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• Verified

Smt-config

Define default Smtlink config and custom Smtlink config

Definitions and Theorems

Function: smtlink-config-p

(defun smtlink-config-p (x)
 (declare (xargs :guard t))
 (let ((acl2::__function__ 'smtlink-config-p))
  (declare (ignorable acl2::__function__))
  (and
    (mbe :logic
         (and (alistp x)
              (equal (strip-cars x)
                     '(interface-dir smt-module
                                     smt-class smt-cmd pythonpath)))
         :exec (fty::alist-with-carsp
                    x
                    '(interface-dir smt-module
                                    smt-class smt-cmd pythonpath)))
    (b* ((interface-dir (cdr (std::da-nth 0 x)))
         (smt-module (cdr (std::da-nth 1 x)))
         (smt-class (cdr (std::da-nth 2 x)))
         (smt-cmd (cdr (std::da-nth 3 x)))
         (pythonpath (cdr (std::da-nth 4 x))))
      (and (stringp interface-dir)
           (stringp smt-module)
           (stringp smt-class)
           (stringp smt-cmd)
           (stringp pythonpath))))))

Theorem: consp-when-smtlink-config-p

(defthm consp-when-smtlink-config-p
  (implies (smtlink-config-p x) (consp x))
  :rule-classes :compound-recognizer)

Function: smtlink-config-fix$inline

(defun smtlink-config-fix$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (let ((acl2::__function__ 'smtlink-config-fix))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((interface-dir (str-fix (cdr (std::da-nth 0 x))))
              (smt-module (str-fix (cdr (std::da-nth 1 x))))
              (smt-class (str-fix (cdr (std::da-nth 2 x))))
              (smt-cmd (str-fix (cdr (std::da-nth 3 x))))
              (pythonpath (str-fix (cdr (std::da-nth 4 x)))))
           (list (cons 'interface-dir interface-dir)
                 (cons 'smt-module smt-module)
                 (cons 'smt-class smt-class)
                 (cons 'smt-cmd smt-cmd)
                 (cons 'pythonpath pythonpath)))
         :exec x)))

Theorem: smtlink-config-p-of-smtlink-config-fix

(defthm smtlink-config-p-of-smtlink-config-fix
  (b* ((new-x (smtlink-config-fix$inline x)))
    (smtlink-config-p new-x))
  :rule-classes :rewrite)

Theorem: smtlink-config-fix-when-smtlink-config-p

(defthm smtlink-config-fix-when-smtlink-config-p
  (implies (smtlink-config-p x)
           (equal (smtlink-config-fix x) x)))

Function: smtlink-config-equiv$inline

(defun smtlink-config-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (smtlink-config-p acl2::x)
                              (smtlink-config-p acl2::y))))
  (equal (smtlink-config-fix acl2::x)
         (smtlink-config-fix acl2::y)))

Theorem: smtlink-config-equiv-is-an-equivalence

(defthm smtlink-config-equiv-is-an-equivalence
  (and (booleanp (smtlink-config-equiv x y))
       (smtlink-config-equiv x x)
       (implies (smtlink-config-equiv x y)
                (smtlink-config-equiv y x))
       (implies (and (smtlink-config-equiv x y)
                     (smtlink-config-equiv y z))
                (smtlink-config-equiv x z)))
  :rule-classes (:equivalence))

Theorem: smtlink-config-equiv-implies-equal-smtlink-config-fix-1

(defthm smtlink-config-equiv-implies-equal-smtlink-config-fix-1
  (implies (smtlink-config-equiv acl2::x x-equiv)
           (equal (smtlink-config-fix acl2::x)
                  (smtlink-config-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: smtlink-config-fix-under-smtlink-config-equiv

(defthm smtlink-config-fix-under-smtlink-config-equiv
  (smtlink-config-equiv (smtlink-config-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-smtlink-config-fix-1-forward-to-smtlink-config-equiv

(defthm
      equal-of-smtlink-config-fix-1-forward-to-smtlink-config-equiv
  (implies (equal (smtlink-config-fix acl2::x)
                  acl2::y)
           (smtlink-config-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-smtlink-config-fix-2-forward-to-smtlink-config-equiv

(defthm
      equal-of-smtlink-config-fix-2-forward-to-smtlink-config-equiv
  (implies (equal acl2::x (smtlink-config-fix acl2::y))
           (smtlink-config-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: smtlink-config-equiv-of-smtlink-config-fix-1-forward

(defthm smtlink-config-equiv-of-smtlink-config-fix-1-forward
  (implies (smtlink-config-equiv (smtlink-config-fix acl2::x)
                                 acl2::y)
           (smtlink-config-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: smtlink-config-equiv-of-smtlink-config-fix-2-forward

(defthm smtlink-config-equiv-of-smtlink-config-fix-2-forward
  (implies
       (smtlink-config-equiv acl2::x (smtlink-config-fix acl2::y))
       (smtlink-config-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Function: smtlink-config->interface-dir$inline

(defun smtlink-config->interface-dir$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-config->interface-dir))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (str-fix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: stringp-of-smtlink-config->interface-dir

