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• Well-formedness

Constraint-list-wfp

Check if a list of constraints is well-formed, with respect to a list of relation definitions.

Signature

(constraint-list-wfp constrs defs) → yes/no

Arguments

constrs — Guard (constraint-listp constrs).

defs — Guard (definition-listp defs).

Returns

yes/no — Type (booleanp yes/no).

A list of constraints is well-formed iff all the constraints are well-formed.

Definitions and Theorems

Function: constraint-list-wfp

(defun constraint-list-wfp (constrs defs)
  (declare (xargs :guard (and (constraint-listp constrs)
                              (definition-listp defs))))
  (let ((__function__ 'constraint-list-wfp))
    (declare (ignorable __function__))
    (or (endp constrs)
        (and (constraint-wfp (car constrs) defs)
             (constraint-list-wfp (cdr constrs)
                                  defs)))))

Theorem: booleanp-of-constraint-list-wfp

(defthm booleanp-of-constraint-list-wfp
  (b* ((yes/no (constraint-list-wfp constrs defs)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: constraint-list-wfp-of-constraint-list-fix-constrs

(defthm constraint-list-wfp-of-constraint-list-fix-constrs
  (equal (constraint-list-wfp (constraint-list-fix constrs)
                              defs)
         (constraint-list-wfp constrs defs)))

Theorem: constraint-list-wfp-constraint-list-equiv-congruence-on-constrs

(defthm
    constraint-list-wfp-constraint-list-equiv-congruence-on-constrs
  (implies (constraint-list-equiv constrs constrs-equiv)
           (equal (constraint-list-wfp constrs defs)
                  (constraint-list-wfp constrs-equiv defs)))
  :rule-classes :congruence)

Theorem: constraint-list-wfp-of-definition-list-fix-defs

(defthm constraint-list-wfp-of-definition-list-fix-defs
  (equal (constraint-list-wfp constrs (definition-list-fix defs))
         (constraint-list-wfp constrs defs)))

Theorem: constraint-list-wfp-definition-list-equiv-congruence-on-defs

(defthm constraint-list-wfp-definition-list-equiv-congruence-on-defs
  (implies (definition-list-equiv defs defs-equiv)
           (equal (constraint-list-wfp constrs defs)
                  (constraint-list-wfp constrs defs-equiv)))
  :rule-classes :congruence)