code-conjure-0.5.14: synthesize Haskell functions out of partial definitions
Copyright(c) 2021-2024 Rudy Matela
License3-Clause BSD (see the file LICENSE)
MaintainerRudy Matela <rudy@matela.com.br>
Safe HaskellSafe-Inferred
LanguageHaskell2010

Conjure

Description

A library for Conjuring function implementations from tests or partial definitions. (a.k.a.: functional inductive programming)

This is currently an experimental tool in its early stages, don't expect much from its current version. It is just a piece of curiosity in its current state.

Step 1: declare your partial function

square :: Int -> Int
square 0  =  0
square 1  =  1
square 2  =  4

Step 2: declare a list with the potential building blocks:

primitives :: [Prim]
primitives =
  [ pr (0::Int)
  , pr (1::Int)
  , prim "+" ((+) :: Int -> Int -> Int)
  , prim "*" ((*) :: Int -> Int -> Int)
  ]

Step 3: call conjure and see your generated function:

> conjure "square" square primitives
square :: Int -> Int
-- testing 3 combinations of argument values
-- pruning with 14/25 rules
-- looking through 3 candidates of size 1
-- looking through 4 candidates of size 2
-- looking through 9 candidates of size 3
square x  =  x * x
Synopsis

Basic use

conjure :: Conjurable f => String -> f -> [Prim] -> IO () Source #

Conjures an implementation of a partially defined function.

Takes a String with the name of a function, a partially-defined function from a conjurable type, and a list of building blocks encoded as Exprs.

For example, given:

square :: Int -> Int
square 0  =  0
square 1  =  1
square 2  =  4

primitives :: [Prim]
primitives =
  [ pr (0::Int)
  , pr (1::Int)
  , prim "+" ((+) :: Int -> Int -> Int)
  , prim "*" ((*) :: Int -> Int -> Int)
  ]

The conjure function does the following:

> conjure "square" square primitives
square :: Int -> Int
-- pruning with 14/25 rules
-- testing 3 combinations of argument values
-- looking through 3 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 5 candidates of size 3
square x  =  x * x

The primitives list is defined with pr and prim.

type Prim = (Expr, Reification) Source #

A primtive expression (paired with instance reification).

pr :: (Conjurable a, Show a) => a -> Prim Source #

Provides a primitive value to Conjure. To be used on Show instances. (cf. prim)

prim :: Conjurable a => String -> a -> Prim Source #

Provides a primitive value to Conjure. To be used on values that are not Show instances such as functions. (cf. pr)

prif :: Conjurable a => a -> Prim Source #

Provides an if condition bound to the given return type.

primOrdCaseFor :: Conjurable a => a -> Prim Source #

Provides a case condition bound to the given return type.

Advanced use

conjureWithMaxSize :: Conjurable f => Int -> String -> f -> [Prim] -> IO () Source #

Like conjure but allows setting the maximum size of considered expressions instead of the default value of 12.

conjureWithMaxSize 10 "function" function [...]

conjureWith :: Conjurable f => Args -> String -> f -> [Prim] -> IO () Source #

Like conjure but allows setting options through Args/args.

conjureWith args{maxSize = 11} "function" function [...]

data Args Source #

Arguments to be passed to conjureWith or conjpureWith. See args for the defaults.

Constructors

Args 

Fields

args :: Args Source #

Default arguments to conjure.

  • 60 tests
  • functions of up to 12 symbols
  • maximum of one recursive call allowed in candidate bodies
  • maximum evaluation of up to 60 recursions
  • pruning with equations up to size 5
  • search for defined applications for up to 100000 combinations
  • require recursive calls to deconstruct arguments
  • don't show the theory used in pruning
  • do not make candidates unique module testing

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 #

val :: (Typeable a, Show a) => a -> Expr #

O(1). A shorthand for value for values that are Show instances.

> val (0 :: Int)
0 :: Int
> val 'a'
'a' :: Char
> val True
True :: Bool

Example equivalences to value:

val 0     =  value "0" 0
val 'a'   =  value "'a'" 'a'
val True  =  value "True" True

value :: Typeable a => String -> a -> Expr #

O(1). It takes a string representation of a value and a value, returning an Expr with that terminal value. For instances of Show, it is preferable to use val.

