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• Call-graph

Call-graphp

Recognizer for call-graph.

Signature

(call-graphp x) → *

Definitions and Theorems

Function: call-graphp

(defun call-graphp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (qualified-identp (caar x))
         (qualified-ident-option-setp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (call-graphp (cdr x)))))))

Theorem: booleanp-of-call-graphp

(defthm booleanp-of-call-graphp
  (booleanp (call-graphp x)))

Theorem: mapp-when-call-graphp

(defthm mapp-when-call-graphp
  (implies (call-graphp x) (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: call-graphp-of-tail

(defthm call-graphp-of-tail
  (implies (call-graphp x)
           (call-graphp (omap::tail x))))

Theorem: qualified-identp-of-head-key-when-call-graphp

(defthm qualified-identp-of-head-key-when-call-graphp
  (implies (and (call-graphp x)
                (not (omap::emptyp x)))
           (qualified-identp (mv-nth 0 (omap::head x)))))

Theorem: qualified-ident-option-setp-of-head-val-when-call-graphp

(defthm qualified-ident-option-setp-of-head-val-when-call-graphp
  (implies (and (call-graphp x)
                (not (omap::emptyp x)))
           (qualified-ident-option-setp (mv-nth 1 (omap::head x)))))

Theorem: call-graphp-of-update

(defthm call-graphp-of-update
  (implies (and (call-graphp x)
                (qualified-identp k)
                (qualified-ident-option-setp v))
           (call-graphp (omap::update k v x))))

Theorem: call-graphp-of-update*

(defthm call-graphp-of-update*
  (implies (and (call-graphp x) (call-graphp y))
           (call-graphp (omap::update* x y))))

Theorem: call-graphp-of-delete

(defthm call-graphp-of-delete
  (implies (call-graphp x)
           (call-graphp (omap::delete k x))))

Theorem: call-graphp-of-delete*

(defthm call-graphp-of-delete*
  (implies (call-graphp x)
           (call-graphp (omap::delete* k x))))

Theorem: qualified-identp-when-assoc-call-graphp-binds-free-x

(defthm qualified-identp-when-assoc-call-graphp-binds-free-x
  (implies (and (omap::assoc k x) (call-graphp x))
           (qualified-identp k)))

Theorem: qualified-identp-of-car-of-assoc-call-graphp

(defthm qualified-identp-of-car-of-assoc-call-graphp
  (implies (and (call-graphp x) (omap::assoc k x))
           (qualified-identp (car (omap::assoc k x)))))

Theorem: qualified-ident-option-setp-of-cdr-of-assoc-call-graphp

(defthm qualified-ident-option-setp-of-cdr-of-assoc-call-graphp
  (implies (and (call-graphp x) (omap::assoc k x))
           (qualified-ident-option-setp (cdr (omap::assoc k x)))))

Theorem: qualified-ident-option-setp-of-lookup-when-call-graphp

(defthm qualified-ident-option-setp-of-lookup-when-call-graphp
  (implies (and (call-graphp x) (omap::assoc k x))
           (qualified-ident-option-setp (omap::lookup k x))))