-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Minimalistic toolkit for simple mathematical expression.
--
-- This is a minimalistic toolkit for simple mathematical expression
-- developed for debug purposes similar to 'simple-reflect' package but
-- based on slightly different principles. In particular, we use ordinary
-- syntactic trees instead of turning them into strings. There is a
-- primitive manipulation capability like
--
--
-- >>> simplify $ (x + 0) * 1 - x * (3 - 2)
-- 0
--
--
-- Besides an expression visualization feature is supported.
--
--
-- See tutorial for details.
@package simple-expr
@version 0.1.0.0
-- | Simple expressions base types and manipulations.
module Debug.SimpleExpr.Expr
-- | Initializes a single integer number expression.
--
-- Examples of usage
--
--
-- >>> a = number 42
--
-- >>> a
-- 42
--
-- >>> :t a
-- a :: SimpleExpr
--
number :: Integer -> SimpleExpr
-- | Initializes a single symbolic variable expression.
--
-- Examples of usage
--
--
-- >>> x = variable "x"
--
-- >>> x
-- x
--
-- >>> :t x
-- x :: SimpleExpr
--
variable :: String -> SimpleExpr
-- | Inituialize unarry function
--
-- Examples of usage
--
--
-- >>> x = variable "x"
--
-- >>> f = unaryFunc "f"
--
-- >>> f x
-- f(x)
--
-- >>> :t x
-- x :: SimpleExpr
--
-- >>> :t f
-- f :: SimpleExpr -> SimpleExpr
--
unaryFunc :: String -> SimpleExpr -> SimpleExpr
-- | Inituialize unarry function
--
-- Examples of usage
--
--
-- >>> x = variable "x"
--
-- >>> y = variable "y"
--
-- >>> (-*-) = binaryFunc "-*-"
--
-- >>> x -*- y
-- x-*-y
--
-- >>> :t x
-- x :: SimpleExpr
--
-- >>> :t (-*-)
-- (-*-) :: SimpleExpr -> SimpleExpr -> SimpleExpr
--
-- >>> :t x-*-y
-- x-*-y :: SimpleExpr
--
binaryFunc :: String -> SimpleExpr -> SimpleExpr -> SimpleExpr
-- | Simplify expression using some primitive rules like '0 * x -> 0'
-- specified in simplifyStep implementation.
--
-- Examples of usage
--
--
-- >>> import Prelude (($))
--
-- >>> import Debug.SimpleExpr (variable, simplify)
--
-- >>> import NumHask ((+), (-), (*))
--
--
--
-- >>> x = variable "x"
--
-- >>> simplify $ (x + 0) * 1 - x * (3 - 2)
-- 0
--
simplify :: SimpleExpr -> SimpleExpr
-- | Minimalistic simplification step.
--
-- Examples of usage
--
--
-- >>> import Prelude (($), id)
--
-- >>> import NumHask ((+), (*), (**))
--
--
--
-- >>> simplifyStep id (0 + (0 + (0 + 10)))
-- 0+(0+10)
--
--
--
-- >>> simplifyStep id (1 * (0 + (10 ** 1)))
-- 0+(10^1)
--
simplifyStep :: (SimpleExpr -> SimpleExpr) -> SimpleExpr -> SimpleExpr
-- | Expression F-algebra functional.
data SimpleExprF a
NumberF :: Integer -> SimpleExprF a
VariableF :: String -> SimpleExprF a
BinaryFuncF :: String -> a -> a -> SimpleExprF a
SymbolicFuncF :: String -> [a] -> SimpleExprF a
-- | Simple expression type, see tutorial
type SimpleExpr = Fix SimpleExprF
-- | Expression typeclass. It includes SimpleExpr as well as list
-- and tuples of SimpleExpr etc.
type Expr = ListOf SimpleExpr
-- | Entity that is representable as a list of in general other entities.
-- In particular, X is a list of single [X], see the
-- example below.
--
-- Examples of usage
--
--
-- >>> data Atom = Atom String deriving Show
--
-- >>> type Particle = ListOf Atom
--
--
--
-- >>> content (Atom "He") :: [Atom]
-- [Atom "He"]
--
--
--
-- >>> content (Atom "H", Atom "H") :: [Atom]
-- [Atom "H",Atom "H"]
--
--
--
-- >>> content [Atom "H", Atom "O", Atom "H"] :: [Atom]
-- [Atom "H",Atom "O",Atom "H"]
--
class ListOf inner outer
-- | Returns a list of entities the argument consists of.
content :: ListOf inner outer => outer -> [inner]
-- | Returns the list of head dependencies of an expression.
