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• Semantics

Lookup-rulename

Collect all the alternatives associated to a rule name from some rules.

Signature

(lookup-rulename rulename rules) → alternation

Arguments

rulename — Guard (rulenamep rulename).

rules — Guard (rulelistp rules).

Returns

alternation — Type (alternationp alternation).

For well-formed rules, this function is an appropriate way to test whether rulename appears (on the left side of) some rule in rules. The reason is that well-formed rules must have non-empty alternations as definientia.

Definitions and Theorems

Function: lookup-rulename

(defun lookup-rulename (rulename rules)
  (declare (xargs :guard (and (rulenamep rulename)
                              (rulelistp rules))))
  (b* ((rulename (mbe :logic (rulename-fix rulename)
                      :exec rulename)))
    (cond ((endp rules) nil)
          (t (let ((rule (car rules)))
               (if (equal (rule->name rule) rulename)
                   (append (rule->definiens rule)
                           (lookup-rulename rulename (cdr rules)))
                 (lookup-rulename rulename (cdr rules))))))))

Theorem: alternationp-of-lookup-rulename

(defthm alternationp-of-lookup-rulename
  (b* ((alternation (lookup-rulename rulename rules)))
    (alternationp alternation))
  :rule-classes :rewrite)

Theorem: lookup-rulename-of-rulename-fix-rulename

(defthm lookup-rulename-of-rulename-fix-rulename
  (equal (lookup-rulename (rulename-fix rulename)
                          rules)
         (lookup-rulename rulename rules)))

Theorem: lookup-rulename-rulename-equiv-congruence-on-rulename

(defthm lookup-rulename-rulename-equiv-congruence-on-rulename
  (implies (rulename-equiv rulename rulename-equiv)
           (equal (lookup-rulename rulename rules)
                  (lookup-rulename rulename-equiv rules)))
  :rule-classes :congruence)

Theorem: lookup-rulename-of-rulelist-fix-rules

(defthm lookup-rulename-of-rulelist-fix-rules
  (equal (lookup-rulename rulename (rulelist-fix rules))
         (lookup-rulename rulename rules)))

Theorem: lookup-rulename-rulelist-equiv-congruence-on-rules

(defthm lookup-rulename-rulelist-equiv-congruence-on-rules
  (implies (rulelist-equiv rules rules-equiv)
           (equal (lookup-rulename rulename rules)
                  (lookup-rulename rulename rules-equiv)))
  :rule-classes :congruence)