This is a sequence of three perfect verbs, so strictly speaking that would mean they function as statements. That is, the psalmist is appealing to God’s past investigations that have found innocence. David points to how thoroughly God knows him.
But the case can be made for understanding these perfects as precatives, which are the same form as the Hebrew perfect, but occur in contexts where they serve in the function of beseeching or requesting,1 and thus should be read as commands (imperatives). In support of this suggestion is the fact that in Psalm 17:1 there are three imperatives, and in Psalm 17:2 there is the jussive (an imperative in the third-person: “Let your eyes behold the right!).2,3 It is as though David is then inviting not merely investigation but also pressure—the kind of trying, testing, and visitation of which Job had a horrific experience (see Job 7:18; Job 23:10; Job 34:36).
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3 Si tu sondes mon cœur, si tu le visites la nuit,Si tu m'éprouves, tu ne trouveras rien:Ma pensée n'est pas autre que ce qui sort de ma bouche.