• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
      • Svex-stvs
      • Svex-decomposition-methodology
      • Sv-versus-esim
      • Svex-decomp
      • Svex-compose-dfs
      • Svex-compilation
        • Alias-normalization
          • Alias-norm.lisp
            • Lhs-alias-canonicalize-replace-top
            • Aliases-bound-fix
            • Lhs-pairs-set-aliases
            • Setalias
            • Lhs-replace-range
            • Lhatom-bound-fix
            • Constraintlist-subst-from-svexarr
            • Aliases-add-pair
            • Lhs-alias-canonicalize-top
            • Lhs-varbound-fix
            • Aliases-bound-fix-aux
            • Canonicalize-alias-pairs
            • Aliases-finish-canonicalize
            • Assigns-subst
            • Aliases-put-pairs
            • Getalias
            • Lhs-alias-norm
            • Constraintlist-subst-from-svexarr-nrev
            • Assigns-subst-nrev
            • Svex-subst-from-svexarr-memo-ok
            • Collect-aliases
            • Aliases-fix
            • Aliases-empty
        • Svex-design-flatten-and-normalize
        • Svex-design-compile
        • Svex-composition
        • Compile.lisp
        • Assign->segment-drivers
        • Segment-driver-map-resolve
        • Assigns->segment-drivers
      • Moddb
      • Svmods
      • Svstmt
      • Sv-tutorial
      • Expressions
      • Symbolic-test-vector
      • Vl-to-svex
    • Fgl
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Alias-norm.lisp

Setalias

Signature

(setalias n x aliases) → aliases1

Arguments

n — Guard (natp n).

x — Guard (lhs-p x).

aliases — Guard (aliases-normorderedp aliases).

Returns

aliases1 — Type (aliases-normorderedp aliases1).

Definitions and Theorems

Function: setalias$inline

(defun setalias$inline (n x aliases)
  (declare (xargs :stobjs (aliases)))
  (declare (xargs :guard (and (natp n)
                              (lhs-p x)
                              (aliases-normorderedp aliases))))
  (declare (xargs :guard (and (lhs-vars-normorderedp n 0 x)
                              (< n (aliass-length aliases)))))
  (let ((__function__ 'setalias))
    (declare (ignorable __function__))
    (mbe :logic
         (let ((aliases (aliases-bound-fix aliases)))
           (set-alias n (lhs-varbound-fix (nfix n) 0 x)
                      aliases))
         :exec (set-alias n x aliases))))

Theorem: aliases-normorderedp-of-setalias

(defthm aliases-normorderedp-of-setalias
  (b* ((aliases1 (setalias$inline n x aliases)))
    (aliases-normorderedp aliases1))
  :rule-classes :rewrite)

Theorem: setalias$inline-of-nfix-n

(defthm setalias$inline-of-nfix-n
  (equal (setalias$inline (nfix n) x aliases)
         (setalias$inline n x aliases)))

Theorem: setalias$inline-nat-equiv-congruence-on-n

(defthm setalias$inline-nat-equiv-congruence-on-n
  (implies (nat-equiv n n-equiv)
           (equal (setalias$inline n x aliases)
                  (setalias$inline n-equiv x aliases)))
  :rule-classes :congruence)

Theorem: setalias$inline-of-lhs-fix-x

(defthm setalias$inline-of-lhs-fix-x
  (equal (setalias$inline n (lhs-fix x) aliases)
         (setalias$inline n x aliases)))

Theorem: setalias$inline-lhs-equiv-congruence-on-x

(defthm setalias$inline-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (setalias$inline n x aliases)
                  (setalias$inline n x-equiv aliases)))
  :rule-classes :congruence)

Theorem: setalias$inline-of-aliases-bound-fix-aliases

(defthm setalias$inline-of-aliases-bound-fix-aliases
  (equal (setalias$inline n x (aliases-bound-fix aliases))
         (setalias$inline n x aliases)))

Theorem: setalias$inline-aliases-equiv-congruence-on-aliases

(defthm setalias$inline-aliases-equiv-congruence-on-aliases
  (implies (aliases-equiv aliases aliases-equiv)
           (equal (setalias$inline n x aliases)
                  (setalias$inline n x aliases-equiv)))
  :rule-classes :congruence)

Theorem: len-of-setalias-incr

(defthm len-of-setalias-incr
  (<= (len aliases)
      (len (setalias n x aliases)))
  :rule-classes :linear)

Theorem: len-of-setalias

(defthm len-of-setalias
  (implies (< (nfix n) (len aliases))
           (equal (len (setalias n x aliases))
                  (len aliases))))

Theorem: getalias-of-setalias-split

(defthm getalias-of-setalias-split
  (equal (getalias n (setalias m v aliases))
         (if (equal (nfix n) (nfix m))
             (lhs-varbound-fix (nfix n) 0 v)
           (getalias n aliases))))

Theorem: getalias-of-setalias-same

(defthm getalias-of-setalias-same
  (equal (getalias n (setalias n v aliases))
         (lhs-varbound-fix (nfix n) 0 v)))

Theorem: getalias-of-setalias-diff

(defthm getalias-of-setalias-diff
  (implies (not (equal (nfix n) (nfix m)))
           (equal (getalias n (setalias m v aliases))
                  (getalias n aliases))))