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Hoare logic organized program proofs around preconditions, commands and postconditions, creating a compositional calculus that still shapes verification tools and software contracts.
Dijkstra's weakest-precondition calculus turned program semantics into a backward calculation from desired postconditions toward the conditions needed for correct execution.
Amir Pnueli brought temporal logic into program verification, giving concurrent and reactive systems a language for safety, liveness and behavior across time.
Model checking combined temporal logic with exhaustive state-space algorithms, allowing finite-state hardware and software designs to be checked automatically and failures returned as counterexamples.
Z made abstract state, invariants and operations into a mathematical specification language, while Abrial's later B work pushed formal methods toward refinement and verified construction.
TLA+ combines state-transition modeling, temporal logic and model checking so engineers can find concurrency and distributed-system design errors before implementation.
Coq turned constructive type theory into an interactive proof environment where mathematical proofs become machine-checkable terms and verified programs can be extracted from formal developments.
CompCert used Coq to prove semantic preservation across a realistic optimizing C compiler, closing the assurance gap between verified source programs and generated assembly.
seL4 connected a high-performance microkernel implementation to a formal specification with machine-checked proofs, pushing software verification into the privileged operating-system core.
Robert Floyd's assertion method turned program correctness into a mathematical problem by attaching logical conditions to control flow and proving that execution preserves them.