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• Call-graph

Call-graph-transitive-closure

Build a transitive closure for some identifier in the given call graph.

Signature

(call-graph-transitive-closure ident call-graph) → called

Arguments

ident — Guard (identp ident).

call-graph — Guard (ident-ident-option-set-mapp call-graph).

Returns

called — Type (ident-option-setp called).

If a function f calls g (i.e. the call graph has an edge from f to g), g is in f's transitive closure. If h calls i, and h is in f's transitive closure, then i is also in f's transitive closure).

Definitions and Theorems

Function: call-graph-transitive-closure0

(defun call-graph-transitive-closure0 (ident?s call-graph acc steps)
 (declare (type (unsigned-byte 60) steps))
 (declare
      (xargs :guard (and (ident-option-setp ident?s)
                         (ident-ident-option-set-mapp call-graph)
                         (ident-option-setp acc))))
 (let ((__function__ 'call-graph-transitive-closure0))
   (declare (ignorable __function__))
   (b* (((when (or (int= 0
                         (mbe :logic
                              (if (natp (acl2::the-fixnat steps))
                                  (acl2::the-fixnat steps)
                                0)
                              :exec (acl2::the-fixnat steps)))
                   (emptyp ident?s)))
         (ident-option-set-fix acc))
        (ident? (head ident?s))
        ((when (not ident?))
         (call-graph-transitive-closure0 (tail ident?s)
                                         call-graph (insert nil acc)
                                         (- steps 1)))
        (lookup (omap::assoc ident? call-graph))
        (ident?s (if lookup (union (difference (cdr lookup) acc)
                                   (tail ident?s))
                   (tail ident?s)))
        (acc (if lookup (union (cdr lookup) acc)
               acc)))
     (call-graph-transitive-closure0
          ident?s call-graph acc (- steps 1)))))

Theorem: ident-option-setp-of-call-graph-transitive-closure0

(defthm ident-option-setp-of-call-graph-transitive-closure0
 (b*
  ((called
     (call-graph-transitive-closure0 ident?s call-graph acc steps)))
  (ident-option-setp called))
 :rule-classes :rewrite)

Function: call-graph-transitive-closure

(defun call-graph-transitive-closure (ident call-graph)
 (declare
      (xargs :guard (and (identp ident)
                         (ident-ident-option-set-mapp call-graph))))
 (let ((__function__ 'call-graph-transitive-closure))
   (declare (ignorable __function__))
   (call-graph-transitive-closure0
        (insert ident nil)
        call-graph nil
        (acl2::the-fixnat (- (expt 2 acl2::*fixnat-bits*) 1)))))

Theorem: ident-option-setp-of-call-graph-transitive-closure

(defthm ident-option-setp-of-call-graph-transitive-closure
  (b* ((called (call-graph-transitive-closure ident call-graph)))
    (ident-option-setp called))
  :rule-classes :rewrite)