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R1cs-subset

R1cs-systemp

Check if a PFCS is an R1CS.

Signature
(r1cs-systemp sys) → yes/no
Arguments: sys — Guard (systemp sys).
Returns: yes/no — Type (booleanp yes/no).

There must be no definitions, and all the constraints must be in R1CS form.

Definitions and Theorems

Function: r1cs-systemp

(defun r1cs-systemp (sys)
  (declare (xargs :guard (systemp sys)))
  (let ((__function__ 'r1cs-systemp))
    (declare (ignorable __function__))
    (and (endp (system->definitions sys))
         (r1cs-constraint-listp (system->constraints sys)))))

Theorem: booleanp-of-r1cs-systemp

(defthm booleanp-of-r1cs-systemp
  (b* ((yes/no (r1cs-systemp sys)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: r1cs-systemp-of-system-fix-sys

(defthm r1cs-systemp-of-system-fix-sys
  (equal (r1cs-systemp (system-fix sys))
         (r1cs-systemp sys)))

Theorem: r1cs-systemp-system-equiv-congruence-on-sys

(defthm r1cs-systemp-system-equiv-congruence-on-sys
  (implies (system-equiv sys sys-equiv)
           (equal (r1cs-systemp sys)
                  (r1cs-systemp sys-equiv)))
  :rule-classes :congruence)