Perl 6 grammar for Lambda-calculus

Lambda.pm

grammar Lambda {

=for description
    I was trying to write a grammar for Lambda-calculus,
    and I failed parsing a simple 'λx.x x' string.

    rule TOP { ^ <expression> $ }

    rule expression {
        | \( ~ \) <expression> 
        | <abstraction>

        | <application>   # THIS WORKS
        | <variable>      #

        #| <variable>     # THIS DOES NOT
        #| <application>  # .. ???
    }

    token variable { <alpha> <digit>* }
    token abstraction { 'λ' <variable>+ \. <expression> }
    token application { <variable> ** 2..* % \s }

}

say Lambda.parse: 'λx.x x';

# vim: ft=perl6