--
-- Examples of usage
--
--
-- >>> import Prelude (($), id)
--
-- >>> import NumHask ((+), (*))
--
--
--
-- >>> dependencies (variable "x" + (variable "y" * variable "z"))
-- [x,y·z]
--
dependencies :: SimpleExpr -> [SimpleExpr]
-- | Shows expression adding brackets if it is needed for a context.
showWithBrackets :: SimpleExpr -> String
instance GHC.Classes.Eq a => GHC.Classes.Eq (Debug.SimpleExpr.Expr.SimpleExprF a)
instance GHC.Base.Functor Debug.SimpleExpr.Expr.SimpleExprF
instance Debug.SimpleExpr.Expr.ListOf inner ()
instance Debug.SimpleExpr.Expr.ListOf inner inner
instance (Debug.SimpleExpr.Expr.ListOf inner outer1, Debug.SimpleExpr.Expr.ListOf inner outer2) => Debug.SimpleExpr.Expr.ListOf inner (outer1, outer2)
instance (Debug.SimpleExpr.Expr.ListOf inner outer1, Debug.SimpleExpr.Expr.ListOf inner outer2, Debug.SimpleExpr.Expr.ListOf inner outer3) => Debug.SimpleExpr.Expr.ListOf inner (outer1, outer2, outer3)
instance (Debug.SimpleExpr.Expr.ListOf inner outer1, Debug.SimpleExpr.Expr.ListOf inner outer2, Debug.SimpleExpr.Expr.ListOf inner outer3, Debug.SimpleExpr.Expr.ListOf inner outer4) => Debug.SimpleExpr.Expr.ListOf inner (outer1, outer2, outer3, outer4)
instance (Debug.SimpleExpr.Expr.ListOf inner outer1, Debug.SimpleExpr.Expr.ListOf inner outer2, Debug.SimpleExpr.Expr.ListOf inner outer3, Debug.SimpleExpr.Expr.ListOf inner outer4, Debug.SimpleExpr.Expr.ListOf inner outer5) => Debug.SimpleExpr.Expr.ListOf inner (outer1, outer2, outer3, outer4, outer5)
instance Debug.SimpleExpr.Expr.ListOf inner outer => Debug.SimpleExpr.Expr.ListOf inner [outer]
instance GHC.Show.Show Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Additive.Additive Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Additive.Subtractive Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Multiplicative.Multiplicative Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Ring.Distributive Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Multiplicative.Divisive Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Field.Field Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Field.ExpField Debug.SimpleExpr.Expr.SimpleExpr
instance NumHask.Algebra.Field.TrigField Debug.SimpleExpr.Expr.SimpleExpr
instance GHC.Num.Num Debug.SimpleExpr.Expr.SimpleExpr
instance Data.Functor.Classes.Eq1 Debug.SimpleExpr.Expr.SimpleExprF
instance NumHask.Data.Integral.FromIntegral (Debug.SimpleExpr.Expr.SimpleExprF a) GHC.Integer.Type.Integer
instance NumHask.Data.Integral.FromIntegral (Data.Fix.Fix Debug.SimpleExpr.Expr.SimpleExprF) GHC.Integer.Type.Integer
-- | Tools for transforming simple expressions to graphs from
-- graphite.
module Debug.SimpleExpr.GraphUtils
-- | Transforms an expression to graph.
--
-- Examples of usage
--
--
-- >>> import Debug.SimpleExpr (variable)
--
-- >>> import NumHask ((+), (-))
--
--
--
-- >>> x = variable "x"
--
-- >>> y = variable "y"
--
-- >>> exprToGraph [x + y, x - y]
-- fromList [("x",[("x+y",()),("x-y",())]),("x+y",[]),("x-y",[]),("y",[("x+y",()),("x-y",())])]
--
exprToGraph :: Expr d => d -> DGraph String ()
-- | Visualizes an expression.
--
-- Examples of usage
--
--
-- >>> import Debug.SimpleExpr (number, variable)
--
-- >>> import NumHask ((+), (-))
--
-- >>> import Data.Graph.VisualizeAlternative (plotDGraphPng)
--
--
--
-- >>> plotExpr (number 1 + variable "x")
--
--
--
--
-- >>> x = variable "x"
--
-- >>> y = variable "y"
--
--
--
-- >>> plotExpr [x + y, x - y]
--
--
plotExpr :: Expr d => d -> IO ThreadId
-- | A copy of toDirectedDot method from Visualize but the
-- parameter Sfdp is replaced by Dot.
plotDGraphPng :: (Hashable v, Ord v, PrintDot v, Show v, Show e) => DGraph v e -> FilePath -> IO FilePath
-- | Transforms a simple expression to graph.
simpleExprToGraph :: SimpleExpr -> DGraph String ()
-- | Appends a node to a graph using string valued keys.
--
-- The first argumet is the new node name.
