Formalizing the signatures of operators and statements

[vpetrovykh]

The improvements mentioned in issue #111 provide a way to describe the signatures of EdgeDB operators and built-ins.

function	args	result
-A, also +	A	A
NOT A	A	bool
A+B, also -, /, *, etc.	A, B	A
A AND B, also OR	A, B	bool
A = B, also !=	A, B	bool
A ?= B	OPTIONAL A, OPTIONAL B	bool
A ?? B	OPTIONAL A, SET OF B	SET OF A
A IF B ELSE C	SET OF A, B, SET OF C	SET OF A
EXISTS A	SET OF A	bool
DISTINCT A	SET OF A	SET OF A
A UNION B	SET OF A, SET OF B	SET OF A, actually a set of union type of A and B
A IN B, also NOT IN	A, SET OF B	bool
UPDATE A FILTER B SET ...	A, SET OF B	A
SELECT A FILTER B ORDER BY C OFFSET D LIMIT E	A, SET OF B, OPTIONAL C, OPTIONAL D, OPTIONAL E	SET OF A
WITH CARDINALITY '1' SELECT A ...	same as above	A
INSERT A	n/a	A
DELETE A	A	A
UPDATE A FILTER B SET ...	A, SET OF B	A

Incidentally, the syntax sugar proposed in #109 can now be rewritten as {}??A, which will render A a SET OF parameter in the expression. The reason why we want the second parameter of ?? to be a SET OF is the practicality of typical usage for defaults. Consider:

SELECT (
   {} ?? (SELECT Default FILTER Default.foo = 1),
   {} ?? (SELECT Default FILTER Default.foo = 2)
)

If Default were not inside a SET OF, then on element-wise evaluation one of the tuple elements would always be {} because of the FILTER.

FSET OF is a placeholder name for "fenceless SET OF", meaning that all by itself the function does not distribute over union, but when composed with anything else, it does (and behaves like an element-wise). This property is needed to express how LIMIT and ORDER BY work (and why A and SELECT A ORDER BY A are equivalent).

Typically all clauses have signature of the type FSET OF a CLAUSE SET OF b. Some clauses have additional restrictions. ORDER BY requires its second argument to be a singleton. LIMIT and OFFSET not only require the second argument to be singleton, but also unrelated to the first argument.

[vpetrovykh]

FSETOF turned out to be less general and useful than it seemed originally. It really only applies to paths (so part of the link-as-function signature), but nothing else needs it.

Incidentally after review SELECT is treated as a SET OF overall when it is an expression. In fact, every statement as expression is a SET OF. This simplifies a lot of rules and makes certain grammar more intuitive.

[vpetrovykh]

Since UNION is SET OF in both arguments, it means that {A, B, C} is also SET OF in A, B, and C.

If we generalize the {...} as an operator with 0 or more operands, then it would make sense to extend the SET OF rule to all of the operands. This includes the case of 1 operand. This would mean that the expression User is not equivalent to either (SELECT User) or {User}. However, {User} and (SELECT User) are equivalent expressions.