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dl-magic-rewrite rules query-rel adn args returns:
{:rules <rewritten-rules> :seed <magic-seed-fact>}
Worklist over (rel, adn) pairs starts from the query and stops
when no new pairs appear. For each rule with head matching a
worklist pair:
- Adorned rule: head :- magic_<rel>^<adn>(bound), body...
- Propagation rules: for each positive non-builtin body lit
at position i:
magic_<lit-rel>^<lit-adn>(bound-of-lit) :-
magic_<rel>^<adn>(bound-of-head),
body[0..i-1]
- Add (lit-rel, lit-adn) to the worklist.
Built-ins, negation, and aggregates pass through without
generating propagation rules. EDB facts are unchanged.
3 new tests cover seed structure, equivalence on chain-3 (full
closure, 6 ancestor tuples — magic helps only when the EDB has
nodes outside the seed's transitive cone), and same-query-answers
under the rewritten program. Total 202/202.
Wiring up a `dl-saturate-magic!` driver and large-graph perf
benchmarks is left for a future iteration.
344 lines
12 KiB
Plaintext
344 lines
12 KiB
Plaintext
;; lib/datalog/magic.sx — adornment analysis + sideways info passing.
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;;
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;; First step of the magic-sets transformation (Phase 6). Right now
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;; the saturator does not consume these — they are introspection
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;; helpers that future magic-set rewriting will build on top of.
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;;
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;; Definitions:
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;; - An *adornment* of an n-ary literal is an n-character string
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;; of "b" (bound — value already known at the call site) and
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;; "f" (free — to be derived).
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;; - SIPS (Sideways Information Passing Strategy) walks the body
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;; of an adorned rule left-to-right tracking which variables
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;; have been bound so far, computing each body literal's
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;; adornment in turn.
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;;
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;; Usage:
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;;
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;; (dl-adorn-goal '(ancestor tom X))
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;; => "bf"
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;;
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;; (dl-rule-sips
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;; {:head (ancestor X Z)
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;; :body ((parent X Y) (ancestor Y Z))}
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;; "bf")
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;; => ({:lit (parent X Y) :adornment "bf"}
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;; {:lit (ancestor Y Z) :adornment "bf"})
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;; Per-arg adornment under the current bound-var name set.
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(define
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dl-adorn-arg
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(fn
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(arg bound)
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(cond
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((dl-var? arg)
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(if (dl-member-string? (symbol->string arg) bound) "b" "f"))
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(else "b"))))
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;; Adornment for the args of a literal (after the relation name).
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(define
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dl-adorn-args
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(fn
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(args bound)
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(cond
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((= (len args) 0) "")
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(else
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(str
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(dl-adorn-arg (first args) bound)
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(dl-adorn-args (rest args) bound))))))
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;; Adornment of a top-level goal under the empty bound-var set.
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(define
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dl-adorn-goal
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(fn (goal) (dl-adorn-args (rest goal) (list))))
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;; Adornment of a literal under an explicit bound set.
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(define
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dl-adorn-lit
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(fn (lit bound) (dl-adorn-args (rest lit) bound)))
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;; The set of variable names made bound by walking a positive
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;; literal whose adornment is known. Free positions add their
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;; vars to the bound set.
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(define
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dl-vars-bound-by-lit
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(fn
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(lit bound)
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(let ((args (rest lit)) (out (list)))
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(do
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(for-each
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(fn (a)
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(when
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(and (dl-var? a)
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(not (dl-member-string? (symbol->string a) bound))
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(not (dl-member-string? (symbol->string a) out)))
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(append! out (symbol->string a))))
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args)
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out))))
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;; Walk the rule body left-to-right tracking bound vars seeded by the
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;; head adornment. Returns a list of {:lit :adornment} entries.
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;;
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;; Negation, comparison, and built-ins are passed through with their
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;; adornment computed from the current bound set; they don't add new
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;; bindings (except `is`, which binds its left arg if a var). Aggregates
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;; are treated like is — the result var becomes bound.
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(define
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dl-init-head-bound
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(fn
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(head adornment)
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(let ((args (rest head)) (out (list)))
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(do
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(define
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dl-ihb-loop
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(fn
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(i)
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(when
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(< i (len args))
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(do
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(let
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((c (slice adornment i (+ i 1)))
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(a (nth args i)))
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(when
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(and (= c "b") (dl-var? a))
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(let ((n (symbol->string a)))
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(when
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(not (dl-member-string? n out))
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(append! out n)))))
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(dl-ihb-loop (+ i 1))))))
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(dl-ihb-loop 0)
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out))))
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(define
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dl-rule-sips
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(fn
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(rule head-adornment)
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(let
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((bound (dl-init-head-bound (get rule :head) head-adornment))
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(out (list)))
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(do
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(for-each
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(fn
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(lit)
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(cond
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((and (dict? lit) (has-key? lit :neg))
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(let ((target (get lit :neg)))
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(append!
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out
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{:lit lit :adornment (dl-adorn-lit target bound)})))
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((dl-builtin? lit)
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(let ((adn (dl-adorn-lit lit bound)))
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(do
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(append! out {:lit lit :adornment adn})
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;; `is` binds its left arg (if var) once RHS is ground.
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(when
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(and (= (dl-rel-name lit) "is") (dl-var? (nth lit 1)))
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(let ((n (symbol->string (nth lit 1))))
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(when
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(not (dl-member-string? n bound))
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(append! bound n)))))))
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((and (list? lit) (dl-aggregate? lit))
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(let ((adn (dl-adorn-lit lit bound)))
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(do
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(append! out {:lit lit :adornment adn})
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;; Result var (first arg) becomes bound.