--
-- The second argument is the list of dependent nodes.
appendNodeToGraph :: String -> [String] -> DGraph String () -> DGraph String ()
-- | Minimalistic toolkit for simple mathematical expression developed for
-- debug purposes. See Tutorial for a quick introduction.
module Debug.SimpleExpr
-- | Initializes a single integer number expression.
--
-- Examples of usage
--
--
-- >>> a = number 42
--
-- >>> a
-- 42
--
-- >>> :t a
-- a :: SimpleExpr
--
number :: Integer -> SimpleExpr
-- | Initializes a single symbolic variable expression.
--
-- Examples of usage
--
--
-- >>> x = variable "x"
--
-- >>> x
-- x
--
-- >>> :t x
-- x :: SimpleExpr
--
variable :: String -> SimpleExpr
-- | Inituialize unarry function
--
-- Examples of usage
--
--
-- >>> x = variable "x"
--
-- >>> f = unaryFunc "f"
--
-- >>> f x
-- f(x)
--
-- >>> :t x
-- x :: SimpleExpr
--
-- >>> :t f
-- f :: SimpleExpr -> SimpleExpr
--
unaryFunc :: String -> SimpleExpr -> SimpleExpr
-- | Inituialize unarry function
--
-- Examples of usage
--
--
-- >>> x = variable "x"
--
-- >>> y = variable "y"
--
-- >>> (-*-) = binaryFunc "-*-"
--
-- >>> x -*- y
-- x-*-y
--
-- >>> :t x
-- x :: SimpleExpr
--
-- >>> :t (-*-)
-- (-*-) :: SimpleExpr -> SimpleExpr -> SimpleExpr
--
-- >>> :t x-*-y
-- x-*-y :: SimpleExpr
--
binaryFunc :: String -> SimpleExpr -> SimpleExpr -> SimpleExpr
-- | Simplify expression using some primitive rules like '0 * x -> 0'
-- specified in simplifyStep implementation.
--
-- Examples of usage
--
--
-- >>> import Prelude (($))
--
-- >>> import Debug.SimpleExpr (variable, simplify)
--
-- >>> import NumHask ((+), (-), (*))
--
--
--
-- >>> x = variable "x"
--
-- >>> simplify $ (x + 0) * 1 - x * (3 - 2)
-- 0
--
simplify :: SimpleExpr -> SimpleExpr
-- | Simple expression type, see tutorial
type SimpleExpr = Fix SimpleExprF
-- | Expression typeclass. It includes SimpleExpr as well as list
-- and tuples of SimpleExpr etc.
type Expr = ListOf SimpleExpr
-- | Visualizes an expression.
--
-- Examples of usage
--
--
-- >>> import Debug.SimpleExpr (number, variable)
--
-- >>> import NumHask ((+), (-))
--
-- >>> import Data.Graph.VisualizeAlternative (plotDGraphPng)
--
--
--
-- >>> plotExpr (number 1 + variable "x")
--
--
--
--
-- >>> x = variable "x"
--
-- >>> y = variable "y"
--
--
--
-- >>> plotExpr [x + y, x - y]
--
--
plotExpr :: Expr d => d -> IO ThreadId
-- | Transforms an expression to graph.
--
-- Examples of usage
--
--
-- >>> import Debug.SimpleExpr (variable)
--
-- >>> import NumHask ((+), (-))
--
--
--
-- >>> x = variable "x"
--
-- >>> y = variable "y"
--
-- >>> exprToGraph [x + y, x - y]
-- fromList [("x",[("x+y",()),("x-y",())]),("x+y",[]),("x-y",[]),("y",[("x+y",()),("x-y",())])]
--
exprToGraph :: Expr d => d -> DGraph String ()
-- | A copy of plotDGraph method from Visualize but the
-- parameter Sfdp is replaced by Dot.
plotDGraph :: (Hashable v, Ord v, PrintDot v, Show v, Show e) => DGraph v e -> IO ThreadId
-- | A copy of toDirectedDot method from Visualize but the
-- parameter Sfdp is replaced by Dot.
plotDGraphPng :: (Hashable v, Ord v, PrintDot v, Show v, Show e) => DGraph v e -> FilePath -> IO FilePath
-- | Returns the list of head dependencies of an expression.
--
-- Examples of usage
--
--
-- >>> import Prelude (($), id)
--
-- >>> import NumHask ((+), (*))
--
--
--
-- >>> dependencies (variable "x" + (variable "y" * variable "z"))
-- [x,y·z]
--
dependencies :: SimpleExpr -> [SimpleExpr]
-- | Returns a list of entities the argument consists of.
content :: ListOf inner outer => outer -> [inner]
-- | Tutorial, Quick start or Demo for 'simple-expr' package.
module Debug.SimpleExpr.Tutorial