The type of the result of a call of a built-in function, exact to the values of its arguments (D-161, step C).

Feel.Analysis.Calls.result_type/3 gives a call the types that the signatures of the function say (the kinds of the result and Null). That is true and not exact: not(b) for a b that is true is false, string length(s) for a s in {"a", "b"} is 1, abs(n) for an n in [-5..3] is [0..5], and none of them is null unless an argument is. A family of rules (a module under Feel.Analysis.Images) says that, for the functions it names, from the types of the arguments:

@behaviour Feel.Analysis.Images

def names, do: ["not"]
def image("not", [argument]), do: {:ok, ...}

image/2 gives the whole type of the result, Null included, or :none for arguments the family has no rule for, and the signatures answer. A rule is a claim about the run, so it is checked against it: Feel.ImageCheck (test/support) runs the function on the values at the edges of the types of the arguments (Feel.Type.Witness.edges/2) and holds the result to the rule. Every value the run gives is in the type, and a null that the type has is one that some arguments give: the first is soundness (a type that is too small is a wrong answer, D-159), the second is that a null is in a type only if a value can cause it (D-161).

The arguments are the types of the call as it is analyzed (Feel.IR.type/1: with the sets of values), in the order of the parameters, and only the ones that are given (an optional parameter that is left out is not in the list). A rule is not asked for a call that an extension may answer, whose function is not the one the rule is for.

What a rule does about null

The run gives null for a null argument, for an argument of a kind the function does not take (with an error), and for the values of the right kinds that the function has no result for. with_null/2 adds Null for the first, and the rule says the others: a null that is not in the type of the result has to be one that no value of the arguments causes. A function that takes null as it takes any other value (is, string(null), get or else) says so in its rule.

Adding a family

A family is a module that has the behaviour, listed in @families below. It names the functions it has rules for, and gives image/2 a clause for each, and a catch-all that is :none. Its test is a grid of argument types for each function, held to the run with Feel.ImageCheck.check!/3.