Documentation.SBV.Examples.ProofTools.Sum

Author : Levent Erkok License : BSD3 Maintainer: [e-mail] Stability : experimental

Example inductive proof to show partial correctness of the traditional for-loop sum algorithm:

    s = 0
    i = 0
    while i <= n:
       s += i
       i++

We prove the loop invariant and establish partial correctness that s is the sum of all numbers up to and including n upon termination.

System state

data S a

System state. We simply have two components, parameterized over the type so we can put in both concrete and symbolic values.

Constructors

S

Fields

• s :: a
• i :: a
• n :: a

Instances

Queriable IO (S SInteger) (S Integer)

Queriable instance for our state

Defined in Documentation.SBV.Examples.ProofTools.Sum

Methods

fresh :: QueryT IO (S SInteger)

extract :: S SInteger -> QueryT IO (S Integer)

Show a => Show (S a)

Defined in Documentation.SBV.Examples.ProofTools.Sum

Methods

showsPrec :: Int -> S a -> ShowS

show :: S a -> String

showList :: [S a] -> ShowS

Generic (S a)

Defined in Documentation.SBV.Examples.ProofTools.Sum

Associated Types

type Rep (S a) :: Type -> Type

Methods

from :: S a -> Rep (S a) x

to :: Rep (S a) x -> S a

Mergeable a => Mergeable (S a)

Defined in Documentation.SBV.Examples.ProofTools.Sum

Methods

symbolicMerge :: Bool -> SBool -> S a -> S a -> S a

select :: (SymVal b, Num b) => [S a] -> S a -> SBV b -> S a

type Rep (S a)

Defined in Documentation.SBV.Examples.ProofTools.Sum

type Rep (S a) = D1 (MetaData "S" "Documentation.SBV.Examples.ProofTools.Sum" "sbv-8.0-4OZZzEgTRNf59WYE3yYwTJ" False) (C1 (MetaCons "S" PrefixI True) (S1 (MetaSel (Just "s") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: (S1 (MetaSel (Just "i") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Just "n") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))

sumCorrect :: IO (InductionResult (S Integer))

Encoding partial correctness of the sum algorithm. We have:

>>> sumCorrect
Q.E.D.