> value "0" (0 :: Integer)
0 :: Integer
> value "'a'" 'a'
'a' :: Char
> value "True" True
True :: Bool
> value "id" (id :: Int -> Int)
id :: Int -> Int
> value "(+)" ((+) :: Int -> Int -> Int)
(+) :: Int -> Int -> Int
> value "sort" (sort :: [Bool] -> [Bool])
sort :: [Bool] -> [Bool]

Conjuring from a specification

conjureFromSpec :: Conjurable f => String -> (f -> Bool) -> [Prim] -> IO () Source #

Conjures an implementation from a function specification.

This function works like conjure but instead of receiving a partial definition it receives a boolean filter / property about the function.

For example, given:

squareSpec :: (Int -> Int) -> Bool
squareSpec square  =  square 0 == 0
                   && square 1 == 1
                   && square 2 == 4

Then:

> conjureFromSpec "square" squareSpec primitives
square :: Int -> Int
-- pruning with 14/25 rules
-- looking through 3 candidates of size 1
-- looking through 4 candidates of size 2
-- looking through 9 candidates of size 3
square x  =  x * x

This allows users to specify QuickCheck-style properties, here is an example using LeanCheck:

import Test.LeanCheck (holds, exists)

squarePropertySpec :: (Int -> Int) -> Bool
squarePropertySpec square  =  and
  [ holds n $ \x -> square x >= x
  , holds n $ \x -> square x >= 0
  , exists n $ \x -> square x > x
  ]  where  n = 60

conjureFromSpecWith :: Conjurable f => Args -> String -> (f -> Bool) -> [Prim] -> IO () Source #

Like conjureFromSpec but allows setting options through Args/args.

conjureFromSpecWith args{maxSize = 11} "function" spec [...]

When using custom types

class (Typeable a, Name a) => Conjurable a where Source #

Class of Conjurable types. Functions are Conjurable if all their arguments are Conjurable, Listable and Showable.

For atomic types that are Listable, instances are defined as:

instance Conjurable Atomic where
  conjureTiers  =  reifyTiers

For atomic types that are both Listable and Eq, instances are defined as:

instance Conjurable Atomic where
  conjureTiers     =  reifyTiers
  conjureEquality  =  reifyEquality

For types with subtypes, instances are defined as:

instance Conjurable Composite where
  conjureTiers     =  reifyTiers
  conjureEquality  =  reifyEquality
  conjureSubTypes x  =  conjureType y
                     .  conjureType z
                     .  conjureType w
    where
    (Composite ... y ... z ... w ...)  =  x

Above x, y, z and w are just proxies. The Proxy type was avoided for backwards compatibility.

Please see the source code of Conjure.Conjurable for more examples.

(cf. reifyTiers, reifyEquality, conjureType)

Minimal complete definition

conjureExpress

Methods

conjureEquality :: a -> Maybe Expr Source #

Returns Just the == function encoded as an Expr when available or Nothing otherwise.

Use reifyEquality when defining this.

conjureTiers :: a -> Maybe [[Expr]] Source #

Returns Just tiers of values encoded as Exprs when possible or Nothing otherwise.

Use reifyTiers when defining this.

conjureSubTypes :: a -> Reification Source #

conjureCases :: a -> [Expr] Source #

Returns a top-level case breakdown.

conjureSize :: a -> Int Source #

Returns the (recursive) size of the given value.

conjureExpress :: a -> Expr -> Expr Source #

Returns a function that deeply reencodes an expression when possible. (id when not available.)

Use reifyExpress when defining this.

Instances

Instances details
Conjurable Int16 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Int32 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Int64 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Int8 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Word16 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Word32 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Word64 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Word8 Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Ordering Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable A Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable B Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable C Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable D Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable E Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable F Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Integer Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable () Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Bool Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Char Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Double Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Float Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Int Source # 
Instance details

Defined in Conjure.Conjurable

Conjurable Word Source # 
Instance details

Defined in Conjure.Conjurable

(RealFloat a, Conjurable a, Listable a, Show a, Eq a, Express a) => Conjurable (Complex a) Source # 
Instance details

Defined in Conjure.Conjurable

(Integral a, Conjurable a, Listable a, Show a, Eq a, Express a) => Conjurable (Ratio a) Source # 
Instance details

