I've always had difficulty in distinguishing phrases from compound words. To me, spelling a compound word without spaces between the constituents seem to be mostly arbitrary. For example the spelling of English words/phrases "mountain lion" and "junglefowl" seem totally arbitrary to me. I don't understand why the first is considered a phrase and the second is considered a word.
Sometimes I hear a definition based on semantic shift along the lines of "if the newly formed entity presents a semantic shift, it's a new word". But there are many phrases with important semantic shifts that are not considered a single word like "beating a dead horse" and vice versa.
I've also observed that some compound words in Turkish (I couldn't think of English examples but I'm sure they exist) present certain phonetic, prosodic or morphological changes compared to their phrasal origins:
"pazar ertesi" ("after Sunday") -> "pazartesi" (Monday) [sound change] "açık göz" ("open eye(d)") -> "açıkgöz" (shrewd) [stress shifts to the last syllable as if it's a single word] "ayak kabı" ("foot cover") -> "ayakkabı" (shoe) [if one adds a suffix that starts with a vowel, it takes an epenthetic "y" instead of a "s", the expected one if it was two words]
To me, these changes prove that, in the minds of the speakers the newly formed entities became new words; they behave like a single word instead of a phrase. So I can understand why they are considered compounds instead of phrases.
Is there any objective definition that separates a compound word from a phrase?