token whitespace = /[ \n\t]+/ [ skip ];
token upper_identifier = /[A-Z_][a-z_A-Z0-9]*/;
token lower_identifier = /[a-z_][a-z_A-Z0-9]*/;
token number = /[0-9]+/;
token kw_data = /data/;
token kw_type = /type/;
token kw_defn = /defn/;
token kw_let = /let/;
token kw_letrec = /letrec/;
token kw_in = /in/;
token kw_case = /case/;
token kw_of = /of/;
token tkn_ocurly = /{/;
token tkn_ccurly = /}/;
token tkn_oparen = /\(/;
token tkn_cparen = /\)/;
token tkn_eq = /=/;
token tkn_comma = /,/;
token tkn_arrow = /->/;
token op_add = /\+/;
token op_sub = /-/;
token op_mul = /\*/;
token op_div = /\//;

rule S = program;

rule program
    = definition program?
    ;

rule definition
    = kw_data upper_identifier tkn_eq data_body
    | kw_type upper_identifier tkn_eq type_body
    | kw_defn lower_identifier params? tkn_eq defn_body
    ;

rule data_body
    = tkn_ocurly data_elems tkn_ccurly
    ;

rule data_elems
    = data_elem
    | data_elem tkn_comma data_elems
    ;

rule data_elem
    = upper_identifier
    | upper_identifier tkn_oparen data_elem_types tkn_cparen
    ;

rule data_elem_types
    = type
    | type tkn_comma data_elem_types
    ;

rule type_body
    = tkn_ocurly type tkn_ccurly
    ;

rule params
    = lower_identifier params?
    ;

rule defn_body
    = tkn_ocurly expr tkn_ccurly
    ;

rule expr
    = expr_add
    | expr_let
    | expr_letrec
    | expr_case
    ;

rule expr_add
    = expr_add op_add expr_mul
    | expr_add op_sub expr_mul
    | expr_mul
    ;

rule expr_mul
    = expr_mul op_mul expr_app
    | expr_mul op_div expr_app
    | expr_app
    ;

rule expr_app
    = expr_app? expr_app_bottom
    ;

rule expr_app_bottom
    = lower_identifier
    | upper_identifier
    | number
    | tkn_oparen expr tkn_cparen
    ;

rule expr_curly
    = tkn_ocurly expr tkn_ccurly
    ;

rule expr_let
    = kw_let lower_identifier tkn_eq expr_curly kw_in expr_curly
    ;

rule expr_letrec
    = kw_letrec lower_identifier tkn_eq expr_curly kw_in expr_curly
    ;

rule expr_case
    = kw_case expr kw_of tkn_ocurly expr_case_branches tkn_ccurly
    ;

rule expr_case_branches
    = expr_case_branch expr_case_branches?
    ;

rule expr_case_branch
    = pattern tkn_arrow expr_curly
    ;

rule pattern
    = lower_identifier
    | upper_identifier
    | upper_identifier tkn_oparen patterns tkn_cparen
    ;

rule patterns
    = lower_identifier
    | lower_identifier tkn_comma patterns
    ;

rule type
    = upper_identifier
    ;