Defined in Conjure.Conjurable

(Conjurable a, Listable a, Show a, Express a) => Conjurable (Maybe a) Source # 
Instance details

Defined in Conjure.Conjurable

(Conjurable a, Listable a, Express a, Show a) => Conjurable [a] Source # 
Instance details

Defined in Conjure.Conjurable

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b) => Conjurable (Either a b) Source # 
Instance details

Defined in Conjure.Conjurable

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b) => Conjurable (a, b) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b) -> [Expr] Source #

conjureEquality :: (a, b) -> Maybe Expr Source #

conjureTiers :: (a, b) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b) -> Reification Source #

conjureIf :: (a, b) -> Expr Source #

conjureCases :: (a, b) -> [Expr] Source #

conjureArgumentCases :: (a, b) -> [[Expr]] Source #

conjureSize :: (a, b) -> Int Source #

conjureExpress :: (a, b) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b) Source #

(Conjurable a, Conjurable b) => Conjurable (a -> b) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a -> b) -> [Expr] Source #

conjureEquality :: (a -> b) -> Maybe Expr Source #

conjureTiers :: (a -> b) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a -> b) -> Reification Source #

conjureIf :: (a -> b) -> Expr Source #

conjureCases :: (a -> b) -> [Expr] Source #

conjureArgumentCases :: (a -> b) -> [[Expr]] Source #

conjureSize :: (a -> b) -> Int Source #

conjureExpress :: (a -> b) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a -> b) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c) => Conjurable (a, b, c) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c) -> [Expr] Source #

conjureEquality :: (a, b, c) -> Maybe Expr Source #

conjureTiers :: (a, b, c) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c) -> Reification Source #

conjureIf :: (a, b, c) -> Expr Source #

conjureCases :: (a, b, c) -> [Expr] Source #

conjureArgumentCases :: (a, b, c) -> [[Expr]] Source #

conjureSize :: (a, b, c) -> Int Source #

conjureExpress :: (a, b, c) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d) => Conjurable (a, b, c, d) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d) -> [Expr] Source #

conjureEquality :: (a, b, c, d) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d) -> Reification Source #

conjureIf :: (a, b, c, d) -> Expr Source #

conjureCases :: (a, b, c, d) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d) -> [[Expr]] Source #

conjureSize :: (a, b, c, d) -> Int Source #

conjureExpress :: (a, b, c, d) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e) => Conjurable (a, b, c, d, e) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e) -> Reification Source #

conjureIf :: (a, b, c, d, e) -> Expr Source #

conjureCases :: (a, b, c, d, e) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e) -> Int Source #

conjureExpress :: (a, b, c, d, e) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f) => Conjurable (a, b, c, d, e, f) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f) -> Reification Source #

conjureIf :: (a, b, c, d, e, f) -> Expr Source #

conjureCases :: (a, b, c, d, e, f) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f) -> Int Source #

conjureExpress :: (a, b, c, d, e, f) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f, Conjurable g, Listable g, Show g, Express g) => Conjurable (a, b, c, d, e, f, g) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f, g) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f, g) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f, g) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f, g) -> Reification Source #

conjureIf :: (a, b, c, d, e, f, g) -> Expr Source #

conjureCases :: (a, b, c, d, e, f, g) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f, g) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f, g) -> Int Source #

conjureExpress :: (a, b, c, d, e, f, g) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f, g) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f, Conjurable g, Listable g, Show g, Express g, Conjurable h, Listable h, Show h, Express h) => Conjurable (a, b, c, d, e, f, g, h) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f, g, h) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f, g, h) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f, g, h) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f, g, h) -> Reification Source #

conjureIf :: (a, b, c, d, e, f, g, h) -> Expr Source #

conjureCases :: (a, b, c, d, e, f, g, h) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f, g, h) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f, g, h) -> Int Source #

conjureExpress :: (a, b, c, d, e, f, g, h) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f, g, h) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f, Conjurable g, Listable g, Show g, Express g, Conjurable h, Listable h, Show h, Express h, Conjurable i, Listable i, Show i, Express i) => Conjurable (a, b, c, d, e, f, g, h, i) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f, g, h, i) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f, g, h, i) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f, g, h, i) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f, g, h, i) -> Reification Source #

