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• Static-semantics

Check-eq/ne-expression

Check if an equality or inequality expression is well-formed.

Signature

(check-eq/ne-expression arg1 
                        arg2 arg1-type arg2-type arg1-obligs 
                        arg2-obligs err-keyword 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).

err-keyword — Guard (keywordp err-keyword).

expr — Guard (expressionp expr).

ctxt — Guard (contextp ctxt).

Returns

result — Type (type-resultp result).

The two types must have a supremum type, which is the one where the (in)equality is checked. Otherwise, the expression is not type-correct. The expression returns a boolean.

Definitions and Theorems

Function: check-eq/ne-expression

(defun check-eq/ne-expression
       (arg1 arg2 arg1-type arg2-type arg1-obligs
             arg2-obligs err-keyword 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)
                             (keywordp err-keyword)
                             (expressionp expr)
                             (contextp ctxt))))
 (declare (ignorable expr))
 (let ((__function__ 'check-eq/ne-expression))
  (declare (ignorable __function__))
  (b* ((supremum (supremum-type arg1-type
                                arg2-type (context->tops ctxt))))
    (if supremum (make-type-result-ok
                      :types (list (type-boolean))
                      :obligations (append arg1-obligs arg2-obligs))
      (type-result-err (list err-keyword (expression-fix arg1)
                             (expression-fix arg2)
                             (type-fix arg1-type)
                             (type-fix arg2-type)))))))

Theorem: type-resultp-of-check-eq/ne-expression

(defthm type-resultp-of-check-eq/ne-expression
 (b*
  ((result
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))
  (type-resultp result))
 :rule-classes :rewrite)

Theorem: check-eq/ne-expression-of-expression-fix-arg1

(defthm check-eq/ne-expression-of-expression-fix-arg1
 (equal (check-eq/ne-expression (expression-fix arg1)
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-expression-equiv-congruence-on-arg1

(defthm check-eq/ne-expression-expression-equiv-congruence-on-arg1
 (implies
   (expression-equiv arg1 arg1-equiv)
   (equal
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1-equiv
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-expression-fix-arg2

(defthm check-eq/ne-expression-of-expression-fix-arg2
 (equal (check-eq/ne-expression arg1 (expression-fix arg2)
                                arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-expression-equiv-congruence-on-arg2

(defthm check-eq/ne-expression-expression-equiv-congruence-on-arg2
 (implies
   (expression-equiv arg2 arg2-equiv)
   (equal
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1 arg2-equiv
                                arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-type-fix-arg1-type

(defthm check-eq/ne-expression-of-type-fix-arg1-type
 (equal (check-eq/ne-expression arg1 arg2 (type-fix arg1-type)
                                arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-type-equiv-congruence-on-arg1-type

(defthm check-eq/ne-expression-type-equiv-congruence-on-arg1-type
 (implies
  (type-equiv arg1-type arg1-type-equiv)
  (equal
       (check-eq/ne-expression arg1
                               arg2 arg1-type arg2-type arg1-obligs
                               arg2-obligs err-keyword expr ctxt)
       (check-eq/ne-expression arg1 arg2
                               arg1-type-equiv arg2-type arg1-obligs
                               arg2-obligs err-keyword expr ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-type-fix-arg2-type

(defthm check-eq/ne-expression-of-type-fix-arg2-type
 (equal
    (check-eq/ne-expression arg1 arg2 arg1-type (type-fix arg2-type)
                            arg1-obligs
                            arg2-obligs err-keyword expr ctxt)
    (check-eq/ne-expression arg1
                            arg2 arg1-type arg2-type arg1-obligs
                            arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-type-equiv-congruence-on-arg2-type

(defthm check-eq/ne-expression-type-equiv-congruence-on-arg2-type
 (implies
  (type-equiv arg2-type arg2-type-equiv)
  (equal
       (check-eq/ne-expression arg1
                               arg2 arg1-type arg2-type arg1-obligs
                               arg2-obligs err-keyword expr ctxt)
       (check-eq/ne-expression arg1 arg2
                               arg1-type arg2-type-equiv arg1-obligs
                               arg2-obligs err-keyword expr ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-proof-obligation-list-fix-arg1-obligs

(defthm
    check-eq/ne-expression-of-proof-obligation-list-fix-arg1-obligs
 (equal
     (check-eq/ne-expression arg1 arg2 arg1-type arg2-type
                             (proof-obligation-list-fix arg1-obligs)
                             arg2-obligs err-keyword expr ctxt)
     (check-eq/ne-expression arg1
                             arg2 arg1-type arg2-type arg1-obligs
                             arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-proof-obligation-list-equiv-congruence-on-arg1-obligs

(defthm
 check-eq/ne-expression-proof-obligation-list-equiv-congruence-on-arg1-obligs
 (implies
  (proof-obligation-list-equiv arg1-obligs arg1-obligs-equiv)
  (equal
       (check-eq/ne-expression arg1
                               arg2 arg1-type arg2-type arg1-obligs
                               arg2-obligs err-keyword expr ctxt)
       (check-eq/ne-expression arg1 arg2
                               arg1-type arg2-type arg1-obligs-equiv
                               arg2-obligs err-keyword expr ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-proof-obligation-list-fix-arg2-obligs

(defthm
    check-eq/ne-expression-of-proof-obligation-list-fix-arg2-obligs
 (equal
     (check-eq/ne-expression arg1
                             arg2 arg1-type arg2-type arg1-obligs
                             (proof-obligation-list-fix arg2-obligs)
                             err-keyword expr ctxt)
     (check-eq/ne-expression arg1
                             arg2 arg1-type arg2-type arg1-obligs
                             arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-proof-obligation-list-equiv-congruence-on-arg2-obligs

(defthm
 check-eq/ne-expression-proof-obligation-list-equiv-congruence-on-arg2-obligs
 (implies
  (proof-obligation-list-equiv arg2-obligs arg2-obligs-equiv)
  (equal
     (check-eq/ne-expression arg1
                             arg2 arg1-type arg2-type arg1-obligs
                             arg2-obligs err-keyword expr ctxt)
     (check-eq/ne-expression arg1 arg2 arg1-type
                             arg2-type arg1-obligs arg2-obligs-equiv
                             err-keyword expr ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-expression-fix-expr

(defthm check-eq/ne-expression-of-expression-fix-expr
 (equal (check-eq/ne-expression arg1 arg2 arg1-type
                                arg2-type arg1-obligs arg2-obligs
                                err-keyword (expression-fix expr)
                                ctxt)
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-expression-equiv-congruence-on-expr

(defthm check-eq/ne-expression-expression-equiv-congruence-on-expr
 (implies
   (expression-equiv expr expr-equiv)
   (equal
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1 arg2 arg1-type
                                arg2-type arg1-obligs arg2-obligs
                                err-keyword expr-equiv ctxt)))
 :rule-classes :congruence)

Theorem: check-eq/ne-expression-of-context-fix-ctxt

(defthm check-eq/ne-expression-of-context-fix-ctxt
 (equal (check-eq/ne-expression arg1 arg2 arg1-type
                                arg2-type arg1-obligs arg2-obligs
                                err-keyword expr (context-fix ctxt))
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-eq/ne-expression-context-equiv-congruence-on-ctxt

(defthm check-eq/ne-expression-context-equiv-congruence-on-ctxt
 (implies
   (context-equiv ctxt ctxt-equiv)
   (equal
        (check-eq/ne-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
        (check-eq/ne-expression arg1 arg2 arg1-type
                                arg2-type arg1-obligs arg2-obligs
                                err-keyword expr ctxt-equiv)))
 :rule-classes :congruence)