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• Setting-up-page-tables

Construct-pml4-table

Construct a PML4 table, one entry at a time, each of which references a Page-Directory-Pointer Table

Signature

(construct-pml4-table entry-number entry-addr pdpt-base-addr acc) 
  → 
*

A PML4 table comprises 512 64-bit entries.

Definitions and Theorems

Function: construct-pml4-table

(defun
 construct-pml4-table
 (entry-number entry-addr pdpt-base-addr acc)
 (declare (type (unsigned-byte 10) entry-number)
          (type (unsigned-byte 52) entry-addr)
          (type (unsigned-byte 40)
                pdpt-base-addr))
 (declare (xargs :guard (physical-addr-qword-alistp acc)))
 (let
  ((__function__ 'construct-pml4-table))
  (declare (ignorable __function__))
  (cond
       ((or (not (integerp entry-number))
            (< entry-number 0)
            (not (unsigned-byte-p 40 (1+ pdpt-base-addr)))
            (not (unsigned-byte-p 10 (1+ entry-number)))
            (not (unsigned-byte-p 52 (+ 8 entry-addr))))
        acc)
       ((< entry-number 512)
        (construct-pml4-table (+ 1 entry-number)
                              (+ 8 entry-addr)
                              (+ 1 pdpt-base-addr)
                              (acons entry-addr
                                     (add-pml4-entry pdpt-base-addr)
                                     acc)))
       (t acc))))

Theorem: true-listp-construct-pml4-table

(defthm
 true-listp-construct-pml4-table
 (implies
  (true-listp acc)
  (true-listp (construct-pml4-table entry-number
                                    entry-addr pdpt-base-addr acc)))
 :rule-classes :type-prescription)

Theorem: consp-construct-pml4-table-helper

(defthm
 consp-construct-pml4-table-helper
 (implies
  (and (unsigned-byte-p 40 (+ 1 pdpt-base-addr))
       (unsigned-byte-p 52 (+ 8 entry-addr)))
  (consp (construct-pml4-table 511 entry-addr pdpt-base-addr acc))))

Theorem: consp-construct-pml4-table

(defthm
  consp-construct-pml4-table
  (implies
       (and (unsigned-byte-p 10 entry-number)
            (< entry-number 512)
            (unsigned-byte-p 40 (1+ pdpt-base-addr))
            (unsigned-byte-p 10 (1+ entry-number))
            (unsigned-byte-p 52 (+ 8 entry-addr)))
       (consp (construct-pml4-table entry-number
                                    entry-addr pdpt-base-addr acc)))
  :rule-classes (:type-prescription :rewrite))

Theorem: physical-addr-qword-alistp-construct-pml4-table-helper

(defthm
 physical-addr-qword-alistp-construct-pml4-table-helper
 (implies
    (and (natp entry-addr)
         (unsigned-byte-p 40 pdpt-base-addr)
         (physical-addr-qword-alistp acc))
    (physical-addr-qword-alistp
         (construct-pml4-table 511 entry-addr pdpt-base-addr acc))))

Theorem: physical-addr-qword-alistp-construct-pml4-table

(defthm
    physical-addr-qword-alistp-construct-pml4-table
    (implies
         (and (unsigned-byte-p 40 pdpt-base-addr)
              (unsigned-byte-p 52 entry-addr)
              (physical-addr-qword-alistp acc))
         (physical-addr-qword-alistp
              (construct-pml4-table entry-number
                                    entry-addr pdpt-base-addr acc)))
    :rule-classes :type-prescription)