speculate-0.4.16: discovery of properties about Haskell functions
Copyright(c) 2016-2019 Rudy Matela
License3-Clause BSD (see the file LICENSE)
MaintainerRudy Matela <rudy@matela.com.br>
Safe HaskellSafe-Inferred
LanguageHaskell2010

Test.Speculate

Description

Speculate: discovery of properties by reasoning from test results

Speculate automatically discovers laws about Haskell functions. Those laws involve:

  • equations, such as id x == x ;
  • inequalities, such as 0 <= x * x ;
  • conditional equations, such as x <= 0 ==> x + abs x == 0 .

_Example:_ the following program prints laws about 0, 1, + and abs.

import Test.Speculate

main :: IO ()
main = speculate args
  { constants =
      [ showConstant (0::Int)
      , showConstant (1::Int)
      , constant "+"   ((+)  :: Int -> Int -> Int)
      , constant "abs" (abs  :: Int -> Int)
      , background
      , constant "<="  ((<=) :: Int -> Int -> Bool)
      ]
  }
Synopsis

Documentation

speculate :: Args -> IO () Source #

Calls Speculate. See the example above (at the top of the file). Its only argument is an Args structure.

data Args Source #

Arguments to Speculate

Constructors

Args 

Fields

args :: Args Source #

Default arguments to Speculate

The constants list

The following combinators are used to build the constants list from Args.

data Expr #

Values of type Expr represent objects or applications between objects. Each object is encapsulated together with its type and string representation. Values encoded in Exprs are always monomorphic.

An Expr can be constructed using:

  • val, for values that are Show instances;
  • value, for values that are not Show instances, like functions;
  • :$, for applications between Exprs.
> val False
False :: Bool
> value "not" not :$ val False
not False :: Bool

An Expr can be evaluated using evaluate, eval or evl.

> evl $ val (1 :: Int) :: Int
1
> evaluate $ val (1 :: Int) :: Maybe Bool
Nothing
> eval 'a' (val 'b')
'b'

Showing a value of type Expr will return a pretty-printed representation of the expression together with its type.

> show (value "not" not :$ val False)
"not False :: Bool"

Expr is like Dynamic but has support for applications and variables (:$, var).

The var underscore convention: Functions that manipulate Exprs usually follow the convention where a value whose String representation starts with '_' represents a variable.

Instances

Instances details
Show Expr

Shows Exprs with their types.

> show (value "not" not :$ val False)
"not False :: Bool"
Instance details

Defined in Data.Express.Core

Methods

showsPrec :: Int -> Expr -> ShowS #

show :: Expr -> String #

showList :: [Expr] -> ShowS #

Eq Expr

O(n). Does not evaluate values when comparing, but rather uses their representation as strings and their types.

This instance works for ill-typed expressions.

Instance details

Defined in Data.Express.Core

Methods

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

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

Ord Expr

O(n). Does not evaluate values when comparing, but rather uses their representation as strings and their types.

This instance works for ill-typed expressions.

Expressions come first when they have smaller complexity (compareComplexity) or when they come first lexicographically (compareLexicographically).

Instance details

Defined in Data.Express.Core

Methods

compare :: Expr -> Expr -> Ordering #

(<) :: Expr -> Expr -> Bool #

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

(>) :: Expr -> Expr -> Bool #

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

max :: Expr -> Expr -> Expr #

min :: Expr -> Expr -> Expr #

hole :: Typeable a => a -> Expr #

O(1). Creates an Expr representing a typed hole of the given argument type.

> hole (undefined :: Int)
_ :: Int
> hole (undefined :: Maybe String)
_ :: Maybe [Char]

A hole is represented as a variable with no name or a value named "_":

hole x = var "" x
hole x = value "_" x

foreground :: Expr Source #

A special Expr value. When provided on the constants list, makes all the following constants foreground constants.

background :: Expr Source #

A special Expr value. When provided on the constants list, makes all the following constants background constants. Background constants can appear in laws about other constants, but not by themselves.

