R. S. Ginzburg, S. S. Khidekel, G. Y. Knyazeva, A. A. Sankin a course in modern english

§ 16. Phraseological Units and Idioms Proper

As can be inferred from the above discussion, the functional approach does not discard idiomaticity as the main feature distinguishing phraseological units from free word-groups, but seeks to establish formal criteria of idiomaticity by analysing the syntactic function of phraseological units in speech.

¹ It should be noted that the status of give up and structurally similar groups as phraseological units is doubted by some linguists who regard up in give up as a particle but not as a word, and consequently the whole is viewed not as a word-group but as a single composite verb. See, e.g., I. V. Arnold. The English Word. M., 1973, pp. 144, 145.