(defthm stringp-of-smtlink-config->interface-dir
  (b* ((interface-dir (smtlink-config->interface-dir$inline x)))
    (stringp interface-dir))
  :rule-classes :rewrite)

Theorem: smtlink-config->interface-dir$inline-of-smtlink-config-fix-x

(defthm smtlink-config->interface-dir$inline-of-smtlink-config-fix-x
  (equal
       (smtlink-config->interface-dir$inline (smtlink-config-fix x))
       (smtlink-config->interface-dir$inline x)))

Theorem: smtlink-config->interface-dir$inline-smtlink-config-equiv-congruence-on-x

(defthm
 smtlink-config->interface-dir$inline-smtlink-config-equiv-congruence-on-x
 (implies (smtlink-config-equiv x x-equiv)
          (equal (smtlink-config->interface-dir$inline x)
                 (smtlink-config->interface-dir$inline x-equiv)))
 :rule-classes :congruence)

Function: smtlink-config->smt-module$inline

(defun smtlink-config->smt-module$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-config->smt-module))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (str-fix (cdr (std::da-nth 1 x))))
         :exec (cdr (std::da-nth 1 x)))))

Theorem: stringp-of-smtlink-config->smt-module

(defthm stringp-of-smtlink-config->smt-module
  (b* ((smt-module (smtlink-config->smt-module$inline x)))
    (stringp smt-module))
  :rule-classes :rewrite)

Theorem: smtlink-config->smt-module$inline-of-smtlink-config-fix-x

(defthm smtlink-config->smt-module$inline-of-smtlink-config-fix-x
  (equal (smtlink-config->smt-module$inline (smtlink-config-fix x))
         (smtlink-config->smt-module$inline x)))

Theorem: smtlink-config->smt-module$inline-smtlink-config-equiv-congruence-on-x

(defthm
 smtlink-config->smt-module$inline-smtlink-config-equiv-congruence-on-x
 (implies (smtlink-config-equiv x x-equiv)
          (equal (smtlink-config->smt-module$inline x)
                 (smtlink-config->smt-module$inline x-equiv)))
 :rule-classes :congruence)

Function: smtlink-config->smt-class$inline

(defun smtlink-config->smt-class$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-config->smt-class))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (str-fix (cdr (std::da-nth 2 x))))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: stringp-of-smtlink-config->smt-class

(defthm stringp-of-smtlink-config->smt-class
  (b* ((smt-class (smtlink-config->smt-class$inline x)))
    (stringp smt-class))
  :rule-classes :rewrite)

Theorem: smtlink-config->smt-class$inline-of-smtlink-config-fix-x

(defthm smtlink-config->smt-class$inline-of-smtlink-config-fix-x
  (equal (smtlink-config->smt-class$inline (smtlink-config-fix x))
         (smtlink-config->smt-class$inline x)))

Theorem: smtlink-config->smt-class$inline-smtlink-config-equiv-congruence-on-x

(defthm
 smtlink-config->smt-class$inline-smtlink-config-equiv-congruence-on-x
 (implies (smtlink-config-equiv x x-equiv)
          (equal (smtlink-config->smt-class$inline x)
                 (smtlink-config->smt-class$inline x-equiv)))
 :rule-classes :congruence)

Function: smtlink-config->smt-cmd$inline

(defun smtlink-config->smt-cmd$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-config->smt-cmd))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (str-fix (cdr (std::da-nth 3 x))))
         :exec (cdr (std::da-nth 3 x)))))

Theorem: stringp-of-smtlink-config->smt-cmd

(defthm stringp-of-smtlink-config->smt-cmd
  (b* ((smt-cmd (smtlink-config->smt-cmd$inline x)))
    (stringp smt-cmd))
  :rule-classes :rewrite)

Theorem: smtlink-config->smt-cmd$inline-of-smtlink-config-fix-x

(defthm smtlink-config->smt-cmd$inline-of-smtlink-config-fix-x
  (equal (smtlink-config->smt-cmd$inline (smtlink-config-fix x))
         (smtlink-config->smt-cmd$inline x)))

Theorem: smtlink-config->smt-cmd$inline-smtlink-config-equiv-congruence-on-x

(defthm
 smtlink-config->smt-cmd$inline-smtlink-config-equiv-congruence-on-x
 (implies (smtlink-config-equiv x x-equiv)
          (equal (smtlink-config->smt-cmd$inline x)
                 (smtlink-config->smt-cmd$inline x-equiv)))
 :rule-classes :congruence)

Function: smtlink-config->pythonpath$inline

(defun smtlink-config->pythonpath$inline (x)
  (declare (xargs :guard (smtlink-config-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-config->pythonpath))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (str-fix (cdr (std::da-nth 4 x))))
         :exec (cdr (std::da-nth 4 x)))))

Theorem: stringp-of-smtlink-config->pythonpath

(defthm stringp-of-smtlink-config->pythonpath
  (b* ((pythonpath (smtlink-config->pythonpath$inline x)))
    (stringp pythonpath))
  :rule-classes :rewrite)

Theorem: smtlink-config->pythonpath$inline-of-smtlink-config-fix-x

(defthm smtlink-config->pythonpath$inline-of-smtlink-config-fix-x
  (equal (smtlink-config->pythonpath$inline (smtlink-config-fix x))
         (smtlink-config->pythonpath$inline x)))

