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• Static-semantics

Check-alternative

Check if a type sum alternative is statically well-formed.

Signature

(check-alternative alternative ctxt) → (mv err? obligs)

Arguments

alternative — Guard (alternativep alternative).

ctxt — Guard (contextp ctxt).

Returns

obligs — Type (proof-obligation-listp obligs).

We check the underlying product type. The guard assumptions on the context are motivated in the same way as in check-type-product.

Definitions and Theorems

Function: check-alternative

(defun check-alternative (alternative ctxt)
  (declare (xargs :guard (and (alternativep alternative)
                              (contextp ctxt))))
  (declare
       (xargs :guard (and (null (context->functions ctxt))
                          (omap::emptyp (context->variables ctxt))
                          (null (context->obligation-vars ctxt))
                          (null (context->obligation-hyps ctxt)))))
  (let ((__function__ 'check-alternative))
    (declare (ignorable __function__))
    (check-type-product (alternative->product alternative)
                        ctxt)))

Theorem: proof-obligation-listp-of-check-alternative.obligs

(defthm proof-obligation-listp-of-check-alternative.obligs
  (b* (((mv ?err? ?obligs)
        (check-alternative alternative ctxt)))
    (proof-obligation-listp obligs))
  :rule-classes :rewrite)

Theorem: check-alternative-of-alternative-fix-alternative

(defthm check-alternative-of-alternative-fix-alternative
  (equal (check-alternative (alternative-fix alternative)
                            ctxt)
         (check-alternative alternative ctxt)))

Theorem: check-alternative-alternative-equiv-congruence-on-alternative

(defthm
      check-alternative-alternative-equiv-congruence-on-alternative
  (implies (alternative-equiv alternative alternative-equiv)
           (equal (check-alternative alternative ctxt)
                  (check-alternative alternative-equiv ctxt)))
  :rule-classes :congruence)

Theorem: check-alternative-of-context-fix-ctxt

(defthm check-alternative-of-context-fix-ctxt
  (equal (check-alternative alternative (context-fix ctxt))
         (check-alternative alternative ctxt)))

Theorem: check-alternative-context-equiv-congruence-on-ctxt

(defthm check-alternative-context-equiv-congruence-on-ctxt
  (implies (context-equiv ctxt ctxt-equiv)
           (equal (check-alternative alternative ctxt)
                  (check-alternative alternative ctxt-equiv)))
  :rule-classes :congruence)