The instances list

The following combinators are used to build the instances list from Args.

reifyEq :: (Typeable a, Eq a) => a -> [Expr] #

O(1). Reifies an Eq instance into a list of Exprs. The list will contain == and /= for the given type. (cf. mkEq, mkEquation)

> reifyEq (undefined :: Int)
[ (==) :: Int -> Int -> Bool
, (/=) :: Int -> Int -> Bool ]
> reifyEq (undefined :: Bool)
[ (==) :: Bool -> Bool -> Bool
, (/=) :: Bool -> Bool -> Bool ]
> reifyEq (undefined :: String)
[ (==) :: [Char] -> [Char] -> Bool
, (/=) :: [Char] -> [Char] -> Bool ]

reifyOrd :: (Typeable a, Ord a) => a -> [Expr] #

O(1). Reifies an Ord instance into a list of Exprs. The list will contain compare, <= and < for the given type. (cf. mkOrd, mkOrdLessEqual, mkComparisonLE, mkComparisonLT)

> reifyOrd (undefined :: Int)
[ (<=) :: Int -> Int -> Bool
, (<) :: Int -> Int -> Bool ]
> reifyOrd (undefined :: Bool)
[ (<=) :: Bool -> Bool -> Bool
, (<) :: Bool -> Bool -> Bool ]
> reifyOrd (undefined :: [Bool])
[ (<=) :: [Bool] -> [Bool] -> Bool
, (<) :: [Bool] -> [Bool] -> Bool ]

reifyEqOrd :: (Typeable a, Ord a) => a -> [Expr] #

O(1). Reifies Eq and Ord instances into a list of Expr.

reifyName :: (Typeable a, Name a) => a -> [Expr] #

O(1). Reifies a Name instance into a list of Exprs. The list will contain name for the given type. (cf. mkName, lookupName, lookupNames)

> reifyName (undefined :: Int)
[name :: Int -> [Char]]
> reifyName (undefined :: Bool)
[name :: Bool -> [Char]]

mkEq :: Typeable a => (a -> a -> Bool) -> [Expr] #

O(1). Builds a reified Eq instance from the given == function. (cf. reifyEq)

> mkEq ((==) :: Int -> Int -> Bool)
[ (==) :: Int -> Int -> Bool
, (/=) :: Int -> Int -> Bool ]

mkOrd :: Typeable a => (a -> a -> Ordering) -> [Expr] #

O(1). Builds a reified Ord instance from the given compare function. (cf. reifyOrd, mkOrdLessEqual)

mkOrdLessEqual :: Typeable a => (a -> a -> Bool) -> [Expr] #

O(1). Builds a reified Ord instance from the given <= function. (cf. reifyOrd, mkOrd)

mkListable :: (Typeable a, Show a) => [[a]] -> [Expr] Source #

mkNameWith :: Typeable a => String -> a -> [Expr] #

O(1). Builds a reified Name instance from the given String and type. (cf. reifyName, mkName)

class Name a where #

If we were to come up with a variable name for the given type what name would it be?

An instance for a given type Ty is simply given by:

instance Name Ty where name _ = "x"

Examples:

> name (undefined :: Int)
"x"
> name (undefined :: Bool)
"p"
> name (undefined :: [Int])
"xs"

This is then used to generate an infinite list of variable names:

> names (undefined :: Int)
["x", "y", "z", "x'", "y'", "z'", "x''", "y''", "z''", ...]
> names (undefined :: Bool)
["p", "q", "r", "p'", "q'", "r'", "p''", "q''", "r''", ...]
> names (undefined :: [Int])
["xs", "ys", "zs", "xs'", "ys'", "zs'", "xs''", "ys''", ...]

Minimal complete definition

Nothing

Methods

name :: a -> String #

O(1).

Returns a name for a variable of the given argument's type.

> name (undefined :: Int)
"x"
> name (undefined :: [Bool])
"ps"
> name (undefined :: [Maybe Integer])
"mxs"

The default definition is:

name _ = "x"

Instances

Instances details
Name Int16 
Instance details

Defined in Data.Express.Name

Methods

name :: Int16 -> String #

Name Int32 
Instance details

Defined in Data.Express.Name

Methods

name :: Int32 -> String #

Name Int64 
Instance details

Defined in Data.Express.Name

Methods

name :: Int64 -> String #

Name Int8 
Instance details

Defined in Data.Express.Name

Methods

name :: Int8 -> String #

Name GeneralCategory 
Instance details

Defined in Data.Express.Name

Name Word16 
Instance details

Defined in Data.Express.Name

Methods

name :: Word16 -> String #

Name Word32 
Instance details

Defined in Data.Express.Name

Methods

name :: Word32 -> String #

Name Word64 
Instance details

Defined in Data.Express.Name

Methods

name :: Word64 -> String #

Name Word8 
Instance details

Defined in Data.Express.Name

Methods

name :: Word8 -> String #

Name Ordering
name (undefined :: Ordering) = "o"
names (undefined :: Ordering) = ["o", "p", "q", "o'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Ordering -> String #

