Mechanized verification of liveness properties for programs with effects, nondeterminism, and nontermination is difficult. Existing temporal reasoning frameworks operate on the level of models (traces, automata) not executable code, creating a verification gap and losing the benefits of modularity and composition enjoyed by structural program logics. Reasoning about infinite traces and automata requires complex (co-)inductive proof techniques and familiarity with proof assistant mechanics (e.g., guardedness checker). We propose a structural approach to the verification of temporal properties with a new temporal logic that we call Ticl. Using Ticl, we internalize complex (co-)inductive proof techniques to structural lemmas and reasoning about variants and invariants. We show that it is possible to perform mechanized proofs of general temporal properties, while working in a high-level of abstraction. We demonstrate the benefits of ticl by giving short, structural proofs of safety and liveness properties for programs with queues, secure memory, and distributed consensus.
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