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Parse-bin-val-rest

Parse an option [ 1*("." 1*BIT) / ("-" 1*BIT) ], which is the rest of the definiens of bin-val.

Signature

(parse-bin-val-rest input) → (mv error? tree rest-input)

Arguments

input — Guard (nat-listp input).

Returns

error? — Type (not error?).

tree — Type (treep tree).

rest-input — Type (nat-listp rest-input).

Definitions and Theorems

Function: parse-bin-val-rest

(defun parse-bin-val-rest (input)
  (declare (xargs :guard (nat-listp input)))
  (seq-backtrack
       input
       ((trees := (parse-1*-dot-1*bit input))
        (return (make-tree-nonleaf :rulename? nil
                                   :branches (list trees))))
       ((tree := (parse-dash-1*bit input))
        (return (make-tree-nonleaf :rulename? nil
                                   :branches (list (list tree)))))
       ((return-raw (mv nil
                        (make-tree-nonleaf :rulename? nil
                                           :branches nil)
                        (nat-list-fix input))))))

Theorem: not-of-parse-bin-val-rest.error?

(defthm not-of-parse-bin-val-rest.error?
  (b* (((mv ?error? ?tree ?rest-input)
        (parse-bin-val-rest input)))
    (not error?))
  :rule-classes :rewrite)

Theorem: treep-of-parse-bin-val-rest.tree

(defthm treep-of-parse-bin-val-rest.tree
  (b* (((mv ?error? ?tree ?rest-input)
        (parse-bin-val-rest input)))
    (treep tree))
  :rule-classes :rewrite)

Theorem: nat-listp-of-parse-bin-val-rest.rest-input

(defthm nat-listp-of-parse-bin-val-rest.rest-input
  (b* (((mv ?error? ?tree ?rest-input)
        (parse-bin-val-rest input)))
    (nat-listp rest-input))
  :rule-classes :rewrite)

Theorem: len-of-parse-bin-val-rest-linear

(defthm len-of-parse-bin-val-rest-linear
  (b* (((mv ?error? ?tree ?rest-input)
        (parse-bin-val-rest input)))
    (<= (len rest-input) (len input)))
  :rule-classes :linear)

Theorem: parse-bin-val-rest-of-nat-list-fix-input

(defthm parse-bin-val-rest-of-nat-list-fix-input
  (equal (parse-bin-val-rest (nat-list-fix input))
         (parse-bin-val-rest input)))

Theorem: parse-bin-val-rest-nat-list-equiv-congruence-on-input

(defthm parse-bin-val-rest-nat-list-equiv-congruence-on-input
  (implies (acl2::nat-list-equiv input input-equiv)
           (equal (parse-bin-val-rest input)
                  (parse-bin-val-rest input-equiv)))
  :rule-classes :congruence)