I have a simple arithmetics with + and * operations on terminals.

My plain parser builds an AST for terms.

I want to write a tree parser which implements the following transformations:

			

			(a + b) + c => a + (b + c);
			

			(a * b) * c => a * (b * c);
			

			(a + b) * c => (a * c) + (b * c);
			

			a * (b + c) => (a * b) + (a * c);
			

		

My simpliest rule shows the error: Ambiguous reference to AST element PLUS in rule expr

			

			expr
			

			:!      ( #(PLUS #(PLUS expr expr) expr) ) => #(PLUS #(PLUS xa:expr xb:expr) xc:expr)
			

			{ #expr = #([PLUS], xa, #([PLUS], xb, xc)); }
			

			|!      ( #(MUL #(MUL expr expr) expr) ) => #(MUL #(MUL ya: expr yb:expr) yc:expr)
			

			{ #expr = #([MUL], ya, #([MUL], yb, yc)); }
			

			|!      ( #(MUL #(PLUS expr expr) expr) ) => #(MUL #(PLUS za:expr zb:expr) zc:expr)
			

			{ #expr = #([PLUS], #([MUL], za, zc ), #([MUL], zb, zc)); }
			

			|!      ( #(MUL expr #(PLUS expr expr)) ) => #(MUL ka:expr #(PLUS kb:expr kc:expr))
			

			{ #expr = #([PLUS], #([MUL], ka, kb), #([MUL], ka, kc)); }
			

			| #(PLUS expr expr)
			

			| #(MUL expr expr)
			

			| ID
			

			;