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Re 1: As documented in tutorial/OperatorInputForms, colon represents two different operations:

symb:expr Pattern[symb,expr] patt:expr Optional[patt,expr] 

If you look at the FullForm of your first three examples, you'll see that they follow these forms. The fourth example arguably is a bug.

Re 2) No, opts:OptionsPattern[] is not a special from. From the rules given above, rules opts: OptionsPattern[] is the first case, assigning the pattern OptionsPattern[] to the symbol opts. OptionsPattern[] is itself a particular kind of pattern, just like _, Except, and KeyValuePattern are particular kinds of patterns. What sets it slightly apart from other patterns is that it sets up special rules for using OptionValue on the RHS of the rule.

More generally, about a year and half ago (so I think for 10.4), I got so fed up with the documentation of OptionsPattern and OptionsValue that I led a mini project to completely rewrite their pages. I think reading both the details and the new examples will give you a lot more insight into this idiom.

Re 1: As documented in Operator Input Forms, colon represents two different operations:

symb:expr Pattern[symb, expr] patt:expr Optional[patt, expr] 

If you look at the FullForm of your first three examples, you'll see that they follow these forms. The fourth example arguably is a bug.

Re 2) No, opts:OptionsPattern[] is not a special form. From the rules given above, rules opts: OptionsPattern[] is the first case, assigning the pattern OptionsPattern[] to the symbol opts. OptionsPattern[] is itself a particular kind of pattern, just like _, Except, and KeyValuePattern are particular kinds of patterns. What sets it slightly apart from other patterns is that it sets up special rules for using OptionValue on the RHS of the rule.

More generally, about a year and half ago (so I think for 10.4), I got so fed up with the documentation of OptionsPattern and OptionsValue that I led a mini project to completely rewrite their pages. I think reading both the details and the new examples will give you a lot more insight into this idiom.

Re 1: As documented in tutorial/OperatorInputForms, colon represents two different operations:

symb:expr Pattern[symb,expr] patt:expr Optional[patt,expr] 

If you look at the FullForm of your first three examples, you'll see that they follow these forms. The fourth example arguably is a bug.

Re 2) No, opts:OptionsPattern[] is not a special from. From the rules given above, rules opts: OptionasPattern[] is the first case, assigning the pattern OptionsPattern[] to the symbol opts. OptionsPattern[] is itself a particular kind of pattern, just like _, Except, and KeyValuePattern are particular kinds of patterns. What sets it slightly apart from other patterns is that it sets up special rules for using OptionValue on the RHS of the rule.

More generally, about a year and half ago (so I think for 10.4), I got so fed up with the documenation of OptionsPattern and OptionsValue that I led a mini project to completely rewrite their pages. I think reading both the details and the new examples will give you a lot more insight into this idiom.

Re 1: As documented in tutorial/OperatorInputForms, colon represents two different operations:

symb:expr Pattern[symb,expr] patt:expr Optional[patt,expr] 

If you look at the FullForm of your first three examples, you'll see that they follow these forms. The fourth example arguably is a bug.

Re 2) No, opts:OptionsPattern[] is not a special from. From the rules given above, rules opts: OptionsPattern[] is the first case, assigning the pattern OptionsPattern[] to the symbol opts. OptionsPattern[] is itself a particular kind of pattern, just like _, Except, and KeyValuePattern are particular kinds of patterns. What sets it slightly apart from other patterns is that it sets up special rules for using OptionValue on the RHS of the rule.

More generally, about a year and half ago (so I think for 10.4), I got so fed up with the documentation of OptionsPattern and OptionsValue that I led a mini project to completely rewrite their pages. I think reading both the details and the new examples will give you a lot more insight into this idiom.

Re 1: As documented in tutorial/OperatorInputForms, colon represents two different operations:

symb:expr Pattern[symb,expr] patt:expr Optional[patt,expr] 

If you look at the FullForm of your first three examples, you'll see that they follow these forms. The fourth example arguably is a bug.

Re 2) No, opts:OptionsPattern[] is not a special from. From the rules given above, rules opts: OptionasPattern[] is the first case, assigning the pattern OptionsPattern[] to the symbol opts. OptionsPattern[] is itself a particular kind of pattern, just like _, Except, and KeyValuePattern are particular kinds of patterns. What sets it slightly apart from other patterns is that tt sets up special rules for using OptionValue on the RHS of the rule.

More generally, about a year and half ago (so I think for 10.4), I got so fed up with the documenation of OptionsPattern and OptionsValue that lead a mini project to completely rewrite their pages. I think reading both the details and the new examples will give you a lot more insight into this idiom.

Re 1: As documented in tutorial/OperatorInputForms, colon represents two different operations:

symb:expr Pattern[symb,expr] patt:expr Optional[patt,expr] 

If you look at the FullForm of your first three examples, you'll see that they follow these forms. The fourth example arguably is a bug.

Re 2) No, opts:OptionsPattern[] is not a special from. From the rules given above, rules opts: OptionasPattern[] is the first case, assigning the pattern OptionsPattern[] to the symbol opts. OptionsPattern[] is itself a particular kind of pattern, just like _, Except, and KeyValuePattern are particular kinds of patterns. What sets it slightly apart from other patterns is that it sets up special rules for using OptionValue on the RHS of the rule.

More generally, about a year and half ago (so I think for 10.4), I got so fed up with the documenation of OptionsPattern and OptionsValue that I led a mini project to completely rewrite their pages. I think reading both the details and the new examples will give you a lot more insight into this idiom.