conjureIf :: (a, b, c, d, e, f, g, h, i) -> Expr Source #

conjureCases :: (a, b, c, d, e, f, g, h, i) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f, g, h, i) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f, g, h, i) -> Int Source #

conjureExpress :: (a, b, c, d, e, f, g, h, i) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f, g, h, i) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f, Conjurable g, Listable g, Show g, Express g, Conjurable h, Listable h, Show h, Express h, Conjurable i, Listable i, Show i, Express i, Conjurable j, Listable j, Show j, Express j) => Conjurable (a, b, c, d, e, f, g, h, i, j) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f, g, h, i, j) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f, g, h, i, j) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f, g, h, i, j) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f, g, h, i, j) -> Reification Source #

conjureIf :: (a, b, c, d, e, f, g, h, i, j) -> Expr Source #

conjureCases :: (a, b, c, d, e, f, g, h, i, j) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f, g, h, i, j) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f, g, h, i, j) -> Int Source #

conjureExpress :: (a, b, c, d, e, f, g, h, i, j) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f, g, h, i, j) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f, Conjurable g, Listable g, Show g, Express g, Conjurable h, Listable h, Show h, Express h, Conjurable i, Listable i, Show i, Express i, Conjurable j, Listable j, Show j, Express j, Conjurable k, Listable k, Show k, Express k) => Conjurable (a, b, c, d, e, f, g, h, i, j, k) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f, g, h, i, j, k) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f, g, h, i, j, k) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f, g, h, i, j, k) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f, g, h, i, j, k) -> Reification Source #

conjureIf :: (a, b, c, d, e, f, g, h, i, j, k) -> Expr Source #

conjureCases :: (a, b, c, d, e, f, g, h, i, j, k) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f, g, h, i, j, k) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f, g, h, i, j, k) -> Int Source #

conjureExpress :: (a, b, c, d, e, f, g, h, i, j, k) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f, g, h, i, j, k) Source #

(Conjurable a, Listable a, Show a, Express a, Conjurable b, Listable b, Show b, Express b, Conjurable c, Listable c, Show c, Express c, Conjurable d, Listable d, Show d, Express d, Conjurable e, Listable e, Show e, Express e, Conjurable f, Listable f, Show f, Express f, Conjurable g, Listable g, Show g, Express g, Conjurable h, Listable h, Show h, Express h, Conjurable i, Listable i, Show i, Express i, Conjurable j, Listable j, Show j, Express j, Conjurable k, Listable k, Show k, Express k, Conjurable l, Listable l, Show l, Express l) => Conjurable (a, b, c, d, e, f, g, h, i, j, k, l) Source # 
Instance details

Defined in Conjure.Conjurable

Methods

conjureArgumentHoles :: (a, b, c, d, e, f, g, h, i, j, k, l) -> [Expr] Source #

conjureEquality :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Maybe Expr Source #

conjureTiers :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Maybe [[Expr]] Source #

conjureSubTypes :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Reification Source #

conjureIf :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Expr Source #

conjureCases :: (a, b, c, d, e, f, g, h, i, j, k, l) -> [Expr] Source #

conjureArgumentCases :: (a, b, c, d, e, f, g, h, i, j, k, l) -> [[Expr]] Source #

conjureSize :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Int Source #

conjureExpress :: (a, b, c, d, e, f, g, h, i, j, k, l) -> Expr -> Expr Source #

conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe (a, b, c, d, e, f, g, h, i, j, k, l) Source #

reifyExpress :: (Express a, Show a) => a -> Expr -> Expr Source #

Reifies the expr function in a Conjurable type instance.

This is to be used in the definition of conjureExpress of Conjurable typeclass instances.

instance ... => Conjurable <Type> where
  ...
  conjureExpress  =  reifyExpress
  ...

reifyEquality :: (Eq a, Typeable a) => a -> Maybe Expr Source #

Reifies equality == in a Conjurable type instance.

This is to be used in the definition of conjureEquality of Conjurable typeclass instances:

instance ... => Conjurable <Type> where
  ...
  conjureEquality  =  reifyEquality
  ...

reifyTiers :: (Listable a, Show a, Typeable a) => a -> Maybe [[Expr]] Source #

Reifies equality to be used in a conjurable type.

