Function chain

Function Chain is the associated sequence of GFs of the members of the chain created by movement.

Example
in (i) John is assigned the function chain (GF1, GF2, GF3), where GF1 = [NP,IP1], GF2 = [NP, IP2] and GF3 = [NP,VP]. This entails that John is assigned the theta-role of the object of killed.

(i) [IP1 Johni was believed [IP2 ti to have been [VP killed ti]]]

Link
Utrecht Lexicon of Linguistics