Theorem: smtlink-config->pythonpath$inline-smtlink-config-equiv-congruence-on-x

(defthm
 smtlink-config->pythonpath$inline-smtlink-config-equiv-congruence-on-x
 (implies (smtlink-config-equiv x x-equiv)
          (equal (smtlink-config->pythonpath$inline x)
                 (smtlink-config->pythonpath$inline x-equiv)))
 :rule-classes :congruence)

Function: smtlink-config

(defun smtlink-config
       (interface-dir smt-module smt-class smt-cmd pythonpath)
  (declare (xargs :guard (and (stringp interface-dir)
                              (stringp smt-module)
                              (stringp smt-class)
                              (stringp smt-cmd)
                              (stringp pythonpath))))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'smtlink-config))
    (declare (ignorable acl2::__function__))
    (b* ((interface-dir (mbe :logic (str-fix interface-dir)
                             :exec interface-dir))
         (smt-module (mbe :logic (str-fix smt-module)
                          :exec smt-module))
         (smt-class (mbe :logic (str-fix smt-class)
                         :exec smt-class))
         (smt-cmd (mbe :logic (str-fix smt-cmd)
                       :exec smt-cmd))
         (pythonpath (mbe :logic (str-fix pythonpath)
                          :exec pythonpath)))
      (list (cons 'interface-dir interface-dir)
            (cons 'smt-module smt-module)
            (cons 'smt-class smt-class)
            (cons 'smt-cmd smt-cmd)
            (cons 'pythonpath pythonpath)))))

Theorem: smtlink-config-p-of-smtlink-config

(defthm smtlink-config-p-of-smtlink-config
  (b* ((x (smtlink-config interface-dir smt-module
                          smt-class smt-cmd pythonpath)))
    (smtlink-config-p x))
  :rule-classes :rewrite)

Theorem: smtlink-config->interface-dir-of-smtlink-config

(defthm smtlink-config->interface-dir-of-smtlink-config
  (equal (smtlink-config->interface-dir
              (smtlink-config interface-dir smt-module
                              smt-class smt-cmd pythonpath))
         (str-fix interface-dir)))

Theorem: smtlink-config->smt-module-of-smtlink-config

(defthm smtlink-config->smt-module-of-smtlink-config
  (equal (smtlink-config->smt-module
              (smtlink-config interface-dir smt-module
                              smt-class smt-cmd pythonpath))
         (str-fix smt-module)))

Theorem: smtlink-config->smt-class-of-smtlink-config

(defthm smtlink-config->smt-class-of-smtlink-config
  (equal (smtlink-config->smt-class
              (smtlink-config interface-dir smt-module
                              smt-class smt-cmd pythonpath))
         (str-fix smt-class)))

Theorem: smtlink-config->smt-cmd-of-smtlink-config

(defthm smtlink-config->smt-cmd-of-smtlink-config
  (equal (smtlink-config->smt-cmd
              (smtlink-config interface-dir smt-module
                              smt-class smt-cmd pythonpath))
         (str-fix smt-cmd)))

Theorem: smtlink-config->pythonpath-of-smtlink-config

(defthm smtlink-config->pythonpath-of-smtlink-config
  (equal (smtlink-config->pythonpath
              (smtlink-config interface-dir smt-module
                              smt-class smt-cmd pythonpath))
         (str-fix pythonpath)))

Theorem: smtlink-config-of-fields

(defthm smtlink-config-of-fields
  (equal (smtlink-config (smtlink-config->interface-dir x)
                         (smtlink-config->smt-module x)
                         (smtlink-config->smt-class x)
                         (smtlink-config->smt-cmd x)
                         (smtlink-config->pythonpath x))
         (smtlink-config-fix x)))

Theorem: smtlink-config-fix-when-smtlink-config

(defthm smtlink-config-fix-when-smtlink-config
  (equal (smtlink-config-fix x)
         (smtlink-config (smtlink-config->interface-dir x)
                         (smtlink-config->smt-module x)
                         (smtlink-config->smt-class x)
                         (smtlink-config->smt-cmd x)
                         (smtlink-config->pythonpath x))))

Theorem: equal-of-smtlink-config

(defthm equal-of-smtlink-config
 (equal
     (equal (smtlink-config interface-dir
                            smt-module smt-class smt-cmd pythonpath)
            x)
     (and (smtlink-config-p x)
          (equal (smtlink-config->interface-dir x)
                 (str-fix interface-dir))
          (equal (smtlink-config->smt-module x)
                 (str-fix smt-module))
          (equal (smtlink-config->smt-class x)
                 (str-fix smt-class))
          (equal (smtlink-config->smt-cmd x)
                 (str-fix smt-cmd))
          (equal (smtlink-config->pythonpath x)
                 (str-fix pythonpath)))))

Theorem: smtlink-config-of-str-fix-interface-dir

(defthm smtlink-config-of-str-fix-interface-dir
  (equal (smtlink-config (str-fix interface-dir)
                         smt-module smt-class smt-cmd pythonpath)
         (smtlink-config interface-dir smt-module
                         smt-class smt-cmd pythonpath)))

