/usr/share/acl2-8.0dfsg/books/hints/subgoalp.lisp is in acl2-books-source 8.0dfsg-1.
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; Original authors: Sol Swords <sswords@centtech.com>
(in-package "ACL2")
(include-book "std/lists/list-defuns" :dir :system) ;; for prefixp
;; Suppose you have a big hairy proof and you're only interested in one
;; subgoal, say Subgoal *1/1.3.5''. You might want to skip over any goals that
;; are not on the way to that one. You can do this with a computed hint --
;; (and (not (on-my-way-to-or-beneath id "Subgoal *1/1.3.5''")) '(:by nil)) --
;; but on-my-way-to-or-beneath isn't defined. Here we provide subgoalp and
;; non-subgoal-p.
;; The reason non-subgoal-p is not just (not (subgoalp x)): the fuzziness of
;; inductive pools and forcing rounds, which sometimes make it impossible to
;; know for sure whether one goal is descended from another. For example,
;; "Subgoal *1/1" may or may not be descended from "Subgoal 2" -- the clause
;; IDs don't track that dependency across induction or forcing rounds. So:
;; (subgoalp A B) means: A is definitely descended from B, provided A and B
;; are both produced in the same proof. (Subtlety: (subgoalp "Subgoal 1'''"
;; "Subgoal 1.1") is true, but a given proof may not reach "Subgoal 1'''"
;; before reaching "Subgoal 1.1").
;; (non-subgoal-p A B) means A is definitely NOT descended from B.
;; So the proper computed hint for the use case above is:
;; (and (non-subgoal-p "Subgoal *1/1.3.5''" id) ;; "not on my way to...
;; (not (subgoalp id "Subgoal *1/1.3.5''")) ;; "not beneath..."
;; '(:by nil))
;; We arrange that either string or clause-id forms of inputs are usable in
;; both slots for subgoal-p and non-subgoal-p.
(defun subgoalp-ids (id1 id2)
(and
;; Can't tell for sure that one is descended from another unless they are in
;; the same forcing-round and induction level.
(equal (access clause-id id1 :forcing-round)
(access clause-id id2 :forcing-round))
(equal (access clause-id id1 :pool-lst)
(access clause-id id2 :pool-lst))
(let* ((case-lst1 (access clause-id id1 :case-lst))
(case-lst2 (access clause-id id2 :case-lst)))
(and (prefixp case-lst2 case-lst1)
(or (not (equal case-lst1 case-lst2))
(<= (access clause-id id2 :primes)
(access clause-id id1 :primes)))))))
(defun non-subgoal-p-ids (id1 id2)
(let* ((forcing-round1 (access clause-id id1 :forcing-round))
(forcing-round2 (access clause-id id2 :forcing-round)))
(or
;; id1 is definitely not descended from id2 if id1 is in an earlier forcing round.
(< forcing-round1 forcing-round2)
;; Otherwise, we only can know for sure if they're in the same forcing round:
(and (equal forcing-round1 forcing-round2)
(let* ((pool-lst1 (access clause-id id1 :pool-lst))
(pool-lst2 (access clause-id id2 :pool-lst)))
;; id1 is definitely not descended from id2 unless id2's pool list is a prefix of id1's.
(or (not (prefixp pool-lst2 pool-lst1))
;; Otherwise, we only can know for sure if they're in the same induction round:
(and (equal pool-lst2 pool-lst1)
(let* ((case-lst1 (access clause-id id1 :case-lst))
(case-lst2 (access clause-id id2 :case-lst)))
;; same sort of thing for case-lst as for pool-lst
(or (not (prefixp case-lst2 case-lst1))
;; Otherwise, we only can know for sure if they're in the same induction round:
(and (equal case-lst2 case-lst1)
;; finally, id1 is not descended from id2 if id2 is a later prime:
(< (access clause-id id1 :primes)
(access clause-id id2 :primes))))))))))))
(local (defthm prefixp-self
(prefixp x x)
:hints(("Goal" :in-theory (enable prefixp)))))
(local (defthm non-subgoal-p-ids-implies-not-subgoalp-ids
(implies (non-subgoal-p-ids id1 id2)
(not (subgoalp-ids id1 id2)))))
(program)
(defun subgoalp (goal1 goal2)
(subgoalp-ids (if (stringp goal1)
(parse-clause-id goal1)
goal1)
(if (stringp goal2)
(parse-clause-id goal2)
goal2)))
(defun non-subgoal-p (goal1 goal2)
(non-subgoal-p-ids (if (stringp goal1)
(parse-clause-id goal1)
goal1)
(if (stringp goal2)
(parse-clause-id goal2)
goal2)))
(assert-event (non-subgoal-p "Goal" "Subgoal 1"))
(assert-event (not (non-subgoal-p "Subgoal 1" "Goal")))
(assert-event (non-subgoal-p "Subgoal 1" "Subgoal *1/1"))
(assert-event (not (non-subgoal-p "Subgoal *1/1" "Subgoal 1")))
(assert-event (non-subgoal-p "Subgoal *2/2" "Subgoal *1/2"))
(assert-event (non-subgoal-p "Subgoal *1/2" "Subgoal *2/2"))
(assert-event (non-subgoal-p "Goal" "[1]Goal"))
(assert-event (not (non-subgoal-p "[1]Goal" "Goal")))
(assert-event (not (non-subgoal-p "Subgoal 1.2" "Subgoal 1")))
(assert-event (non-subgoal-p "Subgoal 1" "Subgoal 1.2"))
(assert-event (non-subgoal-p "Subgoal 1.3" "Subgoal 1.2"))
(defun irrelevant-subgoal-p (curr-goal target-goal)
;; Returns T if curr-goal is not either a potential ancestor or potential
;; descendant of target-goal.
(and (non-subgoal-p target-goal curr-goal) ;; Not an ancestor
(not (subgoalp curr-goal target-goal)))) ;; Not a descendant.
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