language

sample program:
a
a b
a b c
a (b c)
(a b) c
(a (b c)) d
(a b c) d
a | b
a*
(a | b)*
a -> b
a -> b -> c
a b -> c
a | b -> c
(a | b) -> c
a | (b -> c)
f <- a b -> c

the binary operators are ' ',  ' -> ',  ' <- ',  ' | ' and '\n'
there is a unary operator '*'
all binary operators are right-associative
spaces, stars and parentheses delimit words, e.g. "a|b" is a single word while "a | b" is several
extra space is not allowed, e.g. "f *" since '*' is not a valid name but an operator

precedence:
0. '\n'
1. ' <- ', ' -> '
2. ' | '
3. ' '
4. ' * '