CAS.Dumb.Tree

Documentation

data CAS' γ s² s¹ s⁰

Constructors

Symbol !s⁰

Function !s¹ (CAS' γ s² s¹ s⁰)

Operator !s² (CAS' γ s² s¹ s⁰) (CAS' γ s² s¹ s⁰)

OperatorChain (CAS' γ s² s¹ s⁰) [(s², CAS' γ s² s¹ s⁰)]

Gap !γ

Instances

(UnicodeSymbols c, RenderableEncapsulations c) => Show (Pattern c)

Methods

showsPrec :: Int -> Pattern c -> ShowS

show :: Pattern c -> String

showList :: [Pattern c] -> ShowS

(UnicodeSymbols c, RenderableEncapsulations c) => Show (Expression c)

Methods

showsPrec :: Int -> Expression c -> ShowS

show :: Expression c -> String

showList :: [Expression c] -> ShowS

(SymbolClass σ, SCConstraint σ String) => Floating (AlgebraExpr' γ σ String)

Methods

pi :: AlgebraExpr' γ σ String

exp :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

log :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

sqrt :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

(**) :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

logBase :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

sin :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

cos :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

tan :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

asin :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

acos :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

atan :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

sinh :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

cosh :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

tanh :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

asinh :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

acosh :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

atanh :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

log1p :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

expm1 :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

log1pexp :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

log1mexp :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

(SymbolClass σ, SCConstraint σ String) => Fractional (AlgebraExpr' γ σ String)

Methods

(/) :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

recip :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

fromRational :: Rational -> AlgebraExpr' γ σ String

Functor (CAS' γ s² s¹)

Methods

fmap :: (a -> b) -> CAS' γ s² s¹ a -> CAS' γ s² s¹ b

(<$) :: a -> CAS' γ s² s¹ b -> CAS' γ s² s¹ a

(SymbolClass σ, SCConstraint σ String) => Num (AlgebraExpr' γ σ String)

Methods

(+) :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

(-) :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

(*) :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

negate :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

abs :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

signum :: AlgebraExpr' γ σ String -> AlgebraExpr' γ σ String

fromInteger :: Integer -> AlgebraExpr' γ σ String

(ASCIISymbols c, RenderableEncapsulations c) => Show (CAS (Infix c) (Encapsulation c) (Symbol c))

Methods

showsPrec :: Int -> CAS (Infix c) (Encapsulation c) (Symbol c) -> ShowS

show :: CAS (Infix c) (Encapsulation c) (Symbol c) -> String

showList :: [CAS (Infix c) (Encapsulation c) (Symbol c)] -> ShowS

(Unwieldy s², Unwieldy s¹, Unwieldy s⁰) => Unwieldy (CAS s² s¹ s⁰)

Methods

unwieldiness :: CAS s² s¹ s⁰ -> Unwieldiness

(Eq γ, Eq s², Eq s¹, Eq s⁰) => Eq (CAS' γ s² s¹ s⁰)

Methods

(==) :: CAS' γ s² s¹ s⁰ -> CAS' γ s² s¹ s⁰ -> Bool

(/=) :: CAS' γ s² s¹ s⁰ -> CAS' γ s² s¹ s⁰ -> Bool

(ASCIISymbols c, RenderableEncapsulations c, Monoid c) => Show (CAS' GapId (Infix c) (Encapsulation c) (Symbol c))

Methods

showsPrec :: Int -> CAS' GapId (Infix c) (Encapsulation c) (Symbol c) -> ShowS

show :: CAS' GapId (Infix c) (Encapsulation c) (Symbol c) -> String

showList :: [CAS' GapId (Infix c) (Encapsulation c) (Symbol c)] -> ShowS

Generic (CAS' γ s² s¹ s⁰)

Associated Types

type Rep (CAS' γ s² s¹ s⁰) :: * -> *

Methods

from :: CAS' γ s² s¹ s⁰ -> Rep (CAS' γ s² s¹ s⁰) x

to :: Rep (CAS' γ s² s¹ s⁰) x -> CAS' γ s² s¹ s⁰

(Hashable γ, Hashable s⁰, Hashable s¹, Hashable s²) => Hashable (CAS' γ s² s¹ s⁰)

Methods

hashWithSalt :: Int -> CAS' γ s² s¹ s⁰ -> Int

hash :: CAS' γ s² s¹ s⁰ -> Int

type Rep (CAS' γ s² s¹ s⁰)

type Rep (CAS' γ s² s¹ s⁰) = D1 * (MetaData "CAS'" "CAS.Dumb.Tree" "dumb-cas-0.2.0.0-7IYgzAjTkpnBGEioFdhdFE" False) ((:+:) * ((:+:) * (C1 * (MetaCons "Symbol" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * s⁰))) (C1 * (MetaCons "Function" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * s¹)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (CAS' γ s² s¹ s⁰)))))) ((:+:) * (C1 * (MetaCons "Operator" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * s²)) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (CAS' γ s² s¹ s⁰))) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (CAS' γ s² s¹ s⁰)))))) ((:+:) * (C1 * (MetaCons "OperatorChain" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (CAS' γ s² s¹ s⁰))) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * [(s², CAS' γ s² s¹ s⁰)])))) (C1 * (MetaCons "Gap" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 * γ))))))

chainableInfixL

Arguments

:: (s² -> Bool)

