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• Static-semantics

Check-sum-field-expression

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

Signature

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

Arguments

tname — Guard (identifierp tname).

target — Guard (expressionp target).

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

alternative — Guard (identifierp alternative).

field — Guard (identifierp field).

expr — Guard (expressionp expr).

ctxt — Guard (contextp ctxt).

Returns

result — Type (type-resultp result).

The type of the expression must be a defined sum type, or a subtype of a defined sum type: we calculate the maximal supertype of the expression's type, and ensure that it is a defined sum type; since sum types are not subtypes, calculating the maximal supertype cannot ``skip'' a sum type.

We generate a proof obligation saying that the target expression has the specified alternative.

We find the type of the field in the alternative of the sum type: this is the type of the whole expression.

Definitions and Theorems

Function: check-sum-field-expression

(defun check-sum-field-expression
       (tname target target-result
              alternative field expr ctxt)
 (declare (xargs :guard (and (identifierp tname)
                             (expressionp target)
                             (type-resultp target-result)
                             (identifierp alternative)
                             (identifierp field)
                             (expressionp expr)
                             (contextp ctxt))))
 (let ((__function__ 'check-sum-field-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-field-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-field-type-mismatch type)))
      (oblig?
           (non-trivial-proof-obligation
                (context->obligation-vars ctxt)
                (context->obligation-hyps ctxt)
                (make-expression-sum-test :type tname
                                          :target target
                                          :alternative alternative)
                expr))
      (product
           (get-alternative-product alternative
                                    (type-sum->alternatives tsum)))
      ((when (not product))
       (type-result-err (list :sum-field-no-alternative
                              tsum (identifier-fix alternative))))
      (ftype (get-field-type field (type-product->fields product)))
      ((when (not ftype))
       (type-result-err (list :no-field-in-product
                              (identifier-fix field)
                              product))))
    (make-type-result-ok
         :types (list ftype)
         :obligations (append target-result.obligations oblig?))))))

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

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

Theorem: check-sum-field-expression-of-identifier-fix-tname

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

Theorem: check-sum-field-expression-identifier-equiv-congruence-on-tname

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: check-sum-field-expression-of-identifier-fix-field

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

Theorem: check-sum-field-expression-identifier-equiv-congruence-on-field

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

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

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

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

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

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

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

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

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