%{

open Ast

%}

%token EOF

%token <int> INT

%token <string> ID

%token LPAREN RPAREN

%token PLUS MINUS STAR EQUALS LTE

%token TRUE FALSE

%token IF THEN ELSE

%token LET IN

%token FUN ARROW

%token REC

%nonassoc ELSE IN ARROW

%left LTE

%left PLUS MINUS

%left STAR

%start program

%type <Ast.expr> program expr unary app primary

%%

program:

| e = expr; EOF { e }

;

expr:

| e1 = expr; op = bin_op; e2 = expr { EBinOp(op, e1, e2) }

| IF; e1 = expr; THEN; e2 = expr; ELSE; e3 = expr { EIf(e1, e2, e3) }

| FUN; x = ID; ARROW; e = expr { EFun(x, e) }

| LET; x = ID; EQUALS; e1 = expr; IN; e2 = expr { ELet(x, e1, e2) }

| LET; REC; x = ID; EQUALS; e1 = expr; IN; e2 = expr { ELet(x, ERec(x, e1), e2) }

| e = unary { e }

;

%inline bin_op:

| PLUS { Add }

| MINUS { Sub }

| STAR { Mul }

| LTE { Lte }

;

unary:

| op = un_op; e = unary { EUnOp(op, e) }

| e = app { e }

;

%inline un_op:

| MINUS { Neg }

;

app:

| e1 = app; e2 = primary { EApp(e1, e2) }

| e = primary { e }

;

primary:

| i = INT { EInt i }

| id = ID { EVar id }

| TRUE { EBool true }

| FALSE { EBool false }

| LPAREN; e = expr; RPAREN { e }

;