Condition that all operators in the chain must fulfill to be joined by this one

-> s²

The operator we want to add

-> CAS' γ s² s¹ s⁰

-> CAS' γ s² s¹ s⁰

-> CAS' γ s² s¹ s⁰

chainableInfixR

Arguments

:: (s² -> Bool)

Condition that all operators in the chain must fulfill to be joined by this one

-> s²

The operator we want to add

-> CAS' γ s² s¹ s⁰

-> CAS' γ s² s¹ s⁰

-> CAS' γ s² s¹ s⁰

chainableInfix

Arguments

:: (s² -> Bool)

Condition that all operators in the chain must fulfill to be joined by this one

-> s²

The operator we want to add

-> CAS' γ s² s¹ s⁰

-> CAS' γ s² s¹ s⁰

-> CAS' γ s² s¹ s⁰

associativeOperator :: Eq s² => s² -> CAS' γ s² s¹ s⁰ -> CAS' γ s² s¹ s⁰ -> CAS' γ s² s¹ s⁰

type CAS = CAS' Void

data Equality' γ s² s¹ s⁰

Constructors

(:=) infixr 4

Fields

• originalExpression :: !(CAS' γ s² s¹ s⁰)
• transformationOptions :: [Equality' γ s² s¹ s⁰]

(:=:) infixr 4

Fields

• originalExpression :: !(CAS' γ s² s¹ s⁰)
• transformedExpression :: !(CAS' γ s² s¹ s⁰)

type Equality = Equality' Void

type GapId = Int

type Expattern s² s¹ s⁰ = CAS' GapId s² s¹ s⁰

type Eqspattern s² s¹ s⁰ = Equality' GapId s² s¹ s⁰

matchPattern :: forall s⁰ s¹ s². (Eq s⁰, Eq s¹, Eq s²) => Expattern s² s¹ s⁰ -> CAS s² s¹ s⁰ -> Maybe (Map GapId (CAS s² s¹ s⁰))

(&~:) :: (Eq s⁰, Eq s¹, Eq s²) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> CAS s² s¹ s⁰ infixl 1

expr &~: pat :=: rep replaces every occurence of pat within expr with rep.

For example, 𝑎·𝑏 − 𝑐·𝑑 &~: ㄅ·ㄘ :=: ㄘ·ㄅ yields 𝑏·𝑎 − 𝑑·𝑐.

(&~?) :: (Eq s⁰, Eq s¹, Eq s²) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> [CAS s² s¹ s⁰] infixl 1

expr &~? pat :=: rep gives every possible way pat can be replaced exactly once within expr.

For example, 𝑎·𝑏 − 𝑐·𝑑 &~? ㄅ·ㄘ :=: ㄘ·ㄅ yields [𝑏·𝑎 − 𝑐·𝑑, 𝑎·𝑏 − 𝑑·𝑐].

(&~!) :: (Eq s⁰, Eq s¹, Eq s², Show (CAS s² s¹ s⁰), Show (CAS' GapId s² s¹ s⁰)) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> CAS s² s¹ s⁰ infixl 1

expr &~! pat :=: rep replaces pat exactly once in expr. If this is not possible, an error is raised. If multiple occurences match, the leftmost is preferred.

fillGaps :: Map GapId (CAS s² s¹ s⁰) -> Expattern s² s¹ s⁰ -> Maybe (CAS s² s¹ s⁰)

exploreEquality :: (Eq s⁰, Eq s¹, Eq s²) => [Expattern s² s¹ s⁰] -> CAS s² s¹ s⁰ -> Equality s² s¹ s⁰

showStructure :: CAS' γ s² s¹ s⁰ -> String

type Unwieldiness = Double

class Unwieldy e where

Minimal complete definition

unwieldiness

Methods

unwieldiness :: e -> Unwieldiness

Instances

Unwieldy c => Unwieldy (Symbol c)

Methods

unwieldiness :: Symbol c -> Unwieldiness

Unwieldy c => Unwieldy (Symbol c)

Methods

unwieldiness :: Symbol c -> Unwieldiness

(Unwieldy s², Unwieldy s¹, Unwieldy s⁰) => Unwieldy (CAS s² s¹ s⁰)

Methods

unwieldiness :: CAS s² s¹ s⁰ -> Unwieldiness

bigFirstPreference :: Unwieldiness

How much it is preferred to start an operator-chain with the most complex subexpression (e.g. with the highest-order monomial).