128 lines
2.8 KiB
Plaintext
128 lines
2.8 KiB
Plaintext
|
; -------------------------------------------------------------------------
|
||
|
|
; Boogie universal background predicate
|
||
|
|
; Copyright (c), Microsoft Corp.
|
||
|
|
(DEFPRED (<: t u))
|
||
|
|
|
||
|
|
(BG_PUSH (AND
|
||
|
|
|
||
|
|
; select/store axioms, 1 index argument
|
||
|
|
|
||
|
|
(FORALL (A i v)
|
||
|
|
(EQ (select1 (store1 A i v) i) v))
|
||
|
|
|
||
|
|
(FORALL (A i j v)
|
||
|
|
(IMPLIES (NEQ i j)
|
||
|
|
(EQ
|
||
|
|
(select1 (store1 A i v) j)
|
||
|
|
(select1 A j))))
|
||
|
|
|
||
|
|
; select/store axioms, 2 index arguments
|
||
|
|
|
||
|
|
(FORALL (A o f v)
|
||
|
|
(EQ (select2 (store2 A o f v) o f) v))
|
||
|
|
|
||
|
|
(FORALL (A o f p g v)
|
||
|
|
(IMPLIES (NEQ o p)
|
||
|
|
(EQ
|
||
|
|
(select2 (store2 A o f v) p g)
|
||
|
|
(select2 A p g))))
|
||
|
|
|
||
|
|
(FORALL (A o f p g v)
|
||
|
|
(IMPLIES (NEQ f g)
|
||
|
|
(EQ
|
||
|
|
(select2 (store2 A o f v) p g)
|
||
|
|
(select2 A p g))))
|
||
|
|
|
||
|
|
; formula/term axioms
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (boolIff x y) |@true|)
|
||
|
|
(IFF (EQ x |@true|) (EQ y |@true|))))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (boolImplies x y) |@true|)
|
||
|
|
(IMPLIES (EQ x |@true|) (EQ y |@true|))))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (boolAnd x y) |@true|)
|
||
|
|
(AND (EQ x |@true|) (EQ y |@true|))))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (boolOr x y) |@true|)
|
||
|
|
(OR (EQ x |@true|) (EQ y |@true|))))
|
||
|
|
|
||
|
|
(FORALL (x)
|
||
|
|
(PATS (boolNot x))
|
||
|
|
(IFF
|
||
|
|
(EQ (boolNot x) |@true|)
|
||
|
|
(NEQ x |@true|)))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (anyEqual x y) |@true|)
|
||
|
|
(EQ x y)))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(PATS (anyNeq x y))
|
||
|
|
(IFF
|
||
|
|
(EQ (anyNeq x y) |@true|)
|
||
|
|
(NEQ x y)))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (intLess x y) |@true|)
|
||
|
|
(< x y)))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (intAtMost x y) |@true|)
|
||
|
|
(<= x y)))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (intAtLeast x y) |@true|)
|
||
|
|
(>= x y)))
|
||
|
|
|
||
|
|
(FORALL (x y)
|
||
|
|
(IFF
|
||
|
|
(EQ (intGreater x y) |@true|)
|
||
|
|
(> x y)))
|
||
|
|
|
||
|
|
; false is not true
|
||
|
|
|
||
|
|
(DISTINCT |@false| |@true|)
|
||
|
|
|
||
|
|
; <: is a partial order: it is reflexive, transitive, and anti-symmetric
|
||
|
|
|
||
|
|
(FORALL (t)
|
||
|
|
(PATS (<: t t))
|
||
|
|
(<: t t))
|
||
|
|
|
||
|
|
(FORALL (t u v)
|
||
|
|
(PATS (MPAT (<: t u) (<: u v)))
|
||
|
|
(IMPLIES
|
||
|
|
(AND (<: t u ) (<: u v))
|
||
|
|
(<: t v)))
|
||
|
|
|
||
|
|
(FORALL (t u)
|
||
|
|
(PATS (MPAT (<: t u) (<: u t)))
|
||
|
|
(IMPLIES
|
||
|
|
(AND (<: t u) (<: u t))
|
||
|
|
(EQ t u)))
|
||
|
|
|
||
|
|
;; The following axiom gives a way to typed produce verification conditions,
|
||
|
|
;; that is, verification conditions where the terms are typable. To use these,
|
||
|
|
;; the VCExpressionGenerator.{CastTo,CastFrom} methods must be overridden.
|
||
|
|
;; Look for USE_SORTED_LOGIC in VCGeneration/VCExpr.ssc.
|
||
|
|
; (FORALL (val T U)
|
||
|
|
; (PATS (TypeConvert (TypeConvert val T U) U T))
|
||
|
|
; (EQ (TypeConvert (TypeConvert val T U) U T) val))
|
||
|
|
|
||
|
|
)) ;; AND, BG_PUSH
|
||
|
|
; End Boogie universal background predicate
|
||
|
|
; -------------------------------------------------------------------------
|