T. F. Melham’s scientific contributions

... Comparatively speaking, formal verification is an effective method for finding the abovementioned errors. At present, some formal software systems (or theorem provers) have been developed for this purpose, including HOL4 [12], HOL Light [13], Isabelle/HOL [14], Coq [15], PVS [16], ACL2 [17] and Mizar [18]. Before conducting formal verification, one generally has to formalize the corresponding mathematical theories in a prover. ...

Reference:

Formalization of Geometric Algebra in HOL Light

... To mitigate this, symbolic model checkers like NuSMVCimatti et al. [2002] employ binary decision diagrams, which offer a more efficient representation of stateful dynamics. Additionally, bounded model checkers likeCBMC Kroening and Tautschnig [2014] adopt a different strategy by unrolling the transition system for a predetermined number of steps, thereby circumventing the need to explore the entire state space.In contrast, theorem proving techniquesGordon and Melham [1993],Fitting [2012],Bibel [2013],Loveland [2016] boast greater generality and expressiveness but typically necessitate human intervention, commonly leveraging proof assistants to facilitate correctness verification through human-machine collaboration. Prominent proof assistants enable a more interactive and comprehensive way of correctness verification, including IsabelleNipkow et al. [2002], F*Swamy et al. [2016], and Lean4 Moura and Ullrich[2021]. ...

Reference:

Transition-Oriented Programming: Developing Provably Correct Systems