This is to be used in the definition of conjureTiers of Conjurable typeclass instances:

instance ... => Conjurable <Type> where
  ...
  conjureTiers  =  reifyTiers
  ...

conjureType :: Conjurable a => a -> Reification Source #

To be used in the implementation of conjureSubTypes.

instance ... => Conjurable <Type> where
  ...
  conjureSubTypes x  =  conjureType (field1 x)
                     .  conjureType (field2 x)
                     .  ...
                     .  conjureType (fieldN x)
  ...

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 A Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: A -> String #

Name B Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: B -> String #

Name C Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: C -> String #

Name D Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: D -> String #

Name E Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: E -> String #

Name F Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: F -> 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 #

class (Show a, Typeable a) => Express a where #

Express typeclass instances provide an expr function that allows values to be deeply encoded as applications of Exprs.

expr False  =  val False
expr (Just True)  =  value "Just" (Just :: Bool -> Maybe Bool) :$ val True

The function expr can be contrasted with the function val:

  • val always encodes values as atomic Value Exprs -- shallow encoding.
  • expr ideally encodes expressions as applications (:$) between Value Exprs -- deep encoding.

Depending on the situation, one or the other may be desirable.

Instances can be automatically derived using the TH function deriveExpress.

The following example shows a datatype and its instance:

data Stack a = Stack a (Stack a) | Empty
instance Express a => Express (Stack a) where
  expr s@(Stack x y) = value "Stack" (Stack ->>: s) :$ expr x :$ expr y
  expr s@Empty       = value "Empty" (Empty   -: s)

To declare expr it may be useful to use auxiliary type binding operators: -:, ->:, ->>:, ->>>:, ->>>>:, ->>>>>:, ...

