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Create-canonical-address-list

Signature

(create-canonical-address-list count addr) → *

Given a canonical address addr, create-canonical-address-list creates a list of canonical addresses where the first address is addr and the last address is the last canonical address in the range addr to addr + count.

Definitions and Theorems

Function: create-canonical-address-list

(defun create-canonical-address-list (count addr)
  (declare (xargs :guard (natp count)))
  (let ((__function__ 'create-canonical-address-list))
    (declare (ignorable __function__))
    (if (or (zp count)
            (not (canonical-address-p addr)))
        nil
      (cons addr
            (create-canonical-address-list (1- count)
                                           (1+ addr))))))

Theorem: true-listp-create-canonical-address-list

(defthm true-listp-create-canonical-address-list
  (true-listp (create-canonical-address-list cnt lin-addr))
  :rule-classes (:rewrite :type-prescription))

Theorem: canonical-address-listp-create-canonical-address-list

(defthm canonical-address-listp-create-canonical-address-list
  (canonical-address-listp
       (create-canonical-address-list count addr))
  :rule-classes (:rewrite :type-prescription))

Theorem: create-canonical-address-list-1

(defthm create-canonical-address-list-1
  (implies (canonical-address-p x)
           (equal (create-canonical-address-list 1 x)
                  (list x))))

Theorem: len-of-create-canonical-address-list

(defthm len-of-create-canonical-address-list
  (implies (and (canonical-address-p (+ -1 addr count))
                (canonical-address-p addr)
                (natp count))
           (equal (len (create-canonical-address-list count addr))
                  count)))

Theorem: car-create-canonical-address-list

(defthm car-create-canonical-address-list
  (implies (and (canonical-address-p addr)
                (posp count))
           (equal (car (create-canonical-address-list count addr))
                  addr)))

Theorem: cdr-create-canonical-address-list

(defthm cdr-create-canonical-address-list
  (implies (and (canonical-address-p addr)
                (posp count))
           (equal (cdr (create-canonical-address-list count addr))
                  (create-canonical-address-list (1- count)
                                                 (1+ addr)))))

Theorem: consp-of-create-canonical-address-list

(defthm consp-of-create-canonical-address-list
  (implies (and (canonical-address-p addr)
                (natp count)
                (< 0 count))
           (consp (create-canonical-address-list count addr))))

Theorem: create-canonical-address-list-split

(defthm create-canonical-address-list-split
 (implies
     (and (canonical-address-p addr)
          (canonical-address-p (+ k addr))
          (natp j)
          (natp k))
     (equal (create-canonical-address-list (+ k j)
                                           addr)
            (append (create-canonical-address-list k addr)
                    (create-canonical-address-list j (+ k addr))))))