Name Integer
name (undefined :: Integer) = "x"
names (undefined :: Integer) = ["x", "y", "z", "x'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Integer -> String #

Name ()
name (undefined :: ()) = "u"
names (undefined :: ()) = ["u", "v", "w", "u'", "v'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: () -> String #

Name Bool
name (undefined :: Bool) = "p"
names (undefined :: Bool) = ["p", "q", "r", "p'", "q'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Bool -> String #

Name Char
name (undefined :: Char) = "c"
names (undefined :: Char) = ["c", "d", "e", "c'", "d'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Char -> String #

Name Double
name (undefined :: Double) = "x"
names (undefined :: Double) = ["x", "y", "z", "x'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Double -> String #

Name Float
name (undefined :: Float) = "x"
names (undefined :: Float) = ["x", "y", "z", "x'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Float -> String #

Name Int
name (undefined :: Int) = "x"
names (undefined :: Int) = ["x", "y", "z", "x'", "y'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Int -> String #

Name Word 
Instance details

Defined in Data.Express.Name

Methods

name :: Word -> String #

Name (Complex a)
name (undefined :: Complex) = "x"
names (undefined :: Complex) = ["x", "y", "z", "x'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Complex a -> String #

Name (Ratio a)
name (undefined :: Rational) = "q"
names (undefined :: Rational) = ["q", "r", "s", "q'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Ratio a -> String #

Name a => Name (Maybe a)
names (undefined :: Maybe Int) = ["mx", "mx1", "mx2", ...]
nemes (undefined :: Maybe Bool) = ["mp", "mp1", "mp2", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Maybe a -> String #

Name a => Name [a]
names (undefined :: [Int]) = ["xs", "ys", "zs", "xs'", ...]
names (undefined :: [Bool]) = ["ps", "qs", "rs", "ps'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: [a] -> String #

(Name a, Name b) => Name (Either a b)
names (undefined :: Either Int Int) = ["exy", "exy1", ...]
names (undefined :: Either Int Bool) = ["exp", "exp1", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: Either a b -> String #

(Name a, Name b) => Name (a, b)
names (undefined :: (Int,Int)) = ["xy", "zw", "xy'", ...]
names (undefined :: (Bool,Bool)) = ["pq", "rs", "pq'", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b) -> String #

Name (a -> b)
names (undefined :: ()->()) = ["f", "g", "h", "f'", ...]
names (undefined :: Int->Int) = ["f", "g", "h", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: (a -> b) -> String #

(Name a, Name b, Name c) => Name (a, b, c)
names (undefined :: (Int,Int,Int)) = ["xyz","uvw", ...]
names (undefined :: (Int,Bool,Char)) = ["xpc", "xpc1", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c) -> String #

(Name a, Name b, Name c, Name d) => Name (a, b, c, d)
names (undefined :: ((),(),(),())) = ["uuuu", "uuuu1", ...]
names (undefined :: (Int,Int,Int,Int)) = ["xxxx", ...]
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d) -> String #

(Name a, Name b, Name c, Name d, Name e) => Name (a, b, c, d, e) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f) => Name (a, b, c, d, e, f) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f, Name g) => Name (a, b, c, d, e, f, g) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f, g) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f, Name g, Name h) => Name (a, b, c, d, e, f, g, h) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f, g, h) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f, Name g, Name h, Name i) => Name (a, b, c, d, e, f, g, h, i) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f, g, h, i) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f, Name g, Name h, Name i, Name j) => Name (a, b, c, d, e, f, g, h, i, j) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f, g, h, i, j) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f, Name g, Name h, Name i, Name j, Name k) => Name (a, b, c, d, e, f, g, h, i, j, k) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f, g, h, i, j, k) -> String #

(Name a, Name b, Name c, Name d, Name e, Name f, Name g, Name h, Name i, Name j, Name k, Name l) => Name (a, b, c, d, e, f, g, h, i, j, k, l) 
Instance details

Defined in Data.Express.Name

Methods

name :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String #

Misc.

report :: Args -> IO () Source #