For types with atomic values, just declare expr = val

Methods

expr :: a -> Expr #

Instances

Instances details
Express Int16 
Instance details

Defined in Data.Express.Express

Methods

expr :: Int16 -> Expr #

Express Int32 
Instance details

Defined in Data.Express.Express

Methods

expr :: Int32 -> Expr #

Express Int64 
Instance details

Defined in Data.Express.Express

Methods

expr :: Int64 -> Expr #

Express Int8 
Instance details

Defined in Data.Express.Express

Methods

expr :: Int8 -> Expr #

Express GeneralCategory 
Instance details

Defined in Data.Express.Express

Methods

expr :: GeneralCategory -> Expr #

Express Word16 
Instance details

Defined in Data.Express.Express

Methods

expr :: Word16 -> Expr #

Express Word32 
Instance details

Defined in Data.Express.Express

Methods

expr :: Word32 -> Expr #

Express Word64 
Instance details

Defined in Data.Express.Express

Methods

expr :: Word64 -> Expr #

Express Word8 
Instance details

Defined in Data.Express.Express

Methods

expr :: Word8 -> Expr #

Express Ordering 
Instance details

Defined in Data.Express.Express

Methods

expr :: Ordering -> Expr #

Express A Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: A -> Expr #

Express B Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: B -> Expr #

Express C Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: C -> Expr #

Express D Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: D -> Expr #

Express E Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: E -> Expr #

Express F Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: F -> Expr #

Express Integer 
Instance details

Defined in Data.Express.Express

Methods

expr :: Integer -> Expr #

Express () 
Instance details

Defined in Data.Express.Express

Methods

expr :: () -> Expr #

Express Bool 
Instance details

Defined in Data.Express.Express

Methods

expr :: Bool -> Expr #

Express Char 
Instance details

Defined in Data.Express.Express

Methods

expr :: Char -> Expr #

Express Double 
Instance details

Defined in Data.Express.Express

Methods

expr :: Double -> Expr #

Express Float 
Instance details

Defined in Data.Express.Express

Methods

expr :: Float -> Expr #

Express Int 
Instance details

Defined in Data.Express.Express

Methods

expr :: Int -> Expr #

Express Word 
Instance details

Defined in Data.Express.Express

Methods

expr :: Word -> Expr #

(RealFloat a, Express a) => Express (Complex a) 
Instance details

Defined in Data.Express.Express

Methods

expr :: Complex a -> Expr #

(Integral a, Express a) => Express (Ratio a) 
Instance details

Defined in Data.Express.Express

Methods

expr :: Ratio a -> Expr #

Express a => Express (Maybe a) 
Instance details

Defined in Data.Express.Express

Methods

expr :: Maybe a -> Expr #

Express a => Express [a] 
Instance details

Defined in Data.Express.Express

Methods

expr :: [a] -> Expr #

(Express a, Express b) => Express (Either a b) 
Instance details

Defined in Data.Express.Express

Methods

expr :: Either a b -> Expr #

(Express a, Express b) => Express (a, b) 
Instance details

Defined in Data.Express.Express

Methods

expr :: (a, b) -> Expr #

(Express a, Express b, Express c) => Express (a, b, c) 
Instance details

Defined in Data.Express.Express

Methods

expr :: (a, b, c) -> Expr #

(Express a, Express b, Express c, Express d) => Express (a, b, c, d) 
Instance details

Defined in Data.Express.Express

Methods

expr :: (a, b, c, d) -> Expr #

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

Defined in Data.Express.Express

Methods

expr :: (a, b, c, d, e) -> Expr #

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

Defined in Data.Express.Express

Methods

expr :: (a, b, c, d, e, f) -> Expr #

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

Defined in Data.Express.Express

Methods

expr :: (a, b, c, d, e, f, g) -> Expr #

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

Defined in Data.Express.Express

Methods

expr :: (a, b, c, d, e, f, g, h) -> Expr #

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

Defined in Data.Express.Express

Methods

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

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

Defined in Data.Express.Express

Methods

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

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

Defined in Data.Express.Express

Methods

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

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

Defined in Data.Express.Express

Methods

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

deriveConjurable :: Name -> DecsQ Source #

Derives an Conjurable instance for the given type Name.

This function needs the TemplateHaskell extension.

If -:, ->:, ->>:, ->>>:, ... are not in scope, this will derive them as well.

For now, this function only derives conjureEquality, conjureTiers and conjureExpress and does not derive conjureSubTypes, conjureArgumentCases and conjureSize. These will be added in future versions. If you plan to use features that depend on these functionalities, please define your instances manually.

deriveConjurableIfNeeded :: Name -> DecsQ Source #

Same as deriveConjurable but does not warn when instance already exists (deriveConjurable is preferable).

For now, this function only derives conjureEquality, conjureTiers and conjureExpress and does not derive conjureSubTypes, conjureArgumentCases and conjureSize. These will be added in future versions. If you plan to use features that depend on these functionalities, please define your instances manually.

deriveConjurableCascading :: Name -> DecsQ Source #

Derives a Conjurable instance for a given type Name cascading derivation of type arguments as well.

For now, this function only derives conjureEquality, conjureTiers and conjureExpress and does not derive conjureSubTypes, conjureArgumentCases and conjureSize. These will be added in future versions. If you plan to use features that depend on these functionalities, please define your instances manually.

Pure interfaces

conjpure :: Conjurable f => String -> f -> [Prim] -> ([[Defn]], [[Defn]], [Expr], Thy) Source #

Like conjure but in the pure world.

Returns a quadruple with:

  1. tiers of implementations
  2. tiers of candidates
  3. a list of tests
  4. the underlying theory

conjpureWith :: Conjurable f => Args -> String -> f -> [Prim] -> ([[Defn]], [[Defn]], [Expr], Thy) Source #

Like conjpure but allows setting options through Args and args.

Helper test types

data A #

Generic type A.

Can be used to test polymorphic functions with a type variable such as take or sort:

take :: Int -> [a] -> [a]
sort :: Ord a => [a] -> [a]

by binding them to the following types:

take :: Int -> [A] -> [A]
sort :: [A] -> [A]

This type is homomorphic to Nat6, B, C, D, E and F.

It is instance to several typeclasses so that it can be used to test functions with type contexts.

Instances

Instances details
Bounded A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

minBound :: A #

maxBound :: A #

Enum A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

succ :: A -> A #

pred :: A -> A #

toEnum :: Int -> A #

fromEnum :: A -> Int #

enumFrom :: A -> [A] #

enumFromThen :: A -> A -> [A] #

enumFromTo :: A -> A -> [A] #

enumFromThenTo :: A -> A -> A -> [A] #

Ix A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

range :: (A, A) -> [A] #

index :: (A, A) -> A -> Int #

unsafeIndex :: (A, A) -> A -> Int #

inRange :: (A, A) -> A -> Bool #

rangeSize :: (A, A) -> Int #

unsafeRangeSize :: (A, A) -> Int #

Num A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

(+) :: A -> A -> A #

(-) :: A -> A -> A #

(*) :: A -> A -> A #

negate :: A -> A #

abs :: A -> A #

signum :: A -> A #

fromInteger :: Integer -> A #

Read A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Integral A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