Theorem: smtlink-config-streqv-congruence-on-interface-dir

(defthm smtlink-config-streqv-congruence-on-interface-dir
 (implies
     (acl2::streqv interface-dir interface-dir-equiv)
     (equal (smtlink-config interface-dir
                            smt-module smt-class smt-cmd pythonpath)
            (smtlink-config interface-dir-equiv smt-module
                            smt-class smt-cmd pythonpath)))
 :rule-classes :congruence)

Theorem: smtlink-config-of-str-fix-smt-module

(defthm smtlink-config-of-str-fix-smt-module
  (equal (smtlink-config interface-dir (str-fix smt-module)
                         smt-class smt-cmd pythonpath)
         (smtlink-config interface-dir smt-module
                         smt-class smt-cmd pythonpath)))

Theorem: smtlink-config-streqv-congruence-on-smt-module

(defthm smtlink-config-streqv-congruence-on-smt-module
 (implies
     (acl2::streqv smt-module smt-module-equiv)
     (equal (smtlink-config interface-dir
                            smt-module smt-class smt-cmd pythonpath)
            (smtlink-config interface-dir smt-module-equiv
                            smt-class smt-cmd pythonpath)))
 :rule-classes :congruence)

Theorem: smtlink-config-of-str-fix-smt-class

(defthm smtlink-config-of-str-fix-smt-class
  (equal (smtlink-config interface-dir
                         smt-module (str-fix smt-class)
                         smt-cmd pythonpath)
         (smtlink-config interface-dir smt-module
                         smt-class smt-cmd pythonpath)))

Theorem: smtlink-config-streqv-congruence-on-smt-class

(defthm smtlink-config-streqv-congruence-on-smt-class
 (implies
     (acl2::streqv smt-class smt-class-equiv)
     (equal (smtlink-config interface-dir
                            smt-module smt-class smt-cmd pythonpath)
            (smtlink-config interface-dir smt-module
                            smt-class-equiv smt-cmd pythonpath)))
 :rule-classes :congruence)

Theorem: smtlink-config-of-str-fix-smt-cmd

(defthm smtlink-config-of-str-fix-smt-cmd
  (equal (smtlink-config interface-dir
                         smt-module smt-class (str-fix smt-cmd)
                         pythonpath)
         (smtlink-config interface-dir smt-module
                         smt-class smt-cmd pythonpath)))

Theorem: smtlink-config-streqv-congruence-on-smt-cmd

(defthm smtlink-config-streqv-congruence-on-smt-cmd
 (implies
     (acl2::streqv smt-cmd smt-cmd-equiv)
     (equal (smtlink-config interface-dir
                            smt-module smt-class smt-cmd pythonpath)
            (smtlink-config interface-dir smt-module
                            smt-class smt-cmd-equiv pythonpath)))
 :rule-classes :congruence)

Theorem: smtlink-config-of-str-fix-pythonpath

(defthm smtlink-config-of-str-fix-pythonpath
  (equal (smtlink-config interface-dir smt-module
                         smt-class smt-cmd (str-fix pythonpath))
         (smtlink-config interface-dir smt-module
                         smt-class smt-cmd pythonpath)))

Theorem: smtlink-config-streqv-congruence-on-pythonpath

(defthm smtlink-config-streqv-congruence-on-pythonpath
 (implies
     (acl2::streqv pythonpath pythonpath-equiv)
     (equal (smtlink-config interface-dir
                            smt-module smt-class smt-cmd pythonpath)
            (smtlink-config interface-dir smt-module
                            smt-class smt-cmd pythonpath-equiv)))
 :rule-classes :congruence)

Theorem: smtlink-config-fix-redef

(defthm smtlink-config-fix-redef
  (equal (smtlink-config-fix x)
         (smtlink-config (smtlink-config->interface-dir x)
                         (smtlink-config->smt-module x)
                         (smtlink-config->smt-class x)
                         (smtlink-config->smt-cmd x)
                         (smtlink-config->pythonpath x)))
  :rule-classes :definition)

Theorem: smtlink-config-p-of-custom-smt-cnf

(defthm smtlink-config-p-of-custom-smt-cnf
  (smtlink-config-p (custom-smt-cnf)))

Function: default-smtlink-config

(defun default-smtlink-config nil
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'default-smtlink-config))
    (declare (ignorable acl2::__function__))
    (change-smtlink-config *default-smtlink-config*)))

Function: string-string-alistp

(defun string-string-alistp (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'string-string-alistp))
    (declare (ignorable acl2::__function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (stringp (caar x))
           (stringp (cdar x))
           (string-string-alistp (cdr x))))))

Theorem: string-string-alistp-of-revappend

(defthm string-string-alistp-of-revappend
  (equal (string-string-alistp (revappend acl2::x acl2::y))
         (and (string-string-alistp (acl2::list-fix acl2::x))
              (string-string-alistp acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-remove

(defthm string-string-alistp-of-remove
  (implies (string-string-alistp acl2::x)
           (string-string-alistp (remove acl2::a acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-last

(defthm string-string-alistp-of-last
  (implies (string-string-alistp (double-rewrite acl2::x))
           (string-string-alistp (last acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-nthcdr

