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• Abstract-syntax

Expression-product-field-list

Lift expression-product-field to lists of field names.

Signature

(expression-product-field-list type target x) → *

Arguments

type — Guard (identifierp type).

target — Guard (expressionp target).

x — Guard (identifier-listp x).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: expression-product-field-list-exec

(defun expression-product-field-list-exec (type target x acc)
  (declare (xargs :guard (and (identifierp type)
                              (expressionp target)
                              (identifier-listp x))))
  (declare (xargs :guard t))
  (let ((__function__ 'expression-product-field-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (expression-product-field-list-exec
             type target (cdr x)
             (cons (expression-product-field type target (car x))
                   acc))
      acc)))

Function: expression-product-field-list-nrev

(defun expression-product-field-list-nrev (type target x acl2::nrev)
 (declare (xargs :stobjs (acl2::nrev)))
 (declare (xargs :guard (and (identifierp type)
                             (expressionp target)
                             (identifier-listp x))))
 (declare (xargs :guard t))
 (let ((__function__ 'expression-product-field-list-nrev))
  (declare (ignorable __function__))
  (if (atom x)
      (acl2::nrev-fix acl2::nrev)
   (let
    ((acl2::nrev (acl2::nrev-push
                      (expression-product-field type target (car x))
                      acl2::nrev)))
    (expression-product-field-list-nrev type target (cdr x)
                                        acl2::nrev)))))

Function: expression-product-field-list

(defun expression-product-field-list (type target x)
 (declare (xargs :guard (and (identifierp type)
                             (expressionp target)
                             (identifier-listp x))))
 (declare (xargs :guard t))
 (let ((__function__ 'expression-product-field-list))
  (declare (ignorable __function__))
  (mbe
      :logic
      (if (consp x)
          (cons (expression-product-field type target (car x))
                (expression-product-field-list type target (cdr x)))
        nil)
      :exec
      (if (atom x)
          nil
        (acl2::with-local-nrev (expression-product-field-list-nrev
                                    type target x acl2::nrev))))))

Theorem: nth-of-expression-product-field-list

(defthm nth-of-expression-product-field-list
 (equal
  (nth acl2::n
       (expression-product-field-list type target acl2::x))
  (and
      (< (nfix acl2::n) (len acl2::x))
      (expression-product-field type target (nth acl2::n acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-nrev-removal

(defthm expression-product-field-list-nrev-removal
  (equal
       (expression-product-field-list-nrev
            type target acl2::x acl2::nrev)
       (append acl2::nrev
               (expression-product-field-list type target acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-exec-removal

(defthm expression-product-field-list-exec-removal
 (equal
  (expression-product-field-list-exec type target acl2::x acl2::acc)
  (revappend (expression-product-field-list type target acl2::x)
             acl2::acc))
 :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-of-rev

(defthm expression-product-field-list-of-rev
  (equal (expression-product-field-list type target (rev acl2::x))
         (rev (expression-product-field-list type target acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-of-list-fix

(defthm expression-product-field-list-of-list-fix
 (equal
      (expression-product-field-list type target (list-fix acl2::x))
      (expression-product-field-list type target acl2::x))
 :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-of-append

(defthm expression-product-field-list-of-append
  (equal
       (expression-product-field-list
            type target (append acl2::a acl2::b))
       (append (expression-product-field-list type target acl2::a)
               (expression-product-field-list type target acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-expression-product-field-list

(defthm cdr-of-expression-product-field-list
  (equal (cdr (expression-product-field-list type target acl2::x))
         (expression-product-field-list type target (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-expression-product-field-list

(defthm car-of-expression-product-field-list
  (equal (car (expression-product-field-list type target acl2::x))
         (and (consp acl2::x)
              (expression-product-field type target (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-under-iff

(defthm expression-product-field-list-under-iff
  (iff (expression-product-field-list type target acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-expression-product-field-list

(defthm consp-of-expression-product-field-list
  (equal (consp (expression-product-field-list type target acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-expression-product-field-list

(defthm len-of-expression-product-field-list
  (equal (len (expression-product-field-list type target acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-expression-product-field-list

(defthm true-listp-of-expression-product-field-list
  (true-listp (expression-product-field-list type target acl2::x))
  :rule-classes :type-prescription)

Theorem: expression-product-field-list-when-not-consp

(defthm expression-product-field-list-when-not-consp
 (implies (not (consp acl2::x))
          (equal (expression-product-field-list type target acl2::x)
                 nil))
 :rule-classes ((:rewrite)))

Theorem: expression-product-field-list-of-cons

(defthm expression-product-field-list-of-cons
 (equal
  (expression-product-field-list type target (cons acl2::a acl2::b))
  (cons (expression-product-field type target acl2::a)
        (expression-product-field-list type target acl2::b)))
 :rule-classes ((:rewrite)))

Theorem: expression-listp-of-expression-product-field-list

(defthm expression-listp-of-expression-product-field-list
  (expression-listp (expression-product-field-list type target x)))

Theorem: expression-product-field-list-of-identifier-fix-type

(defthm expression-product-field-list-of-identifier-fix-type
  (equal (expression-product-field-list (identifier-fix type)
                                        target x)
         (expression-product-field-list type target x)))

Theorem: expression-product-field-list-identifier-equiv-congruence-on-type

(defthm
  expression-product-field-list-identifier-equiv-congruence-on-type
  (implies
       (identifier-equiv type type-equiv)
       (equal (expression-product-field-list type target x)
              (expression-product-field-list type-equiv target x)))
  :rule-classes :congruence)

Theorem: expression-product-field-list-of-expression-fix-target

(defthm expression-product-field-list-of-expression-fix-target
  (equal (expression-product-field-list type (expression-fix target)
                                        x)
         (expression-product-field-list type target x)))

Theorem: expression-product-field-list-expression-equiv-congruence-on-target

(defthm
 expression-product-field-list-expression-equiv-congruence-on-target
 (implies
      (expression-equiv target target-equiv)
      (equal (expression-product-field-list type target x)
             (expression-product-field-list type target-equiv x)))
 :rule-classes :congruence)

Theorem: expression-product-field-list-of-identifier-list-fix-x

(defthm expression-product-field-list-of-identifier-list-fix-x
  (equal (expression-product-field-list
              type target (identifier-list-fix x))
         (expression-product-field-list type target x)))

Theorem: expression-product-field-list-identifier-list-equiv-congruence-on-x

(defthm
 expression-product-field-list-identifier-list-equiv-congruence-on-x
 (implies
      (identifier-list-equiv x x-equiv)
      (equal (expression-product-field-list type target x)
             (expression-product-field-list type target x-equiv)))
 :rule-classes :congruence)