Professor Tucker is a Founding Fellow of the Learned Society of Wales and in July 2010 he was appointed as its inaugural General Secretary, a post he held until May 2017.
Tucker's theoretical work tackles the problems of: how to define or specify properties of the operations and tests of data types; how to program and reason with them; and how to implement them.
The first generalisation, created with Jeffrey Zucker, focuses on imperative programming with abstract data types and covers specifications and verification using Hoare logic.
For example, they showed that: The second generalisation, created with Viggo Stoltenberg-Hansen, focuses on implementing data types using approximations contained in the ordered structures of domain theory.
The general theories have been applied as formal methods in microprocessor verifications, data types, and tools for volume graphics and modelling excitable media including the heart.
Since 2003, Tucker has worked with Edwin Beggs and Felix Costa on a general theory analysing the interface between algorithms and physical equipment.
They show that the mathematics of computation imposes fundamental limits on what can be measured in classical physics: Since 2004, Tucker and Victoria Wang have studied the nature and role of digital data in personal, social and organisational contexts, especially surveillance.