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Learning German on Duolingo, I stumbled on the sentence
Kommst du auch laufen?
Which means:
Are you also coming to run?
And I cannot understand the grammar here.
I thought that if I want to say "I come to run", I use the zu construction. Kommst is not a modal verb, so it should have the 'zu'?
"Kommst du auch zu laufen?"
Maybe it is really a separable verb "laufenkommen"?
Or it is just an annoying exception?
What I'm missing?
The verb kommen is a "half modal". It's sometimes used as it was a modal verb, with a bare infinitive:
Kommst du laufen?
Wir gehen schwimmen.
Sie sieht ihn stürzen.
There are a lot more of such verbs, most about moving to practice another action, or perception.
Kommst du auch zu laufen?
This is ungrammatical. You may actually hear it in some some dialects but it means
Are you having time for running?
That is because to make it grammatical, one inserts a dazu
Kommst du auch dazu, dass du läufst?
Kommst du auch dazu, zu laufen?
and dazu kommen means Are you having time for it?. This is tricky. The verb dazukommen in contrary means coming to the group. The difference is all in the stress. See 'umfahren vs um'fahren.
You could write
Kommst du auch zum Laufen?
instead, making laufen a noun. This phrase may mean both depending on the stress, and that's why the modal phrase is often preferred.
In general and formally you would say
Kommst Du auch, um zu laufen?
or
Kommst Du auch zum Laufen? (in the latter, Laufen would be an event where people meet, not just running)
To my understanding, your example denotes a typical linguistic simplification of the day-to-day language
You‘ve got it almost right, the correct sentence would be „Kommst du auch zum Laufen?“
The comment under your question that says „um... zu“ isn‘t technically wrong either, you could say „kommst du auch um zu laufen?“ but that has a different meaning. „Kommst du auch zum Laufen“ most likely asks „will you be there to run?“ while „kommst du auch um zu laufen?“ kind of implies that you already committed to coming there, and asks if you intent to run, too. „Zum“ means „to“ like to the cinema, to the mall, to the sports event... while „um ... zu“ means „to“ like in „in order to“. „i‘ve came to this place to run an errand“ uses the word „to“ 2 times, the first means „zum (Ort)“ and the second „um... (etwas) zu (tun)“.
