What is the ruling on one who intends for the phrases "You alone we worship," "the straight path," and "the path of those upon whom You have bestowed favor" to be allusions (kināyāt) of a vow (nadhr) to perform specific acts of obedience?

A vow is formed by an explicit statement that includes the word "I vow" (نذرت) or an equivalent phrase indicating commitment, such as "It is incumbent upon me for Allah's sake to do such and such." Jurists have agreed on the validity of a vow when made with an explicit formula. However, they differed on cases where the formula lacks the specific word "vow." Some believe it is valid if the formula indicates commitment, and this is the view of the majority of jurists, while others hold that it is only valid if the word "vow" is explicitly stated.

Furthermore, some Shafi'is believe a vow can be formed through an implicit statement (kinaya) accompanied by intention, such as saying "I commit to the sacrifice" or "I designate this money as charity."

As for the phrases mentioned in the question, they are neither explicit nor implicit vow formulas, and they do not relate to commitment. Therefore, they are not considered vows, even if said with the intention of performing acts of obedience. Just as divorce does not occur through implicit divorce phrases unless the wording can bear the meaning of divorce, similarly, a vow is not formed unless it is with wording that can bear its meaning.