In my view there is no such thing as "formal translation theory," though you might say "a formal translation theory," meaning one theory out of several that look for formal equivalence. Nida gave a supercilious definition: "formal correspondence: quality of a translation in which the features of the form of the source text have been mechanically reproduced in the receptor language" (Nida and Taber, The Theory and Practice of Translation, p. 200).
There are various levels of formal (or literal), which I would represent by: interlinear, Young's, NASB & ESV, NKJV & Holman's.