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• Static-semantics

Check-sum-test-expression

Check if a sum test expression is statically well-formed.

Signature

(check-sum-test-expression target 
                           target-result alternative expr ctxt) 
 
  → 
result

Arguments

target — Guard (expressionp target).

target-result — Guard (type-resultp target-result).

alternative — Guard (identifierp alternative).

expr — Guard (expressionp expr).

ctxt — Guard (contextp ctxt).

Returns

result — Type (type-resultp result).

The type of the target expression must be (a subtype of) a sum type. The alternative must be one of that sum type. The type of the whole expression is boolean.

Definitions and Theorems

Function: check-sum-test-expression

(defun check-sum-test-expression
       (target target-result alternative expr ctxt)
 (declare (xargs :guard (and (expressionp target)
                             (type-resultp target-result)
                             (identifierp alternative)
                             (expressionp expr)
                             (contextp ctxt))))
 (declare (ignorable expr))
 (let ((__function__ 'check-sum-test-expression))
  (declare (ignorable __function__))
  (type-result-case
   target-result :err
   (type-result-err target-result.info)
   :ok
   (b*
     ((type (ensure-single-type target-result.types))
      ((when (not type))
       (type-result-err (list :multi-valued-sum-test-target
                              (expression-fix target)
                              target-result.types)))
      (type (max-supertype type (context->tops ctxt)))
      ((when (not type))
       (type-result-err (list :no-max-supertype type)))
      (tsum (get-type-sum type (context->tops ctxt)))
      ((when (not tsum))
       (type-result-err (list :sum-test-type-mismatch type)))
      (product
           (get-alternative-product alternative
                                    (type-sum->alternatives tsum)))
      ((when (not product))
       (type-result-err (list :sum-test-no-alternative
                              tsum (identifier-fix alternative)))))
    (make-type-result-ok :types (list (type-boolean))
                         :obligations target-result.obligations)))))

Theorem: type-resultp-of-check-sum-test-expression

(defthm type-resultp-of-check-sum-test-expression
  (b* ((result (check-sum-test-expression
                    target
                    target-result alternative expr ctxt)))
    (type-resultp result))
  :rule-classes :rewrite)

Theorem: check-sum-test-expression-of-expression-fix-target

(defthm check-sum-test-expression-of-expression-fix-target
 (equal
   (check-sum-test-expression (expression-fix target)
                              target-result alternative expr ctxt)
   (check-sum-test-expression target
                              target-result alternative expr ctxt)))

Theorem: check-sum-test-expression-expression-equiv-congruence-on-target

(defthm
    check-sum-test-expression-expression-equiv-congruence-on-target
 (implies
  (expression-equiv target target-equiv)
  (equal
   (check-sum-test-expression target
                              target-result alternative expr ctxt)
   (check-sum-test-expression target-equiv
                              target-result alternative expr ctxt)))
 :rule-classes :congruence)

Theorem: check-sum-test-expression-of-type-result-fix-target-result

(defthm check-sum-test-expression-of-type-result-fix-target-result
 (equal
   (check-sum-test-expression target (type-result-fix target-result)
                              alternative expr ctxt)
   (check-sum-test-expression target
                              target-result alternative expr ctxt)))

Theorem: check-sum-test-expression-type-result-equiv-congruence-on-target-result

(defthm
 check-sum-test-expression-type-result-equiv-congruence-on-target-result
 (implies
  (type-result-equiv target-result target-result-equiv)
  (equal
     (check-sum-test-expression target
                                target-result alternative expr ctxt)
     (check-sum-test-expression target target-result-equiv
                                alternative expr ctxt)))
 :rule-classes :congruence)

Theorem: check-sum-test-expression-of-identifier-fix-alternative

(defthm check-sum-test-expression-of-identifier-fix-alternative
 (equal
   (check-sum-test-expression target target-result
                              (identifier-fix alternative)
                              expr ctxt)
   (check-sum-test-expression target
                              target-result alternative expr ctxt)))

Theorem: check-sum-test-expression-identifier-equiv-congruence-on-alternative

(defthm
 check-sum-test-expression-identifier-equiv-congruence-on-alternative
 (implies
  (identifier-equiv alternative alternative-equiv)
  (equal
     (check-sum-test-expression target
                                target-result alternative expr ctxt)
     (check-sum-test-expression target target-result
                                alternative-equiv expr ctxt)))
 :rule-classes :congruence)

Theorem: check-sum-test-expression-of-expression-fix-expr

(defthm check-sum-test-expression-of-expression-fix-expr
 (equal
   (check-sum-test-expression target target-result
                              alternative (expression-fix expr)
                              ctxt)
   (check-sum-test-expression target
                              target-result alternative expr ctxt)))

Theorem: check-sum-test-expression-expression-equiv-congruence-on-expr

(defthm
      check-sum-test-expression-expression-equiv-congruence-on-expr
 (implies
  (expression-equiv expr expr-equiv)
  (equal
     (check-sum-test-expression target
                                target-result alternative expr ctxt)
     (check-sum-test-expression target target-result
                                alternative expr-equiv ctxt)))
 :rule-classes :congruence)

Theorem: check-sum-test-expression-of-context-fix-ctxt

(defthm check-sum-test-expression-of-context-fix-ctxt
 (equal
   (check-sum-test-expression target target-result
                              alternative expr (context-fix ctxt))
   (check-sum-test-expression target
                              target-result alternative expr ctxt)))

Theorem: check-sum-test-expression-context-equiv-congruence-on-ctxt

(defthm check-sum-test-expression-context-equiv-congruence-on-ctxt
 (implies
  (context-equiv ctxt ctxt-equiv)
  (equal
     (check-sum-test-expression target
                                target-result alternative expr ctxt)
     (check-sum-test-expression target target-result
                                alternative expr ctxt-equiv)))
 :rule-classes :congruence)