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• Abstract-syntax

Expression-sum-field-list

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

Signature

(expression-sum-field-list type target alternative x) → *

Arguments

type — Guard (identifierp type).

target — Guard (expressionp target).

alternative — Guard (identifierp alternative).

x — Guard (identifier-listp x).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: expression-sum-field-list-exec

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

Function: expression-sum-field-list-nrev

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

Function: expression-sum-field-list

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: expression-sum-field-list-of-identifier-fix-alternative

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

Theorem: expression-sum-field-list-identifier-equiv-congruence-on-alternative

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

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

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

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

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