Data.SigFig

This module exports everything you need to work with significant figures, including parsing and evaluation.

Types

data Term

The basic datatype to represent measurements, constant terms, and evaluation results

Constructors

Measured

A measured value with a finite number of significant figures and an associated value

Fields

• numSigFigs :: Integer
• value :: BigDecimal

Constant Rational

A constant value with infinite significant figures

Instances

Eq Term

Defined in Data.SigFig.Types

Methods

(==) :: Term -> Term -> Bool

(/=) :: Term -> Term -> Bool

Show Term

Defined in Data.SigFig.Types

Methods

showsPrec :: Int -> Term -> ShowS

show :: Term -> String

showList :: [Term] -> ShowS

data Op

The types of (infix) operators

Constructors

Add

Sub

Mul

Div

Instances

Eq Op

Defined in Data.SigFig.Types

Methods

(==) :: Op -> Op -> Bool

(/=) :: Op -> Op -> Bool

Show Op

Defined in Data.SigFig.Types

Methods

showsPrec :: Int -> Op -> ShowS

show :: Op -> String

showList :: [Op] -> ShowS

data Expr

A datatype to represent (not-yet-evaluated) expressions. Use parse to create such an expression from text.

Constructors

Leaf Term

Leaf of an expression

Prec1 [(Op, Expr)]

Operation of "Precedence 1": addition and subtraction

Prec2 [(Op, Expr)]

Operation of "Precedence 2": multiplication and division

Exp Expr Integer

Exponentiation with a constant integer exponent

Apply Function Expr

Application of a function to an expression argument

Instances

Eq Expr

Defined in Data.SigFig.Types

Methods

(==) :: Expr -> Expr -> Bool

(/=) :: Expr -> Expr -> Bool

Show Expr

Defined in Data.SigFig.Types

Methods

showsPrec :: Int -> Expr -> ShowS

show :: Expr -> String

showList :: [Expr] -> ShowS

data Function

A datatype representing the supported functions.

Constructors

Log10

The function log() in expressions.

Antilog10

The function exp() in expressions.

Instances

Eq Function

Defined in Data.SigFig.Types

Methods

(==) :: Function -> Function -> Bool

(/=) :: Function -> Function -> Bool

Show Function

Defined in Data.SigFig.Types

Methods

showsPrec :: Int -> Function -> ShowS

show :: Function -> String

showList :: [Function] -> ShowS

High-Level Functions

parseEval :: Text -> Either Text Term

Takes an expression in text and returns either an error message or an evaluated term.

parse :: Text -> Either Text Expr

Parse text into either an error message or an expression.

parse' :: Text -> Expr

Like parse, but assume the result is a valid expression and crash otherwise.

evaluate :: Expr -> Either Text Term

Given an expression tree, evaluate it and return either an error or result.

evaluate' :: Expr -> Term

Like evaluate, but assume the result is a valid term and crash otherwise.

display :: Term -> Text

Given a term, display it in the most convenient way possible. This means, if the normal representation of the number accurately represents how many significant figures it has, then display it normally. Adds trailing zeroes if necessary to floats and opts for scientific notation if necessary.

Examples

>>> display $ measured 3 200
"200."

>>> display $ measured 3 4
"4.00"

>>> display $ measured 2 400
"4.0 x 10^2"

>>> display $ measured 2 430
"430"

>>> display $ measured 1 1
"1"

>>> display $ constant (3 % 8)
"0.375"

>>> display $ constant (4 % 9)
"4/9"

>>> display $ measured 2 4.3
"4.3"

displayInformational :: Term -> (Text, Text)

Given a term, return a tuple where the first element is the output of display and the second is an annotation of the type of value. Used in the API.

Examples

>>> displayInformational $ constant 3
("3","constant value")

>>> displayInformational $ measured 2 3.4
("3.4","2 significant figures")

>>> displayInformational $ measured 3 3400
("3.40 x 10^3","3 significant figures")

displayFull :: Term -> Text

Used in the CLI. Not super pretty but gets the job done in terms of displaying enough information.

Examples

>>> displayFull (constant 3.45)
"3.45 (const)"

>>> displayFull (measured 3 8500)
"8.50 x 10^3 (3 s.f.)"

processExpression :: Text -> Text

A convenience function for use in REPLs (used in the CLI). Returns text that can either signify a result or error.

Creating and Manipulating Terms and Expressions

measured :: Integer -> Rational -> Term

Create a measured value

constant :: Rational -> Term

Create a constant value

l :: Term -> Expr

Create a leaf node out of a term, like a "singleton".

lMeasured :: Integer -> Rational -> Expr

Create a leaf node and construct the Measured value argument at the same time. Convenience function.

lConstant :: Rational -> Expr

Create a leaf node and construct the Constant value argument at the same time. Convenience function.

add :: [Expr] -> Expr

Add together a list of Exprs and create a new Expr.

add a b c is similar in idea to a + b + c.

sub :: [Expr] -> Expr

"Subtract together" a list of Exprs and create a new Expr.

sub a b c is similar in idea to a - b - c.

mul :: [Expr] -> Expr

multiply together a list of Exprs and create a new Expr.

mul a b c is similar in idea to a * b * c.

div :: [Expr] -> Expr

"Divide together" a list of Exprs and create a new Expr.

div a b c is similar in idea to a / b / c.

exp :: Expr -> Integer -> Expr

Take an Expr to the power of an integer. Equivalent to Exp.

apply :: Function -> Expr -> Expr

Apply a function to an Expr. Equivalent to Apply.