Copyright	(c) Justus Sagemüller 2017
License	GPL v3
Maintainer	(@) jsagemue $ uni-koeln.de
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

CAS.Dumb.Symbols

Description

Synopsis

Documentation

data SymbolD σ c Source #

Constructors

NatSymbol !Integer
PrimitiveSymbol Char
StringSymbol c

Instances

UnicodeSymbols c => Show (Pattern c)
Methods showsPrec :: Int -> Pattern c -> ShowS show :: Pattern c -> String showList :: [Pattern c] -> ShowS
UnicodeSymbols c => Show (Expression c)
Methods showsPrec :: Int -> Expression c -> ShowS show :: Expression c -> String showList :: [Expression c] -> ShowS
(SymbolClass σ, SCConstraint σ c, Eq c) => Eq (SymbolD σ c) Source #
Methods (==) :: SymbolD σ c -> SymbolD σ c -> Bool (/=) :: SymbolD σ c -> SymbolD σ c -> Bool
(SymbolClass σ, SCConstraint σ String) => Floating (AlgebraExpr' γ σ String) Source #
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) Source #
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
(SymbolClass σ, SCConstraint σ String) => Num (AlgebraExpr' γ σ String) Source #
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 => 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
(ASCIISymbols 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

data Infix s Source #

Constructors

Infix
Fields symbolFixity :: !Fixity infixSymbox :: !s

Instances

Eq s => Eq (Infix s) Source #
Methods (==) :: Infix s -> Infix s -> Bool (/=) :: Infix s -> Infix s -> Bool
UnicodeSymbols c => Show (Pattern c)
Methods showsPrec :: Int -> Pattern c -> ShowS show :: Pattern c -> String showList :: [Pattern c] -> ShowS
UnicodeSymbols 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) Source #
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) Source #
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
(SymbolClass σ, SCConstraint σ String) => Num (AlgebraExpr' γ σ String) Source #
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 => 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
(ASCIISymbols 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

data Encapsulation s Source #

Constructors

Encapsulation
Fields needInnerParens, haveOuterparens :: !Bool leftEncaps, rightEncaps :: !s

Instances

Eq (Encapsulation String) Source #
Methods (==) :: Encapsulation String -> Encapsulation String -> Bool (/=) :: Encapsulation String -> Encapsulation String -> Bool
UnicodeSymbols c => Show (Pattern c)
Methods showsPrec :: Int -> Pattern c -> ShowS show :: Pattern c -> String showList :: [Pattern c] -> ShowS
UnicodeSymbols 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) Source #
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) Source #
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
(SymbolClass σ, SCConstraint σ String) => Num (AlgebraExpr' γ σ String) Source #
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 => 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
(ASCIISymbols 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

type AlgebraExpr σ l = CAS (Infix l) (Encapsulation l) (SymbolD σ l) Source #

type AlgebraExpr' γ σ l = CAS' γ (Infix l) (Encapsulation l) (SymbolD σ l) Source #

type AlgebraPattern σ l = AlgebraExpr' GapId σ l Source #

don'tParenthesise :: Monoid s¹ => CAS' γ (Infix s²) (Encapsulation s¹) s⁰ -> CAS' γ (Infix s²) (Encapsulation s¹) s⁰ Source #

symbolInfix Source #

Arguments

:: s²	The operator we want to describe
-> CAS' γ s² s¹ s⁰
-> CAS' γ s² s¹ s⁰
-> CAS' γ s² s¹ s⁰

symbolFunction :: Monoid s¹ => s¹ -> CAS' γ (Infix s²) (Encapsulation s¹) s⁰ -> CAS' γ (Infix s²) (Encapsulation s¹) s⁰ Source #

class ASCIISymbols c where Source #

Minimal complete definition

fromASCIISymbol, toASCIISymbols

Methods

fromASCIISymbol :: Char -> c Source #

toASCIISymbols :: c -> String Source #

Instances

ASCIISymbols String Source #
Methods fromASCIISymbol :: Char -> String Source # toASCIISymbols :: String -> String Source #

