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• Setting-up-page-tables

Construct-pdp-table

Construct a PDP table, one entry at a time, each of which map a 1GB page.

Signature

(construct-pdp-table entry-number entry-addr page-base-addr acc) 
  → 
*

A PDP table comprises 512 64-bit entries.

Definitions and Theorems

Function: construct-pdp-table

(defun construct-pdp-table
       (entry-number entry-addr page-base-addr acc)
 (declare (type (unsigned-byte 10) entry-number)
          (type (unsigned-byte 52) entry-addr)
          (type (unsigned-byte 22)
                page-base-addr))
 (declare (xargs :guard (alistp acc)))
 (let ((__function__ 'construct-pdp-table))
   (declare (ignorable __function__))
   (cond ((or (not (integerp entry-number))
              (< entry-number 0)
              (not (unsigned-byte-p 22 (1+ page-base-addr)))
              (not (unsigned-byte-p 10 (1+ entry-number)))
              (not (unsigned-byte-p 52 (+ 8 entry-addr))))
          acc)
         ((< entry-number 512)
          (construct-pdp-table (+ 1 entry-number)
                               (+ 8 entry-addr)
                               (+ 1 page-base-addr)
                               (acons entry-addr
                                      (add-pdp-entry page-base-addr)
                                      acc)))
         (t acc))))

Theorem: true-listp-construct-pdp-table

(defthm true-listp-construct-pdp-table
 (implies
  (true-listp acc)
  (true-listp (construct-pdp-table entry-number
                                   entry-addr page-base-addr acc))))

Theorem: consp-construct-pdp-table-helper

(defthm consp-construct-pdp-table-helper
 (implies
   (and (unsigned-byte-p 52 (+ 8 entry-addr))
        (unsigned-byte-p 22 (+ 1 page-base-addr)))
   (consp (construct-pdp-table 511 entry-addr page-base-addr acc))))

Theorem: consp-construct-pdp-table

(defthm consp-construct-pdp-table
  (implies
       (and (< entry-number 512)
            (unsigned-byte-p 10 entry-number)
            (unsigned-byte-p 10 (+ 1 entry-number))
            (unsigned-byte-p 52 (+ 8 entry-addr))
            (unsigned-byte-p 22 (+ 1 page-base-addr)))
       (consp (construct-pdp-table entry-number
                                   entry-addr page-base-addr acc)))
  :rule-classes (:type-prescription :rewrite))

Theorem: physical-addr-qword-alistp-construct-pdp-table-helper

(defthm physical-addr-qword-alistp-construct-pdp-table-helper
 (implies
     (and (natp entry-addr)
          (physical-addr-qword-alistp acc)
          (unsigned-byte-p 22 page-base-addr))
     (physical-addr-qword-alistp
          (construct-pdp-table 511 entry-addr page-base-addr acc))))

Theorem: physical-addr-qword-alistp-construct-pdp-table

(defthm physical-addr-qword-alistp-construct-pdp-table
 (implies (and (natp entry-addr)
               (physical-addr-qword-alistp acc)
               (unsigned-byte-p 22 page-base-addr))
          (physical-addr-qword-alistp
               (construct-pdp-table entry-number
                                    entry-addr page-base-addr acc)))
 :rule-classes (:type-prescription :rewrite))