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• Abstract-syntax-operations

Apply-pre-inc/dec-ops

Apply a sequence of pre-increment and pre-decrement operators to an expression.

Signature

(apply-pre-inc/dec-ops ops expr) → new-expr

Arguments

ops — Guard (inc/dec-op-listp ops).

expr — Guard (exprp expr).

Returns

new-expr — Type (exprp new-expr).

The first one in the list will be the outermost, and the last one in the list will be the innermost.

Definitions and Theorems

Function: apply-pre-inc/dec-ops

(defun apply-pre-inc/dec-ops (ops expr)
  (declare (xargs :guard (and (inc/dec-op-listp ops)
                              (exprp expr))))
  (b* (((when (endp ops)) (expr-fix expr))
       (op (car ops))
       (expr (apply-pre-inc/dec-ops (cdr ops) expr)))
    (inc/dec-op-case op
                     :inc (make-expr-unary :op (unop-preinc)
                                           :arg expr
                                           :info nil)
                     :dec (make-expr-unary :op (unop-predec)
                                           :arg expr
                                           :info nil))))

Theorem: exprp-of-apply-pre-inc/dec-ops

(defthm exprp-of-apply-pre-inc/dec-ops
  (b* ((new-expr (apply-pre-inc/dec-ops ops expr)))
    (exprp new-expr))
  :rule-classes :rewrite)

Theorem: apply-pre-inc/dec-ops-of-inc/dec-op-list-fix-ops

(defthm apply-pre-inc/dec-ops-of-inc/dec-op-list-fix-ops
  (equal (apply-pre-inc/dec-ops (inc/dec-op-list-fix ops)
                                expr)
         (apply-pre-inc/dec-ops ops expr)))

Theorem: apply-pre-inc/dec-ops-inc/dec-op-list-equiv-congruence-on-ops

(defthm
      apply-pre-inc/dec-ops-inc/dec-op-list-equiv-congruence-on-ops
  (implies (inc/dec-op-list-equiv ops ops-equiv)
           (equal (apply-pre-inc/dec-ops ops expr)
                  (apply-pre-inc/dec-ops ops-equiv expr)))
  :rule-classes :congruence)

Theorem: apply-pre-inc/dec-ops-of-expr-fix-expr

(defthm apply-pre-inc/dec-ops-of-expr-fix-expr
  (equal (apply-pre-inc/dec-ops ops (expr-fix expr))
         (apply-pre-inc/dec-ops ops expr)))

Theorem: apply-pre-inc/dec-ops-expr-equiv-congruence-on-expr

(defthm apply-pre-inc/dec-ops-expr-equiv-congruence-on-expr
  (implies (expr-equiv expr expr-equiv)
           (equal (apply-pre-inc/dec-ops ops expr)
                  (apply-pre-inc/dec-ops ops expr-equiv)))
  :rule-classes :congruence)