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• FiniteFields.eo

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cvc5-cvc5-1.2.0.proofs.eo.cpc.theories.FiniteFields.eo Maven / Gradle / Ivy

(include "../theories/Arith.eo")

; disclaimer: >
;   This sort is not in the SMT-LIB standard. All further function
;   symbols over this sort are also not part of the SMT-LIB standard.
(declare-const FiniteField (-> Int Type))

; define: $bv_bitwidth
; args:
; - T Type: The finite field type.
; return: The (integer value) size for a given finite field type.
(define $ff_size ((T Type))
  (eo::match ((n Int)) T (((FiniteField n) n))))

; A finite field constant is a term having 2 integer children.
; note: we do not support the native syntax for finite field values.
(declare-const ff.value
    (-> (! Int :var p) Int (FiniteField p)))

(declare-parameterized-const ff.add ((p Int))
    (-> (FiniteField p) (FiniteField p) (FiniteField p)) 
    :right-assoc-nil (ff.value p 0)
)
(declare-const ff.neg
    (-> (! Int :var p :implicit)
        (FiniteField p) (FiniteField p))
)
(declare-parameterized-const ff.mul ((p Int))
    (-> (FiniteField p) (FiniteField p) (FiniteField p))
    :right-assoc-nil (ff.value p 1)
)
(declare-parameterized-const ff.bitsum ((p Int))
    (-> (FiniteField p) (FiniteField p) (FiniteField p))
    :right-assoc-nil (ff.value p 0)
)