(defthm string-string-alistp-of-nthcdr
  (implies (string-string-alistp (double-rewrite acl2::x))
           (string-string-alistp (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-butlast

(defthm string-string-alistp-of-butlast
  (implies (string-string-alistp (double-rewrite acl2::x))
           (string-string-alistp (butlast acl2::x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-update-nth

(defthm string-string-alistp-of-update-nth
 (implies
    (string-string-alistp (double-rewrite acl2::x))
    (iff (string-string-alistp (update-nth acl2::n acl2::y acl2::x))
         (and (and (consp acl2::y)
                   (stringp (car acl2::y))
                   (stringp (cdr acl2::y)))
              (or (<= (nfix acl2::n) (len acl2::x))
                  (and (consp nil)
                       (stringp (car nil))
                       (stringp (cdr nil)))))))
 :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-repeat

(defthm string-string-alistp-of-repeat
  (iff (string-string-alistp (acl2::repeat acl2::n acl2::x))
       (or (and (consp acl2::x)
                (stringp (car acl2::x))
                (stringp (cdr acl2::x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-take

(defthm string-string-alistp-of-take
  (implies (string-string-alistp (double-rewrite acl2::x))
           (iff (string-string-alistp (take acl2::n acl2::x))
                (or (and (consp nil)
                         (stringp (car nil))
                         (stringp (cdr nil)))
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-union-equal

(defthm string-string-alistp-of-union-equal
  (equal (string-string-alistp (union-equal acl2::x acl2::y))
         (and (string-string-alistp (acl2::list-fix acl2::x))
              (string-string-alistp (double-rewrite acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-intersection-equal-2

(defthm string-string-alistp-of-intersection-equal-2
  (implies
       (string-string-alistp (double-rewrite acl2::y))
       (string-string-alistp (intersection-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-intersection-equal-1

(defthm string-string-alistp-of-intersection-equal-1
  (implies
       (string-string-alistp (double-rewrite acl2::x))
       (string-string-alistp (intersection-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-set-difference-equal

(defthm string-string-alistp-of-set-difference-equal
 (implies
      (string-string-alistp acl2::x)
      (string-string-alistp (set-difference-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: string-string-alistp-when-subsetp-equal

(defthm string-string-alistp-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (string-string-alistp acl2::y))
                (equal (string-string-alistp acl2::x)
                       (true-listp acl2::x)))
       (implies (and (string-string-alistp acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (equal (string-string-alistp acl2::x)
                       (true-listp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-rcons

(defthm string-string-alistp-of-rcons
  (iff (string-string-alistp (acl2::rcons acl2::a acl2::x))
       (and (and (consp acl2::a)
                 (stringp (car acl2::a))
                 (stringp (cdr acl2::a)))
            (string-string-alistp (acl2::list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-append

(defthm string-string-alistp-of-append
  (equal (string-string-alistp (append acl2::a acl2::b))
         (and (string-string-alistp (acl2::list-fix acl2::a))
              (string-string-alistp acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-rev

(defthm string-string-alistp-of-rev
  (equal (string-string-alistp (acl2::rev acl2::x))
         (string-string-alistp (acl2::list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-duplicated-members

(defthm string-string-alistp-of-duplicated-members
 (implies (string-string-alistp acl2::x)
          (string-string-alistp (acl2::duplicated-members acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-difference

(defthm string-string-alistp-of-difference
  (implies (string-string-alistp acl2::x)
           (string-string-alistp (set::difference acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-intersect-2

(defthm string-string-alistp-of-intersect-2
  (implies (string-string-alistp acl2::y)
           (string-string-alistp (set::intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-intersect-1

(defthm string-string-alistp-of-intersect-1
  (implies (string-string-alistp acl2::x)
           (string-string-alistp (set::intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-union

(defthm string-string-alistp-of-union
  (iff (string-string-alistp (set::union acl2::x acl2::y))
       (and (string-string-alistp (set::sfix acl2::x))
            (string-string-alistp (set::sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-mergesort

(defthm string-string-alistp-of-mergesort
  (iff (string-string-alistp (set::mergesort acl2::x))
       (string-string-alistp (acl2::list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-delete

(defthm string-string-alistp-of-delete
  (implies (string-string-alistp acl2::x)
           (string-string-alistp (set::delete acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-insert

(defthm string-string-alistp-of-insert
  (iff (string-string-alistp (set::insert acl2::a acl2::x))
       (and (string-string-alistp (set::sfix acl2::x))
            (and (consp acl2::a)
                 (stringp (car acl2::a))
                 (stringp (cdr acl2::a)))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-sfix

(defthm string-string-alistp-of-sfix
  (iff (string-string-alistp (set::sfix acl2::x))
       (or (string-string-alistp acl2::x)
           (not (set::setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-list-fix

(defthm string-string-alistp-of-list-fix
  (implies (string-string-alistp acl2::x)
           (string-string-alistp (acl2::list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-string-string-alistp-compound-recognizer

(defthm true-listp-when-string-string-alistp-compound-recognizer
  (implies (string-string-alistp acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: string-string-alistp-when-not-consp

(defthm string-string-alistp-when-not-consp
  (implies (not (consp acl2::x))
           (equal (string-string-alistp acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-cdr-when-string-string-alistp

