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• Svex-mono-eval
• 4vec-monotonicity

Svex-mono-eval-monotonicity

(svex-mono-eval x) always approximates (svex-eval x env), for any environment.

Definitions and Theorems

Theorem: svex-mono-eval-monotonic

(defthm svex-mono-eval-monotonic
  (implies (svex-env-<<= env1 env2)
           (4vec-<<= (svex-mono-eval x env1)
                     (svex-mono-eval x env2))))

Theorem: svex-call-mono-eval-monotonic

(defthm svex-call-mono-eval-monotonic
  (implies (svex-env-<<= env1 env2)
           (4vec-<<= (svex-call-mono-eval x env1)
                     (svex-call-mono-eval x env2))))

Theorem: svex-fn/args-mono-eval-monotonic

(defthm svex-fn/args-mono-eval-monotonic
  (implies (svex-env-<<= env1 env2)
           (4vec-<<= (svex-fn/args-mono-eval fn args env1)
                     (svex-fn/args-mono-eval fn args env2))))

Theorem: svexlist-mono-eval-monotonic

(defthm svexlist-mono-eval-monotonic
  (implies (svex-env-<<= env1 env2)
           (4veclist-<<= (svexlist-mono-eval x env1)
                         (svexlist-mono-eval x env2))))

Theorem: svex-alist-mono-eval-monotonic

(defthm svex-alist-mono-eval-monotonic
  (implies (svex-env-<<= env1 env2)
           (svex-env-<<= (svex-alist-mono-eval x env1)
                         (svex-alist-mono-eval x env2))))

Theorem: svex-eval-gte-mono-eval

(defthm svex-eval-gte-mono-eval
  (4vec-<<= (svex-mono-eval x env)
            (svex-eval x env)))

Theorem: svexlist-eval-gte-mono-eval

(defthm svexlist-eval-gte-mono-eval
  (4veclist-<<= (svexlist-mono-eval x env)
                (svexlist-eval x env)))

Theorem: svex-alist-eval-gte-mono-eval

(defthm svex-alist-eval-gte-mono-eval
  (svex-env-<<= (svex-alist-mono-eval x env)
                (svex-alist-eval x env)))

Theorem: svex-eval-gte-xeval

(defthm svex-eval-gte-xeval
  (4vec-<<= (svex-xeval x)
            (svex-eval x env)))

Theorem: svexlist-eval-gte-xeval

(defthm svexlist-eval-gte-xeval
  (4veclist-<<= (svexlist-xeval x)
                (svexlist-eval x env)))

Theorem: svex-alist-eval-gte-xeval

(defthm svex-alist-eval-gte-xeval
  (svex-env-<<= (svex-alist-xeval x)
                (svex-alist-eval x env)))

Accordingly, we can often use svex-mono-eval in place of svex-eval.

Theorem: svex-eval-when-2vec-p-of-minval

(defthm svex-eval-when-2vec-p-of-minval
  (implies (and (syntaxp (not (equal env ''nil)))
                (2vec-p (svex-mono-eval n env)))
           (equal (svex-eval n env)
                  (svex-mono-eval n env))))

Theorem: logbitp-when-4vec-<<=-svex-eval-strong

(defthm logbitp-when-4vec-<<=-svex-eval-strong
 (implies
  (syntaxp (not (equal env ''nil)))
  (and
   (equal
     (logbitp n (4vec->upper (svex-eval b env)))
     (if (bit->bool
              (b-ior (b-not (logbit n (4vec->upper (svex-xeval b))))
                     (logbit n (4vec->lower (svex-xeval b)))))
         (logbitp n (4vec->upper (svex-xeval b)))
       (bit-n n (4vec->upper (svex-eval b env)))))
   (equal
     (logbitp n (4vec->lower (svex-eval b env)))
     (if (bit->bool
              (b-ior (b-not (logbit n (4vec->upper (svex-xeval b))))
                     (logbit n (4vec->lower (svex-xeval b)))))
         (logbitp n (4vec->lower (svex-xeval b)))
       (bit-n n (4vec->lower (svex-eval b env))))))))