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• Line-and-column-tracking

Line-after-nthcdr

Determine what the new line number should be after we advance n characters.

Signature

(line-after-nthcdr n x line) → new-line

Arguments

n — How many characters to cdr.
    Guard (natp n).

x — Characters we're processing.
    Guard (character-listp x).

line — Current line number.
    Guard (natp line).

Returns

new-line — Type (natp new-line).

This is a logically simple way to express how the line number gets updated. It isn't really meant to be executed.

Definitions and Theorems

Function: line-after-nthcdr

(defun line-after-nthcdr (n x line)
  (declare (xargs :guard (and (natp n)
                              (character-listp x)
                              (natp line))))
  (let ((__function__ 'line-after-nthcdr))
    (declare (ignorable __function__))
    (if (or (zp n) (atom x))
        (lnfix line)
      (line-after-nthcdr (- n 1)
                         (cdr x)
                         (if (eql (car x) #\Newline)
                             (+ 1 (lnfix line))
                           (lnfix line))))))

Theorem: natp-of-line-after-nthcdr

(defthm natp-of-line-after-nthcdr
  (b* ((new-line (line-after-nthcdr n x line)))
    (natp new-line))
  :rule-classes :type-prescription)

Theorem: nat-equiv-implies-equal-line-after-nthcdr-1

(defthm nat-equiv-implies-equal-line-after-nthcdr-1
  (implies (nat-equiv n n-equiv)
           (equal (line-after-nthcdr n x line)
                  (line-after-nthcdr n-equiv x line)))
  :rule-classes (:congruence))

Theorem: nat-equiv-implies-equal-line-after-nthcdr-3

(defthm nat-equiv-implies-equal-line-after-nthcdr-3
  (implies (nat-equiv line line-equiv)
           (equal (line-after-nthcdr n x line)
                  (line-after-nthcdr n x line-equiv)))
  :rule-classes (:congruence))

Theorem: lower-bound-of-line-after-nthcdr

(defthm lower-bound-of-line-after-nthcdr
  (<= (nfix line)
      (line-after-nthcdr n x line))
  :rule-classes ((:rewrite) (:linear)))

Theorem: upper-bound-1-of-line-after-nthcdr

(defthm upper-bound-1-of-line-after-nthcdr
  (<= (line-after-nthcdr n x line)
      (+ (nfix line) (nfix n)))
  :rule-classes ((:rewrite) (:linear)))

Theorem: upper-bound-2-of-line-after-nthcdr

(defthm upper-bound-2-of-line-after-nthcdr
  (<= (line-after-nthcdr n x line)
      (+ (nfix line) (len x)))
  :rule-classes ((:rewrite) (:linear)))