith "Unreachable"
%}

%token <string> VAR
%token <int> INT
%token <bool> BOOL

%token RPAREN LPAREN
%token ARROW BACKSLASH EQUAL COMMA
%token REC LET IN IF THEN ELSE
%token EOF

%left COMMA

%start main
%type <Infer.expr> main
%%

main:
  | expr; EOF { $1 }
  ;

expr:
  | expr2 { $1 }
  | expr2; expr3 { expr_app $1 $2 }
  | BACKSLASH; VAR; ARROW; expr { Abs ($2, $4) }
  | LET; VAR; EQUAL; expr; IN; expr { Let ($2, $4, $6) }
  | REC; VAR; EQUAL; expr; IN; expr { Rec ($2, $4, $6) }
  | IF; expr; THEN; expr; ELSE; expr { If ($2, $4, $6) }
  | expr4 { Tup (List.rev $1) }
  ;

expr2:
  | VAR { Var $1 }
  | lit { Lit $1 }
  | RPAREN; LPAREN { Tup [] }
  | RPAREN; expr; LPAREN { $2 }
  ;

expr3:
  | expr2 { [$1] }
  | expr2; expr3 { $1 :: $2 }
  ;

expr4:
  | expr; COMMA; expr { [$1; $3] }
  | expr4; COMMA; expr { $3 :: $1 }
  ;

lit:
  | INT { Int $1 }
  | BOOL { Bool $1 }
  ;