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Sparseint$-unary-bitop

Signature

(sparseint$-unary-bitop op x x.height) → (mv res height)

Arguments

op — Guard (integerp op).

x — Guard (sparseint$-p x).

x.height — Guard (natp x.height).

Returns

res — Type (sparseint$-p res).

height — Type (equal height (sparseint$-height res)).

Definitions and Theorems

Function: sparseint$-unary-bitop

(defun sparseint$-unary-bitop (op x x.height)
  (declare (type (unsigned-byte 2) op))
  (declare (xargs :guard (and (integerp op)
                              (sparseint$-p x)
                              (natp x.height))))
  (declare
       (xargs :guard (and (sparseint$-height-correctp x)
                          (equal x.height (sparseint$-height x)))))
  (let ((__function__ 'sparseint$-unary-bitop))
    (declare (ignorable __function__))
    (b* ((x.height (mbe :logic (sparseint$-height x)
                        :exec x.height))
         (op (mbe :logic (loghead 2 op) :exec op)))
      (case op
        (0 (mv (sparseint$-leaf 0) 0))
        (1 (mv (sparseint$-bitnot x) x.height))
        (2 (mv (sparseint$-fix x) x.height))
        (t (mv (sparseint$-leaf -1) 0))))))

Theorem: sparseint$-p-of-sparseint$-unary-bitop.res

(defthm sparseint$-p-of-sparseint$-unary-bitop.res
  (b* (((mv ?res ?height)
        (sparseint$-unary-bitop op x x.height)))
    (sparseint$-p res))
  :rule-classes :rewrite)

Theorem: return-type-of-sparseint$-unary-bitop.height

(defthm return-type-of-sparseint$-unary-bitop.height
  (b* (((mv ?res ?height)
        (sparseint$-unary-bitop op x x.height)))
    (equal height (sparseint$-height res)))
  :rule-classes :rewrite)

Theorem: sparseint$-unary-bitop-height-correctp

(defthm sparseint$-unary-bitop-height-correctp
  (b* (((mv ?res ?height)
        (sparseint$-unary-bitop op x x.height)))
    (implies (sparseint$-height-correctp x)
             (sparseint$-height-correctp res))))

Theorem: sparseint$-unary-bitop-correct

(defthm sparseint$-unary-bitop-correct
  (b* (((mv ?res ?height)
        (sparseint$-unary-bitop op x x.height)))
    (equal (sparseint$-val res)
           (unary-bitop op (sparseint$-val x)))))

Theorem: sparseint$-unary-bitop-of-ifix-op

(defthm sparseint$-unary-bitop-of-ifix-op
  (equal (sparseint$-unary-bitop (ifix op)
                                 x x.height)
         (sparseint$-unary-bitop op x x.height)))

Theorem: sparseint$-unary-bitop-int-equiv-congruence-on-op

(defthm sparseint$-unary-bitop-int-equiv-congruence-on-op
  (implies (int-equiv op op-equiv)
           (equal (sparseint$-unary-bitop op x x.height)
                  (sparseint$-unary-bitop op-equiv x x.height)))
  :rule-classes :congruence)

Theorem: sparseint$-unary-bitop-of-sparseint$-fix-x

(defthm sparseint$-unary-bitop-of-sparseint$-fix-x
  (equal (sparseint$-unary-bitop op (sparseint$-fix x)
                                 x.height)
         (sparseint$-unary-bitop op x x.height)))

Theorem: sparseint$-unary-bitop-sparseint$-equiv-congruence-on-x

(defthm sparseint$-unary-bitop-sparseint$-equiv-congruence-on-x
  (implies (sparseint$-equiv x x-equiv)
           (equal (sparseint$-unary-bitop op x x.height)
                  (sparseint$-unary-bitop op x-equiv x.height)))
  :rule-classes :congruence)

Theorem: sparseint$-unary-bitop-of-nfix-x.height

(defthm sparseint$-unary-bitop-of-nfix-x.height
  (equal (sparseint$-unary-bitop op x (nfix x.height))
         (sparseint$-unary-bitop op x x.height)))

Theorem: sparseint$-unary-bitop-nat-equiv-congruence-on-x.height

(defthm sparseint$-unary-bitop-nat-equiv-congruence-on-x.height
  (implies (nat-equiv x.height x.height-equiv)
           (equal (sparseint$-unary-bitop op x x.height)
                  (sparseint$-unary-bitop op x x.height-equiv)))
  :rule-classes :congruence)