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• Parser-states

Span-join

Join two spans.

Signature

(span-join span1 span2) → span

Arguments

span1 — Guard (spanp span1).

span2 — Guard (spanp span2).

Returns

span — Type (spanp span).

The first span must come before the second one. We return a new span that goes from the start of the first span to the end of the second span.

Definitions and Theorems

Function: span-join

(defun span-join (span1 span2)
  (declare (xargs :guard (and (spanp span1) (spanp span2))))
  (make-span :start (span->start span1)
             :end (span->end span2)))

Theorem: spanp-of-span-join

(defthm spanp-of-span-join
  (b* ((span (span-join span1 span2)))
    (spanp span))
  :rule-classes :rewrite)

Theorem: span-join-of-span-fix-span1

(defthm span-join-of-span-fix-span1
  (equal (span-join (span-fix span1) span2)
         (span-join span1 span2)))

Theorem: span-join-span-equiv-congruence-on-span1

(defthm span-join-span-equiv-congruence-on-span1
  (implies (span-equiv span1 span1-equiv)
           (equal (span-join span1 span2)
                  (span-join span1-equiv span2)))
  :rule-classes :congruence)

Theorem: span-join-of-span-fix-span2

(defthm span-join-of-span-fix-span2
  (equal (span-join span1 (span-fix span2))
         (span-join span1 span2)))

Theorem: span-join-span-equiv-congruence-on-span2

(defthm span-join-span-equiv-congruence-on-span2
  (implies (span-equiv span2 span2-equiv)
           (equal (span-join span1 span2)
                  (span-join span1 span2-equiv)))
  :rule-classes :congruence)