I'm puzzled as to how to express the idea of going shopping. In my student book, I came across a phrase "einkauf gehen", but it was used only in so called frame constructions, such as "Möchtest du einkauf gehen?" or "Ich kann heute nicht einkauf gehen" and so fourth. I'd like to use this phrase in sentences where there are no any modal verbs and to modify "einkauf gehen" into "Ich gehe einkauf". Is it correct and grammatical if I do so? Because I've never encountered such a collocation throughout my book and in these cases saw a sentence "Ich kaufe ein" or "Ich gehe einkaufen".
If your student book really writes "einkauf gehen", then it is wrong.
The correct phrase is "einkaufen gehen" - the ending is mandatory.
Hence, the so called frame constructions should be:
"Möchtest du einkaufen gehen?" or
"Ich kann heute nicht einkaufen gehen."
and so forth.
The sentence whithout modal verbs
"Ich gehe einkaufen".
is correct and grammatical and used on a regular basis by native speakers.
However, skipping the ending -en would be plain wrong.
"Einkauf gehen" is wrong, but in spoken German you can encounter similar structures. People might say things like "Kino gehen" or "McDonald's gehen" without prepositions. An example: "Gehen wir Kino?". This is grammatically incorrect, but common enough that you might encounter it. This doesn't work with verbs, though.
just saw this by accident ... you could say "ich gehe einkaufen" but usualy people say "ich bin einkaufen" bin is like "i am shopping" instead of "i go shopping" the going is more or less indicated since its not even clear if you are actualy walking .. in case you want to make clear you are not using the care you could put some weight on the fact that you are walking there for using the word "gehen" like "ich gehe einkaufen" but most wouldnt think twice if you just say "ich gehe einkaufen" the only thing important here is the "en" at the end of einkaufen since "einkauf" is the (substantiv) you would talk about what you have bought as the "einkauf" .. the summ of what you just bought thats the "einkauf" when you add the en at the end it becomes the verb the act of actualy doing "the einkauf" so "einkaufen" common toung just using "ich bin einkaufen" its coming from the idea of assuming the other one is asking where you are going without even waiting for the actual question and since its a question about where "are" you .. it leads to "i am" .. i am shopping ... -> "ich bin einkaufen" .. it also indicates that its an act you are about to do so you are not actualy einkaufen at that very moment but you are about to go so "ich bin einkaufen" also means .. im about to go shopping
i hope that helps abit (coming from someone living in germany well .. been born here