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+%{
+open Ast
+%}
+
+%token <string> IDENT
+%token LPR RPR
+%token LBR RBR
+%token ARROW ASTERISK BACKSLASH COLON COMMA DOT FATARROW
+%token BOOL TRUE FALSE BOOL_ELIM AT
+%token FST SND
+%token EOF
+
+%right ARROW ASTERISK
+%left IDENT LPR APP BACKSLASH FST SND BOOL TRUE FALSE BOOL_ELIM
+
+%start <Ast.expr> parse
+
+%%
+
+%inline
+locate(X): e = X { Asai.Range.locate_lex $loc e }
+
+%inline
+ident: id = locate(IDENT) { id }
+
+raw_arg: LPR; name = ident; COLON; ty = expr; RPR
+ { { name; ty } }
+
+%inline
+arg: a = locate(raw_arg) { a }
+
+raw_expr:
+ | name = IDENT
+ { Var name }
+ | LPR; e = raw_expr; RPR
+ { e }
+ | BOOL
+ { Bool }
+ | TRUE
+ { True }
+ | FALSE
+ { False }
+ | BOOL_ELIM; scrut = expr; AT; motive_var = ident; ARROW; motive_body = expr;
+ LBR; TRUE; FATARROW; true_case = expr; COMMA; FALSE; FATARROW; false_case = expr; RBR
+ { BoolElim { motive_var; motive_body; true_case; false_case; scrut } }
+
+ | a = arg; ARROW; b = expr
+ { Pi (a, b) }
+ | BACKSLASH; a = ident; ARROW; b = expr
+ { Lam (a, b) }
+ | a = expr; b = expr %prec APP
+ { App (a, b) }
+
+ | a = arg; ASTERISK; b = expr
+ { Sg (a, b) }
+ | LPR; a = expr; COMMA; b = expr; RPR
+ { Pair (a, b) }
+ | FST; p = expr
+ { Fst p }
+ | SND; p = expr
+ { Snd p }
+
+%inline
+expr: e = locate(raw_expr) { e }
+
+parse: e = expr; EOF { e }