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Atc-arrays

Schar-array-write

Write an element to an array of type signed char, using a c integer index.

Signature
(schar-array-write array index element) → new-array
Arguments: array — Guard (schar-arrayp array).; index — Guard (cintegerp index).; element — Guard (scharp element).
Returns: new-array — Type (schar-arrayp new-array).

Definitions and Theorems

Function: schar-array-write

(defun schar-array-write (array index element)
  (declare (xargs :guard (and (schar-arrayp array)
                              (cintegerp index)
                              (scharp element))))
  (declare (xargs :guard (schar-array-index-okp array index)))
  (let ((__function__ 'schar-array-write))
    (declare (ignorable __function__))
    (if (mbt (schar-array-index-okp array index))
        (schar-array-of (update-nth (integer-from-cinteger index)
                                    (schar-fix element)
                                    (schar-array->elements array)))
      (schar-array-fix array))))

Theorem: schar-arrayp-of-schar-array-write

(defthm schar-arrayp-of-schar-array-write
  (b* ((new-array (schar-array-write array index element)))
    (schar-arrayp new-array))
  :rule-classes :rewrite)

Theorem: len-of-schar-array->elements-of-schar-array-write

(defthm len-of-schar-array->elements-of-schar-array-write
 (equal
  (len
    (schar-array->elements (schar-array-write array index element)))
  (len (schar-array->elements array))))

Theorem: schar-array-length-of-schar-array-write

(defthm schar-array-length-of-schar-array-write
 (equal (schar-array-length (schar-array-write array index element))
        (schar-array-length array)))

Theorem: schar-array-write-to-integer-write

(defthm schar-array-write-to-integer-write
 (equal
      (schar-array-write array index val)
      (schar-array-integer-write array (integer-from-cinteger index)
                                 val)))

Theorem: schar-array-write-alt-def

(defthm schar-array-write-alt-def
  (implies (and (schar-arrayp array)
                (cintegerp index)
                (scharp elem)
                (schar-array-index-okp array index))
           (equal (schar-array-write array index elem)
                  (value-array-write (integer-from-cinteger index)
                                     elem array))))

Theorem: schar-array-write-of-schar-array-fix-array

(defthm schar-array-write-of-schar-array-fix-array
  (equal (schar-array-write (schar-array-fix array)
                            index element)
         (schar-array-write array index element)))

Theorem: schar-array-write-schar-array-equiv-congruence-on-array

(defthm schar-array-write-schar-array-equiv-congruence-on-array
  (implies (schar-array-equiv array array-equiv)
           (equal (schar-array-write array index element)
                  (schar-array-write array-equiv index element)))
  :rule-classes :congruence)

Theorem: schar-array-write-of-cinteger-fix-index

(defthm schar-array-write-of-cinteger-fix-index
  (equal (schar-array-write array (cinteger-fix index)
                            element)
         (schar-array-write array index element)))

Theorem: schar-array-write-cinteger-equiv-congruence-on-index

(defthm schar-array-write-cinteger-equiv-congruence-on-index
  (implies (cinteger-equiv index index-equiv)
           (equal (schar-array-write array index element)
                  (schar-array-write array index-equiv element)))
  :rule-classes :congruence)

Theorem: schar-array-write-of-schar-fix-element

(defthm schar-array-write-of-schar-fix-element
  (equal (schar-array-write array index (schar-fix element))
         (schar-array-write array index element)))

Theorem: schar-array-write-schar-equiv-congruence-on-element

(defthm schar-array-write-schar-equiv-congruence-on-element
  (implies (schar-equiv element element-equiv)
           (equal (schar-array-write array index element)
                  (schar-array-write array index element-equiv)))
  :rule-classes :congruence)