Safe Haskell	Safe-Inferred
Language	Haskell2010

Traq.Data.Symbolic

Description

Based on https://hackage.haskell.org/package/numbers-3000.2.0.2

Synopsis

data Sym a
var :: String -> Sym a
con :: a -> Sym a
subst :: (Num a, Eq a) => String -> Sym a -> Sym a -> Sym a
unSym :: Show a => Sym a -> a
simpl :: (Num a, Eq a) => Sym a -> Sym a

Documentation

data Sym a #

Symbolic numbers over some base type for the literals.

Instances

Instances details

(Show r, LeftModule r a) => LeftModule r (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (.*) :: r -> Sym a -> Sym a #
(Show r, RightModule r a) => RightModule r (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (*.) :: Sym a -> r -> Sym a #
Abelian a => Abelian (Sym a) #
Instance details Defined in Traq.Data.Symbolic
Additive a => Additive (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (+) :: Sym a -> Sym a -> Sym a # sinnum1p :: Natural -> Sym a -> Sym a # sumWith1 :: Foldable1 f => (a0 -> Sym a) -> f a0 -> Sym a #
Idempotent a => Idempotent (Sym a) #
Instance details Defined in Traq.Data.Symbolic
Group a => Group (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (-) :: Sym a -> Sym a -> Sym a # negate :: Sym a -> Sym a # subtract :: Sym a -> Sym a -> Sym a # times :: Integral n => n -> Sym a -> Sym a #
Monoidal a => Monoidal (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods zero :: Sym a # sinnum :: Natural -> Sym a -> Sym a # sumWith :: Foldable f => (a0 -> Sym a) -> f a0 -> Sym a #
Multiplicative a => Multiplicative (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (*) :: Sym a -> Sym a -> Sym a # pow1p :: Sym a -> Natural -> Sym a # productWith1 :: Foldable1 f => (a0 -> Sym a) -> f a0 -> Sym a #
Semiring a => Semiring (Sym a) #
Instance details Defined in Traq.Data.Symbolic
Commutative a => Commutative (Sym a) #
Instance details Defined in Traq.Data.Symbolic
Division a => Division (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods recip :: Sym a -> Sym a # (/) :: Sym a -> Sym a -> Sym a # (\\) :: Sym a -> Sym a -> Sym a # (^) :: Integral n => Sym a -> n -> Sym a #
Unital a => Unital (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods one :: Sym a # pow :: Sym a -> Natural -> Sym a # productWith :: Foldable f => (a0 -> Sym a) -> f a0 -> Sym a #
Rig a => Rig (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods fromNatural :: Natural -> Sym a #
Rng a => Rng (Sym a) #
Instance details Defined in Traq.Data.Symbolic
(Floating a, Eq a) => Floating (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods pi :: Sym a # exp :: Sym a -> Sym a # log :: Sym a -> Sym a # sqrt :: Sym a -> Sym a # (**) :: Sym a -> Sym a -> Sym a # logBase :: Sym a -> Sym a -> Sym a # sin :: Sym a -> Sym a # cos :: Sym a -> Sym a # tan :: Sym a -> Sym a # asin :: Sym a -> Sym a # acos :: Sym a -> Sym a # atan :: Sym a -> Sym a # sinh :: Sym a -> Sym a # cosh :: Sym a -> Sym a # tanh :: Sym a -> Sym a # asinh :: Sym a -> Sym a # acosh :: Sym a -> Sym a # atanh :: Sym a -> Sym a # log1p :: Sym a -> Sym a # expm1 :: Sym a -> Sym a # log1pexp :: Sym a -> Sym a # log1mexp :: Sym a -> Sym a #
(Num a, Eq a) => Num (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (+) :: Sym a -> Sym a -> Sym a # (-) :: Sym a -> Sym a -> Sym a # (*) :: Sym a -> Sym a -> Sym a # negate :: Sym a -> Sym a # abs :: Sym a -> Sym a # signum :: Sym a -> Sym a # fromInteger :: Integer -> Sym a #
