please check the grammer

[Unregistered]

I like to run.

[Tdol]

It's OK, but many would use 'running'.

[Casiopea]

I like to run.

In addition, infinitives (e.g., to run) express an unactualized event: the event hasn't happened yet. On the other hand, present participles (e.g., running) express an actualized event: the event has happened.

If you "like" something, it's understood that you like it because you've tried it before, and that's why present participles, or actualized events (e.g., running) tend to go hand-in-hand with the verb "like".

"I like to run" is grammatical, too. It's OK, just as tdol states. The speaker uses "to run", an infinitive, to express the name of the event.