(defthm string-string-alistp-of-cdr-when-string-string-alistp
  (implies (string-string-alistp (double-rewrite acl2::x))
           (string-string-alistp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-cons

(defthm string-string-alistp-of-cons
  (equal (string-string-alistp (cons acl2::a acl2::x))
         (and (and (consp acl2::a)
                   (stringp (car acl2::a))
                   (stringp (cdr acl2::a)))
              (string-string-alistp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-remove-assoc

(defthm string-string-alistp-of-remove-assoc
 (implies
     (string-string-alistp acl2::x)
     (string-string-alistp (remove-assoc-equal acl2::name acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-put-assoc

(defthm string-string-alistp-of-put-assoc
  (implies (and (string-string-alistp acl2::x))
           (iff (string-string-alistp
                     (put-assoc-equal acl2::name acl2::val acl2::x))
                (and (stringp acl2::name)
                     (stringp acl2::val))))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-fast-alist-clean

(defthm string-string-alistp-of-fast-alist-clean
  (implies (string-string-alistp acl2::x)
           (string-string-alistp (fast-alist-clean acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-hons-shrink-alist

(defthm string-string-alistp-of-hons-shrink-alist
  (implies
       (and (string-string-alistp acl2::x)
            (string-string-alistp acl2::y))
       (string-string-alistp (hons-shrink-alist acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: string-string-alistp-of-hons-acons

(defthm string-string-alistp-of-hons-acons
  (equal (string-string-alistp (hons-acons acl2::a acl2::n acl2::x))
         (and (stringp acl2::a)
              (stringp acl2::n)
              (string-string-alistp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-cdr-of-hons-assoc-equal-when-string-string-alistp

(defthm stringp-of-cdr-of-hons-assoc-equal-when-string-string-alistp
  (implies (string-string-alistp acl2::x)
           (iff (stringp (cdr (hons-assoc-equal acl2::k acl2::x)))
                (or (hons-assoc-equal acl2::k acl2::x)
                    (stringp nil))))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-string-string-alistp-rewrite

(defthm alistp-when-string-string-alistp-rewrite
  (implies (string-string-alistp acl2::x)
           (alistp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-string-string-alistp

(defthm alistp-when-string-string-alistp
  (implies (string-string-alistp acl2::x)
           (alistp acl2::x))
  :rule-classes :tau-system)

Theorem: stringp-of-cdar-when-string-string-alistp

(defthm stringp-of-cdar-when-string-string-alistp
  (implies (string-string-alistp acl2::x)
           (iff (stringp (cdar acl2::x))
                (or (consp acl2::x) (stringp nil))))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-caar-when-string-string-alistp

(defthm stringp-of-caar-when-string-string-alistp
  (implies (string-string-alistp acl2::x)
           (iff (stringp (caar acl2::x))
                (or (consp acl2::x) (stringp nil))))
  :rule-classes ((:rewrite)))

Function: string-string-alist-fix$inline

(defun string-string-alist-fix$inline (x)
  (declare (xargs :guard (string-string-alistp x)))
  (let ((acl2::__function__ 'string-string-alist-fix))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (atom x)
             nil
           (if (consp (car x))
               (cons (cons (str-fix (caar x))
                           (str-fix (cdar x)))
                     (string-string-alist-fix (cdr x)))
             (string-string-alist-fix (cdr x))))
         :exec x)))

Theorem: string-string-alistp-of-string-string-alist-fix

(defthm string-string-alistp-of-string-string-alist-fix
  (b* ((fty::newx (string-string-alist-fix$inline x)))
    (string-string-alistp fty::newx))
  :rule-classes :rewrite)

Theorem: string-string-alist-fix-when-string-string-alistp

(defthm string-string-alist-fix-when-string-string-alistp
  (implies (string-string-alistp x)
           (equal (string-string-alist-fix x) x)))

Function: string-string-alist-equiv$inline

(defun string-string-alist-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (string-string-alistp acl2::x)
                              (string-string-alistp acl2::y))))
  (equal (string-string-alist-fix acl2::x)
         (string-string-alist-fix acl2::y)))

Theorem: string-string-alist-equiv-is-an-equivalence

(defthm string-string-alist-equiv-is-an-equivalence
  (and (booleanp (string-string-alist-equiv x y))
       (string-string-alist-equiv x x)
       (implies (string-string-alist-equiv x y)
                (string-string-alist-equiv y x))
       (implies (and (string-string-alist-equiv x y)
                     (string-string-alist-equiv y z))
                (string-string-alist-equiv x z)))
  :rule-classes (:equivalence))

Theorem: string-string-alist-equiv-implies-equal-string-string-alist-fix-1

(defthm
  string-string-alist-equiv-implies-equal-string-string-alist-fix-1
  (implies (string-string-alist-equiv acl2::x x-equiv)
           (equal (string-string-alist-fix acl2::x)
                  (string-string-alist-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: string-string-alist-fix-under-string-string-alist-equiv

(defthm string-string-alist-fix-under-string-string-alist-equiv
  (string-string-alist-equiv (string-string-alist-fix acl2::x)
                             acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-string-string-alist-fix-1-forward-to-string-string-alist-equiv

