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• Omaps

Compatiblep

Check if two omaps are compatible, in the sense that they map their common keys to the same values.

Signature

(compatiblep map1 map2) → yes/no

Arguments

map1 — Guard (mapp map1).

map2 — Guard (mapp map2).

Returns

yes/no — Type (booleanp yes/no).

This definition is not optimal for execution. The compatibility of two omaps can be checked by linearly scanning through them in order. A future version of this operation should have that definition, at least for execution.

Definitions and Theorems

Function: compatiblep

(defun compatiblep (map1 map2)
  (declare (xargs :guard (and (mapp map1) (mapp map2))))
  (let ((__function__ 'compatiblep))
    (declare (ignorable __function__))
    (cond ((emptyp map1) t)
          ((mv-let (key1 val1)
                   (head map1)
             (let ((pair2 (assoc key1 map2)))
               (and pair2 (not (equal val1 (cdr pair2))))))
           nil)
          (t (compatiblep (tail map1) map2)))))

Theorem: booleanp-of-compatiblep

(defthm booleanp-of-compatiblep
  (b* ((yes/no (compatiblep map1 map2)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: compatiblep-when-left-emptyp

(defthm compatiblep-when-left-emptyp
  (implies (emptyp map1)
           (compatiblep map1 map2)))

Theorem: compatiblep-when-right-emptyp

(defthm compatiblep-when-right-emptyp
  (implies (emptyp map2)
           (compatiblep map1 map2)))

Theorem: compatiblep-of-mfix-map1

(defthm compatiblep-of-mfix-map1
  (equal (compatiblep (mfix map1) map2)
         (compatiblep map1 map2)))

Theorem: compatiblep-mequiv-congruence-on-map1

(defthm compatiblep-mequiv-congruence-on-map1
  (implies (mequiv map1 map1-equiv)
           (equal (compatiblep map1 map2)
                  (compatiblep map1-equiv map2)))
  :rule-classes :congruence)

Theorem: compatiblep-of-mfix-map2

(defthm compatiblep-of-mfix-map2
  (equal (compatiblep map1 (mfix map2))
         (compatiblep map1 map2)))

Theorem: compatiblep-mequiv-congruence-on-map2

(defthm compatiblep-mequiv-congruence-on-map2
  (implies (mequiv map2 map2-equiv)
           (equal (compatiblep map1 map2)
                  (compatiblep map1 map2-equiv)))
  :rule-classes :congruence)