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• Alias-norm.lisp

Lhs-varbound-fix

Signature

(lhs-varbound-fix bound offset x) → xx

Arguments

bound — Guard (integerp bound).

offset — Guard (natp offset).

x — Guard (lhs-p x).

Returns

xx — Type (and (lhs-p xx) (lhs-vars-normorderedp bound offset xx)).

Definitions and Theorems

Function: lhs-varbound-fix

(defun lhs-varbound-fix (bound offset x)
 (declare (xargs :guard (and (integerp bound)
                             (natp offset)
                             (lhs-p x))))
 (declare (xargs :guard (lhs-vars-normorderedp bound offset x)))
 (let ((__function__ 'lhs-varbound-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (if (atom x)
       (lhs-fix x)
     (cons (b* (((lhrange xf) (car x)))
             (lhrange xf.w
                      (lhatom-bound-fix bound offset xf.atom)))
           (lhs-varbound-fix bound
                             (+ (lnfix offset) (lhrange->w (car x)))
                             (cdr x))))
   :exec x)))

Theorem: return-type-of-lhs-varbound-fix

(defthm return-type-of-lhs-varbound-fix
  (b* ((xx (lhs-varbound-fix bound offset x)))
    (and (lhs-p xx)
         (lhs-vars-normorderedp bound offset xx)))
  :rule-classes :rewrite)

Theorem: lhs-varbound-fix-when-lhs-vars-normorderedp

(defthm lhs-varbound-fix-when-lhs-vars-normorderedp
  (implies (lhs-vars-normorderedp bound offset x)
           (equal (lhs-varbound-fix bound offset x)
                  (lhs-fix x))))

Theorem: lhs-varbound-fix-of-ifix-bound

(defthm lhs-varbound-fix-of-ifix-bound
  (equal (lhs-varbound-fix (ifix bound) offset x)
         (lhs-varbound-fix bound offset x)))

Theorem: lhs-varbound-fix-int-equiv-congruence-on-bound

(defthm lhs-varbound-fix-int-equiv-congruence-on-bound
  (implies (int-equiv bound bound-equiv)
           (equal (lhs-varbound-fix bound offset x)
                  (lhs-varbound-fix bound-equiv offset x)))
  :rule-classes :congruence)

Theorem: lhs-varbound-fix-of-nfix-offset

(defthm lhs-varbound-fix-of-nfix-offset
  (equal (lhs-varbound-fix bound (nfix offset) x)
         (lhs-varbound-fix bound offset x)))

Theorem: lhs-varbound-fix-nat-equiv-congruence-on-offset

(defthm lhs-varbound-fix-nat-equiv-congruence-on-offset
  (implies (nat-equiv offset offset-equiv)
           (equal (lhs-varbound-fix bound offset x)
                  (lhs-varbound-fix bound offset-equiv x)))
  :rule-classes :congruence)

Theorem: lhs-varbound-fix-of-lhs-fix-x

(defthm lhs-varbound-fix-of-lhs-fix-x
  (equal (lhs-varbound-fix bound offset (lhs-fix x))
         (lhs-varbound-fix bound offset x)))

Theorem: lhs-varbound-fix-lhs-equiv-congruence-on-x

(defthm lhs-varbound-fix-lhs-equiv-congruence-on-x
  (implies (lhs-equiv x x-equiv)
           (equal (lhs-varbound-fix bound offset x)
                  (lhs-varbound-fix bound offset x-equiv)))
  :rule-classes :congruence)