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(when (dl-var? (nth lit 1))
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(let ((n (symbol->string (nth lit 1))))
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(when
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(not (dl-member-string? n bound))
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(append! bound n)))))))
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((and (list? lit) (> (len lit) 0))
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(let ((adn (dl-adorn-lit lit bound)))
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(do
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(append! out {:lit lit :adornment adn})
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(for-each
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(fn (n)
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(when (not (dl-member-string? n bound))
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(append! bound n)))
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(dl-vars-bound-by-lit lit bound)))))))
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(get rule :body))
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out))))
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;; ── Magic predicate naming + bound-args extraction ─────────────
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;; These are building blocks for the magic-sets *transformation*
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;; itself. The transformation (which generates rewritten rules
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;; with magic_<rel>^<adornment> filters) is future work — for now
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;; these helpers can be used to inspect what such a transformation
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;; would produce.
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;; "magic_p^bf" given relation "p" and adornment "bf".
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(define
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dl-magic-rel-name
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(fn (rel adornment) (str "magic_" rel "^" adornment)))
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;; A magic predicate literal:
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;; (magic_<rel>^<adornment> arg1 arg2 ...)
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(define
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dl-magic-lit
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(fn
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(rel adornment bound-args)
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(cons (string->symbol (dl-magic-rel-name rel adornment)) bound-args)))
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;; Extract bound args (those at "b" positions in `adornment`) from a
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;; literal `(rel arg1 arg2 ... argN)`. Returns the list of arg values.
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(define
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dl-bound-args
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(fn
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(lit adornment)
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(let ((args (rest lit)) (out (list)))
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(do
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(define
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dl-ba-loop
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(fn
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(i)
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(when
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(< i (len args))
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(do
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(when
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(= (slice adornment i (+ i 1)) "b")
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(append! out (nth args i)))
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(dl-ba-loop (+ i 1))))))
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(dl-ba-loop 0)
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out))))
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;; ── Magic-sets rewriter ─────────────────────────────────────────
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;;
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;; Given the original rule list and a query (rel, adornment) pair,
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;; generates the magic-rewritten program: a list of rules that
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;; (a) gate each original rule with a `magic_<rel>^<adn>` filter and
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;; (b) propagate the magic relation through SIPS so that only
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;; query-relevant tuples are derived. Seed facts are returned
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;; separately and must be added to the db at evaluation time.
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;;
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;; Output: {:rules <rewritten-rules> :seed <magic-seed-literal>}
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;;
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;; The rewriter only rewrites IDB rules; EDB facts pass through.
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;; Built-in predicates and negation in body literals are kept in
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;; place but do not generate propagation rules of their own.
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(define
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dl-magic-pair-key
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(fn (rel adornment) (str rel "^" adornment)))
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(define
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dl-magic-rewrite
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(fn
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(rules query-rel query-adornment query-args)
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(let
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((seen (list))
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(queue (list))
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(out (list)))
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(do
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(define
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dl-mq-mark!
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(fn
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(rel adornment)
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(let ((k (dl-magic-pair-key rel adornment)))
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(when
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(not (dl-member-string? k seen))
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(do
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(append! seen k)
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(append! queue {:rel rel :adn adornment}))))))
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(define
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dl-mq-rewrite-rule!
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(fn
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(rule adn)
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(let
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((head (get rule :head))
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(body (get rule :body))
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(sips (dl-rule-sips rule adn)))
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(let
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((magic-filter
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(dl-magic-lit
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(dl-rel-name head)
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adn
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(dl-bound-args head adn))))
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(do
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;; Adorned rule: head :- magic-filter, body...
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(let ((new-body (list)))
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(do
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(append! new-body magic-filter)
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(for-each
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(fn (lit) (append! new-body lit))
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body)
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(append! out {:head head :body new-body})))
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;; Propagation rules for each positive non-builtin
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;; body literal at position i.
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(define
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dl-mq-prop-loop
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(fn
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(i)
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(when
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(< i (len body))
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(do
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(let
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((lit (nth body i))
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(sip-entry (nth sips i)))
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(when
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(and (list? lit)
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(> (len lit) 0)
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(not (and (dict? lit) (has-key? lit :neg)))
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(not (dl-builtin? lit))
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(not (dl-aggregate? lit)))
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(let
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((lit-adn (get sip-entry :adornment))
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(lit-rel (dl-rel-name lit)))
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(let
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((prop-head
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(dl-magic-lit
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lit-rel
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lit-adn
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(dl-bound-args lit lit-adn))))
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(let ((prop-body (list)))
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(do
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(append! prop-body magic-filter)
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(define
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dl-mq-prefix-loop
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(fn
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(j)
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(when
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(< j i)
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(do
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(append!
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prop-body
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(nth body j))
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(dl-mq-prefix-loop (+ j 1))))))
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(dl-mq-prefix-loop 0)
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(append!
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out
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{:head prop-head :body prop-body})
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(dl-mq-mark! lit-rel lit-adn)))))))
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(dl-mq-prop-loop (+ i 1))))))
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(dl-mq-prop-loop 0))))))
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(dl-mq-mark! query-rel query-adornment)
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(define
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dl-mq-process
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(fn
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()
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(when
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(> (len queue) 0)
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(let ((item (first queue)))
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(do
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(set! queue (rest queue))
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(let
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((rel (get item :rel)) (adn (get item :adn)))
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(for-each
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(fn
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(rule)
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(when
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(= (dl-rel-name (get rule :head)) rel)
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(dl-mq-rewrite-rule! rule adn)))
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rules))
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(dl-mq-process))))))
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(dl-mq-process)
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{:rules out
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:seed
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(dl-magic-lit
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query-rel
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query-adornment
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query-args)}))))
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