The following words are related to each other and to words based on the element prob-, seen in a number of words ranging from probe to probable and derived from the Latin verb probare, meaning “demonstrate” or “test.”
The noun proof refers to evidence or something that makes an assertion certain or valid. It also applies to a test of an object or substance to evaluate its quality. The term also pertains to the alcoholic strength of a beverage, to a special collector’s issue of a coin (but originally in reference to coin production as a test run), to a test impression or print, or to typeset material produced for correction before a final version is published. As a verb, proof refers to activating yeast, strengthening something, or correcting text; proofread is an alternative to describe the last action, the activity is called proofreading, and one who proofreads is a proofreader. The word functions as an adjective in references to resistance (for example, “Education is intended to be proof against ignorance”), which is condensed in compounds such as foolproof.
Prove (by way of the Old French verb prueve) means “check,” “test,” or “verify,” or “show that one is capable or worthy.” The past tense is rendered as either proved or proven, and the adjectival and adverbial forms are provable (or proven or, rarely, proved), and provably, while one who proves is a prover, and the quality of being provable is provableness. Other than the past-tense forms and the adjectival form provable, these words are not common.
Approve (by way of the old French verb aprover) originally was simply a variant of prove, but it later developed the sense of “agree to,” “allow,” or “sanction.” The action is approval or, more formally, approbation; the noun approver, the verb approbate, and the adjective approbatory are all rare.
To reprove is to censure, correct, or scold; the action is reproof. One who reproves is a reprove (though that usage is rare), and one may be described as scolding reprovingly. These words stem from the Anglo-French verb reprover and ultimately derive from the Latin verb reprobare, the source of reprobate. (The family of related words that retain the prob- element are discussed in this post.)