(defthm
 equal-of-string-string-alist-fix-1-forward-to-string-string-alist-equiv
 (implies (equal (string-string-alist-fix acl2::x)
                 acl2::y)
          (string-string-alist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-string-string-alist-fix-2-forward-to-string-string-alist-equiv

(defthm
 equal-of-string-string-alist-fix-2-forward-to-string-string-alist-equiv
 (implies (equal acl2::x
                 (string-string-alist-fix acl2::y))
          (string-string-alist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: string-string-alist-equiv-of-string-string-alist-fix-1-forward

(defthm
     string-string-alist-equiv-of-string-string-alist-fix-1-forward
  (implies
       (string-string-alist-equiv (string-string-alist-fix acl2::x)
                                  acl2::y)
       (string-string-alist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: string-string-alist-equiv-of-string-string-alist-fix-2-forward

(defthm
     string-string-alist-equiv-of-string-string-alist-fix-2-forward
  (implies
       (string-string-alist-equiv acl2::x
                                  (string-string-alist-fix acl2::y))
       (string-string-alist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: cons-of-str-fix-k-under-string-string-alist-equiv

(defthm cons-of-str-fix-k-under-string-string-alist-equiv
  (string-string-alist-equiv (cons (cons (str-fix acl2::k) acl2::v)
                                   acl2::x)
                             (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-streqv-congruence-on-k-under-string-string-alist-equiv

(defthm cons-streqv-congruence-on-k-under-string-string-alist-equiv
 (implies
  (acl2::streqv acl2::k k-equiv)
  (string-string-alist-equiv (cons (cons acl2::k acl2::v) acl2::x)
                             (cons (cons k-equiv acl2::v) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-str-fix-v-under-string-string-alist-equiv

(defthm cons-of-str-fix-v-under-string-string-alist-equiv
  (string-string-alist-equiv (cons (cons acl2::k (str-fix acl2::v))
                                   acl2::x)
                             (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-streqv-congruence-on-v-under-string-string-alist-equiv

(defthm cons-streqv-congruence-on-v-under-string-string-alist-equiv
 (implies
  (acl2::streqv acl2::v v-equiv)
  (string-string-alist-equiv (cons (cons acl2::k acl2::v) acl2::x)
                             (cons (cons acl2::k v-equiv) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-string-string-alist-fix-y-under-string-string-alist-equiv

(defthm
  cons-of-string-string-alist-fix-y-under-string-string-alist-equiv
 (string-string-alist-equiv (cons acl2::x
                                  (string-string-alist-fix acl2::y))
                            (cons acl2::x acl2::y)))

Theorem: cons-string-string-alist-equiv-congruence-on-y-under-string-string-alist-equiv

(defthm
 cons-string-string-alist-equiv-congruence-on-y-under-string-string-alist-equiv
 (implies (string-string-alist-equiv acl2::y y-equiv)
          (string-string-alist-equiv (cons acl2::x acl2::y)
                                     (cons acl2::x y-equiv)))
 :rule-classes :congruence)

Theorem: string-string-alist-fix-of-acons

(defthm string-string-alist-fix-of-acons
  (equal (string-string-alist-fix (cons (cons acl2::a acl2::b) x))
         (cons (cons (str-fix acl2::a)
                     (str-fix acl2::b))
               (string-string-alist-fix x))))

Theorem: string-string-alist-fix-of-append

(defthm string-string-alist-fix-of-append
  (equal (string-string-alist-fix (append std::a std::b))
         (append (string-string-alist-fix std::a)
                 (string-string-alist-fix std::b))))

Theorem: consp-car-of-string-string-alist-fix

(defthm consp-car-of-string-string-alist-fix
  (equal (consp (car (string-string-alist-fix x)))
         (consp (string-string-alist-fix x))))

Function: check-valid-option

(defun check-valid-option (option value)
  (declare (xargs :guard (and (stringp option) (stringp value))))
  (let ((acl2::__function__ 'check-valid-option))
    (declare (ignorable acl2::__function__))
    (b* (((unless (or (equal option "interface-dir")
                      (equal option "smt-module")
                      (equal option "smt-class")
                      (equal option "smt-cmd")
                      (equal option "pythonpath")))
          nil))
      t)))

Theorem: booleanp-of-check-valid-option

(defthm booleanp-of-check-valid-option
  (b* ((valid? (check-valid-option option value)))
    (booleanp valid?))
  :rule-classes :rewrite)

Function: extract-=-left-and-right

(defun extract-=-left-and-right (lines)
 (declare (xargs :guard (string-listp lines)))
 (let ((acl2::__function__ 'extract-=-left-and-right))
  (declare (ignorable acl2::__function__))
  (b*
   ((lines (str::string-list-fix lines))
    ((unless (consp lines)) nil)
    ((cons first rest) lines)
    (extracted-line (strtok first (list #\=)))
    ((unless (and (consp extracted-line)
                  (endp (cddr extracted-line))
                  (stringp (car extracted-line))
                  (stringp (cadr extracted-line))))
     (er hard?
         'smt-config=>extract-=-left-and-right
         "Smtlink-config wrong ~
  format!~%~q0"
         first))
    ((list option value &) extracted-line)
    ((unless (check-valid-option option value))
     (er
      hard?
      'smt-config=>extract-=-left-and-right
      "There's something
  wrong with the configuration setup in smtlink-config.")))
   (cons (cons (car extracted-line)
               (cadr extracted-line))
         (extract-=-left-and-right rest)))))

