Text.Parsec.Expr.Math

Parse and evaluate mathematical expressions.

Expressions

data Expr a

Mathematical expressions.

Constructors

Num a

Var String

Neg (Expr a)

Add (Expr a) (Expr a)

Sub (Expr a) (Expr a)

Mul (Expr a) (Expr a)

Div (Expr a) (Expr a)

Pow (Expr a) (Expr a)

Sqrt (Expr a)

Exp (Expr a)

Log (Expr a)

Abs (Expr a)

Sin (Expr a)

Cos (Expr a)

Tan (Expr a)

Sec (Expr a)

Csc (Expr a)

Cot (Expr a)

Sinh (Expr a)

Cosh (Expr a)

Tanh (Expr a)

Sech (Expr a)

Csch (Expr a)

Coth (Expr a)

ArcSin (Expr a)

ArcCos (Expr a)

ArcTan (Expr a)

ArcSec (Expr a)

ArcCsc (Expr a)

ArcCot (Expr a)

ArcSinh (Expr a)

ArcCosh (Expr a)

ArcTanh (Expr a)

ArcSech (Expr a)

ArcCsch (Expr a)

ArcCoth (Expr a)

Instances

Show a => Show (Expr a)

Parsing

parse :: Floating a => String -> Either ParseError (Expr a)

Parse a mathematical expression.

 >>> parse "exp(-pi*i)+1"
 Right (Add (Exp (Mul (Neg (Var "pi")) (Var "i"))) (Num 1.0))

data ParseError

The abstract data type ParseError represents parse errors. It provides the source position (SourcePos) of the error and a list of error messages (Message). A ParseError can be returned by the function parse. ParseError is an instance of the Show class.

Instances

Show ParseError

Evaluation

evaluate

Arguments

:: Floating a

=> Map String a

Variable definitions.

-> Maybe (Expr a)

Mathematical expression.

-> Maybe a

Evaluate a mathematical expression using the supplied variable definitions.

 >>> :m + Data.Complex Data.Map
 >>> let def = fromList [("pi", pi), ("i", 0 :+ 1)]
 >>> evaluate def . Just $ Add (Exp (Mul (Neg (Var "pi")) (Var "i"))) (Num 1.0)
 Just (0.0 :+ (-1.2246467991473532e-16))