Learn English – To Capitalize or not to Capitalize Independence

Chicago Manual of Style, the style guide which journal styles in the mathematical and physical sciences are most often based on —including the IEEE, the most widely followed style guide in computer science— follows your option #2, "Programming language".

You don't say what style you are writing to: If you are planning to submit it to a journal or as part of a book, the publisher's guidelines for authors should have sufficient information for you to decide. If you are submitting it as part of degree coursework, your university might or might not have a rule here. Otherwise, consider yourself bound only by the requirement to be consistent.

Principal should be capitalized when used as a title preceding the name of the person but uncapitalized if used as a description following the name. For example,

Let us welcome Principal Bob.

Let us welcome Bob, the principal of the school.

See for example Blue Book of Grammar and Punctuation.