[zhenrongliew]

One read-only way to read converged facts from all three abstract engines (constprop, demand, liveness).

• analyze now returns Analyzed<Engine>: the converged state of exactly one
  analysis. It cannot run again, so every analysis is fresh and has one root.
• AnalysisResults, implemented on Analyzed for each engine:
  • per context: root, contexts, callable_of, fact, facts, response
  • per callable (provided): callables, contexts_of, joined,
    joined_facts, joined_response
• response(ctx) is what a context answers its caller: constprop's return
  product, demand's parameter facts, None for liveness.

Motivation

Engines computed facts for every value in every context, but clients could read only the root's result, through three different APIs, two of which copied. Constprop exposed no per-value facts at all.

Example

main():
  %a, %b = call @pair(1, 2)
  %c, %d = call @pair(3, 4)
  %s = add %a, %d
  ret %s

pair(%x, %y):
  %k = const 10
  %p = add %x, %k
  %q = add %y, %k
  ret %p, %q

Constprop:

Query	API	Answer
main’s return	response(root())	[Const(25)]
%a in main	fact(root(), %a)	Const(11)
All facts in main	facts(root())	%a = 11, %b = 12, %c = 13, %d = 14, %s = 25
Analyzed instances of pair	contexts_of(pair)	pair@[1, 2], pair@[3, 4]

A context distinguishes a callable by its argument values.
Within each pair context, fact(context, value) and response(context) give:

Context	%x	%y	%k	%p	%q	Response
pair@[1, 2]	1	2	10	11	12	[11, 12]
pair@[3, 4]	3	4	10	13	14	[13, 14]

Demand:

Query	API	Answer
Is %a needed?	is_demanded(root(), %a)	Yes
Is %b needed?	is_demanded(root(), %b)	No
Does main need any parameters?	response(root())	[] — it has none
Analyzed instances of pair	contexts_of(pair)	pair@[Live, Dead], pair@[Dead, Live]

The first call needs %p; the second needs %q:

Context	%p	%x	%q	%y	%k	Parameter response
pair@[Live, Dead]	Live	Live	Dead	Dead	Live	[Live, Dead]
pair@[Dead, Live]	Dead	Dead	Live	Live	Live	[Dead, Live]

joined_fact(pair, value) combines demand across contexts: a value is live if any context needs it. Here, every value in pair is live in the combined result.

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[alexcgatea]

LGTM