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• Static-semantics

Check-iff-expression

Check if a coimplication expression is well-formed.

Signature

(check-iff-expression arg1 arg2 arg1-type arg2-type 
                      arg1-obligs arg2-obligs expr ctxt) 
 
  → 
result

Arguments

arg1 — Guard (expressionp arg1).

arg2 — Guard (expressionp arg2).

arg1-type — Guard (typep arg1-type).

arg2-type — Guard (typep arg2-type).

arg1-obligs — Guard (proof-obligation-listp arg1-obligs).

arg2-obligs — Guard (proof-obligation-listp arg2-obligs).

expr — Guard (expressionp expr).

ctxt — Guard (contextp ctxt).

Returns

result — Type (type-resultp result).

The operands must be booleans, and the result is a boolean.

Definitions and Theorems

Function: check-iff-expression

(defun check-iff-expression (arg1 arg2 arg1-type arg2-type
                                  arg1-obligs arg2-obligs expr ctxt)
 (declare (xargs :guard (and (expressionp arg1)
                             (expressionp arg2)
                             (typep arg1-type)
                             (typep arg2-type)
                             (proof-obligation-listp arg1-obligs)
                             (proof-obligation-listp arg2-obligs)
                             (expressionp expr)
                             (contextp ctxt))))
 (declare (ignorable expr))
 (let ((__function__ 'check-iff-expression))
  (declare (ignorable __function__))
  (b*
   (((mv okp obligs)
     (match-type arg1 arg1-type (type-boolean)
                 ctxt))
    ((unless okp)
     (type-result-err (list :type-mismatch-iff (expression-fix arg1)
                            (expression-fix arg2)
                            (type-fix arg1-type)
                            (type-fix arg2-type)
                            (type-boolean))))
    ((acl2::run-when (consp obligs))
     (raise "Internal error: obligations ~x0 for the boolean type."
            obligs))
    ((mv okp obligs)
     (match-type arg2 arg2-type (type-boolean)
                 ctxt))
    ((unless okp)
     (type-result-err (list :type-mismatch-iff (expression-fix arg1)
                            (expression-fix arg2)
                            (type-fix arg1-type)
                            (type-fix arg2-type)
                            (type-boolean))))
    ((acl2::run-when (consp obligs))
     (raise "Internal error: obligations ~x0 for the boolean type."
            obligs)))
   (make-type-result-ok
        :types (list (type-boolean))
        :obligations (append arg1-obligs arg2-obligs)))))

Theorem: type-resultp-of-check-iff-expression

(defthm type-resultp-of-check-iff-expression
  (b*
    ((result
          (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)))
    (type-resultp result))
  :rule-classes :rewrite)

Theorem: check-iff-expression-of-expression-fix-arg1

(defthm check-iff-expression-of-expression-fix-arg1
  (equal (check-iff-expression (expression-fix arg1)
                               arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)
         (check-iff-expression arg1 arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-expression-equiv-congruence-on-arg1

(defthm check-iff-expression-expression-equiv-congruence-on-arg1
 (implies
   (expression-equiv arg1 arg1-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1-equiv arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-expression-fix-arg2

(defthm check-iff-expression-of-expression-fix-arg2
  (equal (check-iff-expression arg1 (expression-fix arg2)
                               arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)
         (check-iff-expression arg1 arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-expression-equiv-congruence-on-arg2

(defthm check-iff-expression-expression-equiv-congruence-on-arg2
 (implies
   (expression-equiv arg2 arg2-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1 arg2-equiv arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-type-fix-arg1-type

(defthm check-iff-expression-of-type-fix-arg1-type
  (equal (check-iff-expression arg1 arg2 (type-fix arg1-type)
                               arg2-type
                               arg1-obligs arg2-obligs expr ctxt)
         (check-iff-expression arg1 arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-type-equiv-congruence-on-arg1-type

(defthm check-iff-expression-type-equiv-congruence-on-arg1-type
 (implies
   (type-equiv arg1-type arg1-type-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1 arg2 arg1-type-equiv arg2-type
                                arg1-obligs arg2-obligs expr ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-type-fix-arg2-type

(defthm check-iff-expression-of-type-fix-arg2-type
 (equal
      (check-iff-expression arg1 arg2 arg1-type (type-fix arg2-type)
                            arg1-obligs arg2-obligs expr ctxt)
      (check-iff-expression arg1 arg2 arg1-type arg2-type
                            arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-type-equiv-congruence-on-arg2-type

(defthm check-iff-expression-type-equiv-congruence-on-arg2-type
 (implies
   (type-equiv arg2-type arg2-type-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1 arg2 arg1-type arg2-type-equiv
                                arg1-obligs arg2-obligs expr ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-proof-obligation-list-fix-arg1-obligs

(defthm
      check-iff-expression-of-proof-obligation-list-fix-arg1-obligs
  (equal
       (check-iff-expression arg1 arg2 arg1-type arg2-type
                             (proof-obligation-list-fix arg1-obligs)
                             arg2-obligs expr ctxt)
       (check-iff-expression arg1 arg2 arg1-type arg2-type
                             arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-proof-obligation-list-equiv-congruence-on-arg1-obligs

(defthm
 check-iff-expression-proof-obligation-list-equiv-congruence-on-arg1-obligs
 (implies
  (proof-obligation-list-equiv arg1-obligs arg1-obligs-equiv)
  (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)
         (check-iff-expression arg1 arg2
                               arg1-type arg2-type arg1-obligs-equiv
                               arg2-obligs expr ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-proof-obligation-list-fix-arg2-obligs

(defthm
      check-iff-expression-of-proof-obligation-list-fix-arg2-obligs
  (equal
       (check-iff-expression arg1
                             arg2 arg1-type arg2-type arg1-obligs
                             (proof-obligation-list-fix arg2-obligs)
                             expr ctxt)
       (check-iff-expression arg1 arg2 arg1-type arg2-type
                             arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-proof-obligation-list-equiv-congruence-on-arg2-obligs

(defthm
 check-iff-expression-proof-obligation-list-equiv-congruence-on-arg2-obligs
 (implies
   (proof-obligation-list-equiv arg2-obligs arg2-obligs-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs-equiv expr ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-expression-fix-expr

(defthm check-iff-expression-of-expression-fix-expr
  (equal (check-iff-expression arg1
                               arg2 arg1-type arg2-type arg1-obligs
                               arg2-obligs (expression-fix expr)
                               ctxt)
         (check-iff-expression arg1 arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-expression-equiv-congruence-on-expr

(defthm check-iff-expression-expression-equiv-congruence-on-expr
 (implies
   (expression-equiv expr expr-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs expr-equiv ctxt)))
 :rule-classes :congruence)

Theorem: check-iff-expression-of-context-fix-ctxt

(defthm check-iff-expression-of-context-fix-ctxt
  (equal (check-iff-expression arg1
                               arg2 arg1-type arg2-type arg1-obligs
                               arg2-obligs expr (context-fix ctxt))
         (check-iff-expression arg1 arg2 arg1-type arg2-type
                               arg1-obligs arg2-obligs expr ctxt)))

Theorem: check-iff-expression-context-equiv-congruence-on-ctxt

(defthm check-iff-expression-context-equiv-congruence-on-ctxt
 (implies
   (context-equiv ctxt ctxt-equiv)
   (equal (check-iff-expression arg1 arg2 arg1-type arg2-type
                                arg1-obligs arg2-obligs expr ctxt)
          (check-iff-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs expr ctxt-equiv)))
 :rule-classes :congruence)