How to dump the symbols in a .a file

man nm

Nm displays the name list (symbol table) of each object file in the argument list. If an argument is an archive, a listing for each object file in the archive will be produced. File can be of the form libx.a(x.o), in which case only symbols from that member of the object file are listed. ... etc

nm -g | c++filt

Mac nm doesn't have the demangle option, so you just run the output through c++filt (a demangler) afterwards.