Theorem: string-string-alistp-of-extract-=-left-and-right

(defthm string-string-alistp-of-extract-=-left-and-right
  (b* ((config-alist (extract-=-left-and-right lines)))
    (string-string-alistp config-alist))
  :rule-classes :rewrite)

Function: process-config

(defun process-config (config-str)
  (declare (xargs :guard (stringp config-str)))
  (let ((acl2::__function__ 'process-config))
    (declare (ignorable acl2::__function__))
    (b* ((lines (strtok config-str (list #\Newline)))
         (config-alist (extract-=-left-and-right lines)))
      config-alist)))

Theorem: string-string-alistp-of-process-config

(defthm string-string-alistp-of-process-config
  (b* ((config-alist (process-config config-str)))
    (string-string-alistp config-alist))
  :rule-classes :rewrite)

Function: change-smt-cnf

(defun change-smt-cnf (config-alist default-cnf)
  (declare (xargs :guard (and (string-string-alistp config-alist)
                              (smtlink-config-p default-cnf))))
  (let ((acl2::__function__ 'change-smt-cnf))
    (declare (ignorable acl2::__function__))
    (b* ((config-alist (string-string-alist-fix config-alist))
         (default-cnf (smtlink-config-fix default-cnf))
         ((unless (consp config-alist))
          default-cnf)
         ((cons first rest) config-alist)
         ((cons option value) first)
         (new-cnf (cond ((equal option "smt-cmd")
                         (change-smtlink-config default-cnf
                                                :smt-cmd value))
                        (t default-cnf))))
      (change-smt-cnf rest new-cnf))))

Theorem: smtlink-config-p-of-change-smt-cnf

(defthm smtlink-config-p-of-change-smt-cnf
  (b* ((smt-cnf (change-smt-cnf config-alist default-cnf)))
    (smtlink-config-p smt-cnf))
  :rule-classes :rewrite)

Function: file-exists

(defun file-exists (smtconfig dir state)
  (declare (xargs :stobjs (state)))
  (declare (xargs :guard (and (stringp smtconfig)
                              (stringp dir))))
  (let ((acl2::__function__ 'file-exists))
    (declare (ignorable acl2::__function__))
    (b* ((cmd (concatenate 'string
                           "test -f " dir "/" smtconfig))
         ((mv exit-status & state)
          (time$ (tshell-call cmd :print t :save t)
                 :msg "; test -f: `~s0`: ~st sec, ~sa bytes~%"
                 :args (list cmd))))
      (if (equal exit-status 0)
          (mv t state)
        (mv nil state)))))

Theorem: booleanp-of-file-exists.exist?

(defthm booleanp-of-file-exists.exist?
  (b* (((mv ?exist? acl2::?state)
        (file-exists smtconfig dir state)))
    (booleanp exist?))
  :rule-classes :rewrite)

Function: find-smtlink-config

(defun find-smtlink-config (smtconfig state)
 (declare (xargs :stobjs (state)))
 (declare (xargs :guard (stringp smtconfig)))
 (let ((acl2::__function__ 'find-smtlink-config))
   (declare (ignorable acl2::__function__))
   (b*
    (((mv & smt_home state)
      (getenv$ "SMT_HOME" state))
     ((mv exists-in-smt_home state)
      (if (stringp smt_home)
          (file-exists smtconfig smt_home state)
        (mv nil state)))
     ((if exists-in-smt_home)
      (prog2$ (cw "Reading smtlink-config from $SMT_HOME...~%")
              (mv smt_home state)))
     ((mv & home state)
      (getenv$ "HOME" state))
     ((mv exists-in-home state)
      (if (stringp home)
          (file-exists smtconfig home state)
        (mv nil state)))
     ((if exists-in-home)
      (prog2$ (cw "Reading smtlink-config from $HOME...~%")
              (mv home state)))
     ((mv & smtlink-pwd state)
      (getenv$ "PWD" state))
     ((mv exists-in-smtlink-pwd state)
      (if (stringp smtlink-pwd)
          (file-exists smtconfig smtlink-pwd state)
        (mv nil state)))
     ((if exists-in-smtlink-pwd)
      (prog2$
           (cw "Reading smtlink-config from Smtlink directory...~%")
           (mv smtlink-pwd state))))
    (mv (prog2$ (er hard? 'smt-config=>find-smtlink-config
                    "Failed to find smtlink-config.~%")
                "")
        state))))

Theorem: stringp-of-find-smtlink-config.dir

(defthm stringp-of-find-smtlink-config.dir
  (b* (((mv ?dir acl2::?state)
        (find-smtlink-config smtconfig state)))
    (stringp dir))
  :rule-classes :rewrite)

Function: default-smt-cnf

(defun default-smt-cnf nil
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'default-smt-cnf))
    (declare (ignorable acl2::__function__))
    *smt-cnf*))

Subtopics

Smtlink-config