The Grammar According to West

> Note the difference between "where" and "such that". "Where" is used when the preceding notation is being defined; "such that" is used when it is already defined and its value is being restricted.

I found this interesting. SQL and Swift use “where” for restrictions. Any other examples in programming languages?

If a programming language wanted to use a keyword for restrictions that isn’t “where” (and still is a single word, hence “such that” doesn’t qualify), what word would be suitable instead? “With”? “Having”?

"Given"?

I don't know SQL, but going solely off Google Images, that'd read like:

SELECT X GIVEN X > 5

LINQ uses "where".

As for single-word alternatives, "if" is common. For example, in Python:

    >>> [(x, y) for x in range(10) for y in range(2, x) if x % y == 0]
    [(4, 2), (6, 2), (6, 3), (8, 2), (8, 4), (9, 3)]

Common Lisp uses "if" but also uses "when":

    * (loop for x from 1 to 100 when (= x (expt (floor (sqrt x)) 2)) collect x)
    (1 4 9 16 25 36 49 64 81 100)

Perl and Common Lisp both use "unless", of course with the sense inverted:

    DB<4> for (1..10) { print "$_ " unless $_ == int($_**.5)**2 }
    2 3 5 6 7 8 10

SQL uses both "where" and "having". You could also reasonably use "suppose", "stipulate", "assert", "wolog", or "let". Lisp M-expressions (and, arguably, Dijkstra's guarded command language) used "→".

For my second question I was actually more thinking of value constrains as type annotations. For example, something like

    struct S
    {
        x : num;
        y : num;
        where x < y
    }

Meaning the compiler would statically verify that x < y for all instances of S at all times. Alternatively, you could also have:

    struct S
    {
        x : num;
        y : num;
    }

    let s : S where s.x < s.y;

to only restrict a specific variable.

"If" wouldn't fit that use case, and neither would "when". I suppose "require" would work, but it also feels different from "such that". The intended meaning of the latter example would be "let s be an S such that s.x < s.y". "Given", as the sibling comment by hallole proposes, also doesn't fit.

A very interesting idea! A couple of functional languages use "when" in a similar way to introduce pattern-matching guards, but I haven't used any languages which support such a general facility for type declarations, though I suspect some dependently-typed languages do. I suppose that at least you would need to limit the condition to terminating computations to be able to verify it at compile time, and perhaps restrict mutation somewhat. (p : S) => { p.x ← 0 } would have to be illegal, for example, though (p : S) => { (p.x, p.y) ← (3, 4) } might be permitted.

These are called refinement types (https://en.wikipedia.org/wiki/Refinement_type).

Provable termination isn’t strictly necessary I think, because compile-time evaluation, or metaprogramming in general, is usually Turing-complete anyway.

Haskell uses where in the sense the article describes.

E.g

   f x = y + 1
     where y = 2 * x

Haskell also has a "let" notation

    f x = let y = 2 * x
      in y + 1

> If a programming language wanted to use a keyword for restrictions that isn’t “where” (and still is a single word, hence “such that” doesn’t qualify), what word would be suitable instead? “With”? “Having”?

If? Python does so with it's list comprehensions:

  [ x for x in range(100) if x % 2 == 0 ]