(Fractional a, Eq a) => Fractional (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (/) :: Sym a -> Sym a -> Sym a # recip :: Sym a -> Sym a # fromRational :: Rational -> Sym a #
Show a => Show (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods showsPrec :: Int -> Sym a -> ShowS # show :: Sym a -> String # showList :: [Sym a] -> ShowS #
Eq a => Eq (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods (==) :: Sym a -> Sym a -> Bool # (/=) :: Sym a -> Sym a -> Bool #
Ord a => Ord (Sym a) #
Instance details Defined in Traq.Data.Symbolic Methods compare :: Sym a -> Sym a -> Ordering # (<) :: Sym a -> Sym a -> Bool # (<=) :: Sym a -> Sym a -> Bool # (>) :: Sym a -> Sym a -> Bool # (>=) :: Sym a -> Sym a -> Bool # max :: Sym a -> Sym a -> Sym a # min :: Sym a -> Sym a -> Sym a #
Semiring Double => LeftModule (Sym Double) (Sym Double) #
Instance details Defined in Traq.Data.Symbolic Methods (.*) :: Sym Double -> Sym Double -> Sym Double #
Semiring Double => RightModule (Sym Double) (Sym Double) #
Instance details Defined in Traq.Data.Symbolic Methods (*.) :: Sym Double -> Sym Double -> Sym Double #
Show size => SizeToPrec (Sym size) (Sym prec) #
Instance details Defined in Traq.Analysis.Prelude Methods sizeToPrec :: Sym size -> Sym prec #
TypingReqs size => TypeCheckPrim (QSearchSym size prec) (Sym size) #
Instance details Defined in Traq.Primitives.Search.Symbolic Methods inferRetTypesPrim :: forall ext' shape m. (m ~ TypeChecker ext', Sym size ~ SizeType ext', shape ~ PrimFnShape (QSearchSym size prec)) => QSearchSym size prec -> shape (FnType (Sym size)) -> m [VarType (Sym size)] #
(TypingReqs size, Show prec, Num prec, Eq prec) => QuantumHavocCostPrim (QSearchSym size prec) (Sym size) (Sym prec) #
Instance details Defined in Traq.Primitives.Search.Symbolic Methods quantumQueryCostsQuantum :: QSearchSym size prec -> FailProb (Sym prec) -> PrimFnShape (QSearchSym size prec) (Sym prec) # quantumQueryCostsUnitary :: QSearchSym size prec -> FailProb (Sym prec) -> PrimFnShape (QSearchSym size prec) (UnitaryQueries (Sym prec)) # quantumExprCosts :: (CostModel cost, Sym prec ~ PrecType cost) => QSearchSym size prec -> FailProb (Sym prec) -> cost #
(TypingReqs size, Show prec, Num prec, Eq prec) => UnitaryCostPrim (QSearchSym size prec) (Sym size) (Sym prec) #
Instance details Defined in Traq.Primitives.Search.Symbolic Methods unitaryQueryCosts :: QSearchSym size prec -> FailProb (Sym prec) -> PrimFnShape (QSearchSym size prec) (UnitaryQueries (Sym prec)) # unitaryExprCosts :: (CostModel cost, Sym prec ~ PrecType cost) => QSearchSym size prec -> FailProb (Sym prec) -> cost #
(PrimSearch (Sym size) (Sym prec)) :<: (QSearchSym size prec) #
Instance details Defined in Traq.Primitives.Search.Symbolic Methods inject :: PrimSearch (Sym size) (Sym prec) -> QSearchSym size prec # project :: QSearchSym size prec -> Maybe (PrimSearch (Sym size) (Sym prec)) #

var :: String -> Sym a #

Create a variable.

con :: a -> Sym a #

Create a constant (useful when it is not a literal).

subst :: (Num a, Eq a) => String -> Sym a -> Sym a -> Sym a #

The expression subst x v e substitutes the expression v for each occurence of the variable x in e.

unSym :: Show a => Sym a -> a #

simpl :: (Num a, Eq a) => Sym a -> Sym a #

Simplify by re-assembling the expression