type RenderingCombinator σ c r Source #

Arguments

= Bool	Should the result be parenthesised?
-> Maybe r	Left context
-> SymbolD σ c	Central expressionfunctioninfix to render
-> Maybe r	Right context
-> r	Rendering result

data ContextFixity Source #

Constructors

AtLHS Fixity
AtRHS Fixity
AtFunctionArgument

Instances

Eq ContextFixity Source #
Methods (==) :: ContextFixity -> ContextFixity -> Bool (/=) :: ContextFixity -> ContextFixity -> Bool

renderSymbolExpression :: forall σ c r. (SymbolClass σ, SCConstraint σ c) => ContextFixity -> RenderingCombinator σ c r -> AlgebraExpr σ c -> r Source #

showsPrecASCIISymbol :: (ASCIISymbols c, SymbolClass σ, SCConstraint σ c) => Int -> AlgebraExpr σ c -> ShowS Source #

class UnicodeSymbols c where Source #

Minimal complete definition

fromUnicodeSymbol, toUnicodeSymbols

Methods

fromUnicodeSymbol :: Char -> c Source #

toUnicodeSymbols :: c -> String Source #

Instances

UnicodeSymbols String Source #
Methods fromUnicodeSymbol :: Char -> String Source # toUnicodeSymbols :: String -> String Source #

showsPrecUnicodeSymbol :: (UnicodeSymbols c, SymbolClass σ, SCConstraint σ c) => Int -> AlgebraExpr σ c -> ShowS Source #

class SymbolClass σ where Source #

Minimal complete definition

fromCharSymbol

Associated Types

type SCConstraint σ :: * -> Constraint Source #

Methods

fromCharSymbol :: (Functor p, SCConstraint σ c) => p σ -> Char -> c Source #

normaliseSymbols :: forall σ c γ s² s¹. (SymbolClass σ, SCConstraint σ c) => CAS' γ s² s¹ (SymbolD σ c) -> CAS' γ s² s¹ (SymbolD σ c) Source #

(%$>) :: forall σ c c' γ s² s¹. (SymbolClass σ, SCConstraint σ c) => (c -> c') -> CAS' γ s² s¹ (SymbolD σ c) -> CAS' γ s² s¹ (SymbolD σ c') infixl 4 Source #

Transform the symbols of an expression, in their underlying representation.

(map succ%$> 𝑎+𝑝) * 𝑥  ≡  (𝑏+𝑞) * 𝑥

continueExpr Source #

Arguments

:: (Eq l, Monoid l)
=> (AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l)	Combinator to use for chaining the new expression to the old ones
-> (AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l)	Transformation to apply to the rightmost expression in the previous chain
-> AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l	Transformation which appends the result.

(&~~!) :: (Eq l, Eq (Encapsulation l), SymbolClass σ, SCConstraint σ l, Show (AlgebraExpr σ l), Show (AlgebraPattern σ l)) => AlgebraExpr σ l -> [AlgebraPattern σ l] -> AlgebraExpr σ l infixl 1 Source #

Apply a sequence of pattern-transformations and yield the result concatenated to the original via the corresponding chain-operator. Because only the rightmost expression in a chain is processed, this can be iterated, giving a chain of intermediate results.

If one of the patterns does not match, this manipulator will raise an error.

(&~~:) :: (Eq l, Eq (Encapsulation l), SymbolClass σ, SCConstraint σ l, Show (AlgebraExpr σ l), Show (AlgebraPattern σ l)) => AlgebraExpr σ l -> [AlgebraPattern σ l] -> AlgebraExpr σ l infixl 1 Source #

Apply a sequence of pattern-transformations, each in every spot possible, and yield the result concatenated to the original via the corresponding chain-operator. Because only the rightmost expression in a chain is processed, this can be iterated, giving a chain of intermediate results.