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• Static-semantics

Check-add/sub/mul-expression

Check if an addition, substraction, or multiplication expression is well-formed.

Signature

(check-add/sub/mul-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 operands must be integers, and the result is an integer.

Definitions and Theorems

Function: check-add/sub/mul-expression

(defun check-add/sub/mul-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-add/sub/mul-expression))
   (declare (ignorable __function__))
   (b*
    (((mv okp obligs)
      (match-type arg1 arg1-type (type-integer)
                  ctxt))
     ((unless okp)
      (type-result-err (list err-keyword (expression-fix arg1)
                             (expression-fix arg2)
                             (type-fix arg1-type)
                             (type-fix arg2-type)
                             (type-integer))))
     ((acl2::run-when (consp obligs))
      (raise "Internal error: obligations ~x0 for the integer type."
             obligs))
     ((mv okp obligs)
      (match-type arg2 arg2-type (type-integer)
                  ctxt))
     ((unless okp)
      (type-result-err (list err-keyword (expression-fix arg1)
                             (expression-fix arg2)
                             (type-fix arg1-type)
                             (type-fix arg2-type)
                             (type-integer))))
     ((acl2::run-when (consp obligs))
      (raise "Internal error: obligations ~x0 for the integer type."
             obligs)))
    (make-type-result-ok
         :types (list (type-integer))
         :obligations (append arg1-obligs arg2-obligs)))))

Theorem: type-resultp-of-check-add/sub/mul-expression

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

Theorem: check-add/sub/mul-expression-of-expression-fix-arg1

(defthm check-add/sub/mul-expression-of-expression-fix-arg1
 (equal
  (check-add/sub/mul-expression (expression-fix arg1)
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
  (check-add/sub/mul-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-add/sub/mul-expression-expression-equiv-congruence-on-arg1

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

Theorem: check-add/sub/mul-expression-of-expression-fix-arg2

(defthm check-add/sub/mul-expression-of-expression-fix-arg2
 (equal
  (check-add/sub/mul-expression arg1 (expression-fix arg2)
                                arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
  (check-add/sub/mul-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-add/sub/mul-expression-expression-equiv-congruence-on-arg2

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

Theorem: check-add/sub/mul-expression-of-type-fix-arg1-type

(defthm check-add/sub/mul-expression-of-type-fix-arg1-type
 (equal
  (check-add/sub/mul-expression arg1 arg2 (type-fix arg1-type)
                                arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)
  (check-add/sub/mul-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-add/sub/mul-expression-type-equiv-congruence-on-arg1-type

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

Theorem: check-add/sub/mul-expression-of-type-fix-arg2-type

(defthm check-add/sub/mul-expression-of-type-fix-arg2-type
 (equal
  (check-add/sub/mul-expression
       arg1 arg2 arg1-type (type-fix arg2-type)
       arg1-obligs
       arg2-obligs err-keyword expr ctxt)
  (check-add/sub/mul-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-add/sub/mul-expression-type-equiv-congruence-on-arg2-type

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

Theorem: check-add/sub/mul-expression-of-proof-obligation-list-fix-arg1-obligs

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

Theorem: check-add/sub/mul-expression-proof-obligation-list-equiv-congruence-on-arg1-obligs

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

Theorem: check-add/sub/mul-expression-of-proof-obligation-list-fix-arg2-obligs

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

Theorem: check-add/sub/mul-expression-proof-obligation-list-equiv-congruence-on-arg2-obligs

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

Theorem: check-add/sub/mul-expression-of-expression-fix-expr

(defthm check-add/sub/mul-expression-of-expression-fix-expr
 (equal
  (check-add/sub/mul-expression arg1 arg2 arg1-type
                                arg2-type arg1-obligs arg2-obligs
                                err-keyword (expression-fix expr)
                                ctxt)
  (check-add/sub/mul-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-add/sub/mul-expression-expression-equiv-congruence-on-expr

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

Theorem: check-add/sub/mul-expression-of-context-fix-ctxt

(defthm check-add/sub/mul-expression-of-context-fix-ctxt
 (equal
  (check-add/sub/mul-expression arg1 arg2 arg1-type
                                arg2-type arg1-obligs arg2-obligs
                                err-keyword expr (context-fix ctxt))
  (check-add/sub/mul-expression arg1
                                arg2 arg1-type arg2-type arg1-obligs
                                arg2-obligs err-keyword expr ctxt)))

Theorem: check-add/sub/mul-expression-context-equiv-congruence-on-ctxt

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