Move α is a feature of many transformational-generative grammars, first developed in the Revised Extended Standard Theory (REST) by Noam Chomsky in the late 1970s and later part of government and binding theory (GB) in the 1980s and the Minimalist Program of the 1990s.
In syntax, Move α is the most general formulation of possible movement permitted by a rule.
[1] This marks a shift of attention in transformational grammar around the 1970s, away from focussing on specific rules to underlying principles constraining them, which culminated into the development of the Principles and Parameters framework in the 1980s.
Because in isolation Move α produces massive overgeneration, it is heavily constrained by the other components of the grammar.
[3] In 1984 Howard Lasnik and Mamoru Saito unified Move α and other syntactic operations, such as Insertion and Deletion, into what they called Affect α,[4] a generalization to the effect of "Do anything to any category".