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• Static-semantics

Align-let-vars-values-aux

Signature

(align-let-vars-values-aux vars index value) 
  → 
(mv var-names var-types values)

Arguments

vars — Guard (typed-variable-listp vars).

index — Guard (natp index).

value — Guard (expressionp value).

Returns

var-names — Type (identifier-listp var-names).

var-types — Type (type-listp var-types).

values — Type (expression-listp values).

Definitions and Theorems

Function: align-let-vars-values-aux

(defun align-let-vars-values-aux (vars index value)
  (declare (xargs :guard (and (typed-variable-listp vars)
                              (natp index)
                              (expressionp value))))
  (let ((__function__ 'align-let-vars-values-aux))
    (declare (ignorable __function__))
    (b* (((when (endp vars)) (mv nil nil nil))
         (var (car vars))
         (name (typed-variable->name var))
         (type (typed-variable->type var))
         (val (make-expression-component :multi value
                                         :index index))
         ((mv names types vals)
          (align-let-vars-values-aux (cdr vars)
                                     (1+ (nfix index))
                                     value)))
      (mv (cons name names)
          (cons type types)
          (cons val vals)))))

Theorem: identifier-listp-of-align-let-vars-values-aux.var-names

(defthm identifier-listp-of-align-let-vars-values-aux.var-names
  (b* (((mv ?var-names
            ?var-types common-lisp::?values)
        (align-let-vars-values-aux vars index value)))
    (identifier-listp var-names))
  :rule-classes :rewrite)

Theorem: type-listp-of-align-let-vars-values-aux.var-types

(defthm type-listp-of-align-let-vars-values-aux.var-types
  (b* (((mv ?var-names
            ?var-types common-lisp::?values)
        (align-let-vars-values-aux vars index value)))
    (type-listp var-types))
  :rule-classes :rewrite)

Theorem: expression-listp-of-align-let-vars-values-aux.values

(defthm expression-listp-of-align-let-vars-values-aux.values
  (b* (((mv ?var-names
            ?var-types common-lisp::?values)
        (align-let-vars-values-aux vars index value)))
    (expression-listp values))
  :rule-classes :rewrite)

Theorem: len-of-align-let-vars-values-aux.names

(defthm len-of-align-let-vars-values-aux.names
  (b* (((mv ?var-names
            ?var-types common-lisp::?values)
        (align-let-vars-values-aux vars index value)))
    (equal (len var-names) (len vars))))

Theorem: len-of-align-let-vars-values-aux.types

(defthm len-of-align-let-vars-values-aux.types
  (b* (((mv ?var-names
            ?var-types common-lisp::?values)
        (align-let-vars-values-aux vars index value)))
    (equal (len var-types) (len vars))))

Theorem: len-of-align-let-vars-values-aux.values

(defthm len-of-align-let-vars-values-aux.values
  (b* (((mv ?var-names
            ?var-types common-lisp::?values)
        (align-let-vars-values-aux vars index value)))
    (equal (len values) (len vars))))

Theorem: align-let-vars-values-aux-of-typed-variable-list-fix-vars

(defthm align-let-vars-values-aux-of-typed-variable-list-fix-vars
  (equal (align-let-vars-values-aux (typed-variable-list-fix vars)
                                    index value)
         (align-let-vars-values-aux vars index value)))

Theorem: align-let-vars-values-aux-typed-variable-list-equiv-congruence-on-vars

(defthm
 align-let-vars-values-aux-typed-variable-list-equiv-congruence-on-vars
 (implies
      (typed-variable-list-equiv vars vars-equiv)
      (equal (align-let-vars-values-aux vars index value)
             (align-let-vars-values-aux vars-equiv index value)))
 :rule-classes :congruence)

Theorem: align-let-vars-values-aux-of-nfix-index

(defthm align-let-vars-values-aux-of-nfix-index
  (equal (align-let-vars-values-aux vars (nfix index)
                                    value)
         (align-let-vars-values-aux vars index value)))

Theorem: align-let-vars-values-aux-nat-equiv-congruence-on-index

(defthm align-let-vars-values-aux-nat-equiv-congruence-on-index
  (implies
       (nat-equiv index index-equiv)
       (equal (align-let-vars-values-aux vars index value)
              (align-let-vars-values-aux vars index-equiv value)))
  :rule-classes :congruence)

Theorem: align-let-vars-values-aux-of-expression-fix-value

(defthm align-let-vars-values-aux-of-expression-fix-value
  (equal
       (align-let-vars-values-aux vars index (expression-fix value))
       (align-let-vars-values-aux vars index value)))

Theorem: align-let-vars-values-aux-expression-equiv-congruence-on-value

(defthm
     align-let-vars-values-aux-expression-equiv-congruence-on-value
  (implies
       (expression-equiv value value-equiv)
       (equal (align-let-vars-values-aux vars index value)
              (align-let-vars-values-aux vars index value-equiv)))
  :rule-classes :congruence)