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• Execution

Stepn

Multi-step execution.

Signature

(stepn n stat feat) → new-stat

Arguments

n — Guard (natp n).

stat — Guard (statp stat).

feat — Guard (featp feat).

Returns

new-stat — Type (statp new-stat).

We perform n steps, or fewer if the error flag is or gets set. If n is 0, we return the state unchanged.

Definitions and Theorems

Function: stepn

(defun stepn (n stat feat)
  (declare (xargs :guard (and (natp n)
                              (statp stat)
                              (featp feat))))
  (declare (xargs :guard (stat-validp stat feat)))
  (let ((__function__ 'stepn))
    (declare (ignorable __function__))
    (cond ((zp n) (stat-fix stat))
          ((errorp stat feat) (stat-fix stat))
          (t (stepn (1- n) (step stat feat) feat)))))

Theorem: statp-of-stepn

(defthm statp-of-stepn
  (b* ((new-stat (stepn n stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: stepn-of-nfix-n

(defthm stepn-of-nfix-n
  (equal (stepn (nfix n) stat feat)
         (stepn n stat feat)))

Theorem: stepn-nat-equiv-congruence-on-n

(defthm stepn-nat-equiv-congruence-on-n
  (implies (acl2::nat-equiv n n-equiv)
           (equal (stepn n stat feat)
                  (stepn n-equiv stat feat)))
  :rule-classes :congruence)

Theorem: stepn-of-stat-fix-stat

(defthm stepn-of-stat-fix-stat
  (equal (stepn n (stat-fix stat) feat)
         (stepn n stat feat)))

Theorem: stepn-stat-equiv-congruence-on-stat

(defthm stepn-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (stepn n stat feat)
                  (stepn n stat-equiv feat)))
  :rule-classes :congruence)

Theorem: stepn-of-feat-fix-feat

(defthm stepn-of-feat-fix-feat
  (equal (stepn n stat (feat-fix feat))
         (stepn n stat feat)))

Theorem: stepn-feat-equiv-congruence-on-feat

(defthm stepn-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (stepn n stat feat)
                  (stepn n stat feat-equiv)))
  :rule-classes :congruence)

Theorem: stat-validp-of-stepn

(defthm stat-validp-of-stepn
  (implies (stat-validp stat feat)
           (b* ((?new-stat (stepn n stat feat)))
             (stat-validp new-stat feat))))