quot :: A -> A -> A #

rem :: A -> A -> A #

div :: A -> A -> A #

mod :: A -> A -> A #

quotRem :: A -> A -> (A, A) #

divMod :: A -> A -> (A, A) #

toInteger :: A -> Integer #

Real A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

toRational :: A -> Rational #

Show A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

showsPrec :: Int -> A -> ShowS #

show :: A -> String #

showList :: [A] -> ShowS #

Conjurable A Source # 
Instance details

Defined in Conjure.Conjurable

Express A Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: A -> Expr #

Name A Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: A -> String #

Eq A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

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

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

Ord A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

compare :: A -> A -> Ordering #

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

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

(>) :: A -> A -> Bool #

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

max :: A -> A -> A #

min :: A -> A -> A #

Listable A 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

tiers :: [[A]] #

list :: [A] #

data B #

Generic type B.

Can be used to test polymorphic functions with two type variables such as map or foldr:

map :: (a -> b) -> [a] -> [b]
foldr :: (a -> b -> b) -> b -> [a] -> b

by binding them to the following types:

map :: (A -> B) -> [A] -> [B]
foldr :: (A -> B -> B) -> B -> [A] -> B

This type is homomorphic to A, Nat6, C, D, E and F.

Instances

Instances details
Bounded B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

minBound :: B #

maxBound :: B #

Enum B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

succ :: B -> B #

pred :: B -> B #

toEnum :: Int -> B #

fromEnum :: B -> Int #

enumFrom :: B -> [B] #

enumFromThen :: B -> B -> [B] #

enumFromTo :: B -> B -> [B] #

enumFromThenTo :: B -> B -> B -> [B] #

Ix B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

range :: (B, B) -> [B] #

index :: (B, B) -> B -> Int #

unsafeIndex :: (B, B) -> B -> Int #

inRange :: (B, B) -> B -> Bool #

rangeSize :: (B, B) -> Int #

unsafeRangeSize :: (B, B) -> Int #

Num B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

(+) :: B -> B -> B #

(-) :: B -> B -> B #

(*) :: B -> B -> B #

negate :: B -> B #

abs :: B -> B #

signum :: B -> B #

fromInteger :: Integer -> B #

Read B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Integral B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

quot :: B -> B -> B #

rem :: B -> B -> B #

div :: B -> B -> B #

mod :: B -> B -> B #

quotRem :: B -> B -> (B, B) #

divMod :: B -> B -> (B, B) #

toInteger :: B -> Integer #

Real B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

toRational :: B -> Rational #

Show B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

showsPrec :: Int -> B -> ShowS #

show :: B -> String #

showList :: [B] -> ShowS #

Conjurable B Source # 
Instance details

Defined in Conjure.Conjurable

Express B Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: B -> Expr #

Name B Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: B -> String #

Eq B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

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

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

Ord B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

compare :: B -> B -> Ordering #

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

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

(>) :: B -> B -> Bool #

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

max :: B -> B -> B #

min :: B -> B -> B #

Listable B 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

tiers :: [[B]] #

list :: [B] #

data C #

Generic type C.

Can be used to test polymorphic functions with three type variables such as uncurry or zipWith:

uncurry :: (a -> b -> c) -> (a, b) -> c
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

by binding them to the following types:

uncurry :: (A -> B -> C) -> (A, B) -> C
zipWith :: (A -> B -> C) -> [A] -> [B] -> [C]

This type is homomorphic to A, B, Nat6, D, E and F.

Instances

Instances details
Bounded C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

minBound :: C #

maxBound :: C #

Enum C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

succ :: C -> C #

pred :: C -> C #

toEnum :: Int -> C #

fromEnum :: C -> Int #

enumFrom :: C -> [C] #

enumFromThen :: C -> C -> [C] #

enumFromTo :: C -> C -> [C] #

enumFromThenTo :: C -> C -> C -> [C] #

Ix C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

range :: (C, C) -> [C] #

index :: (C, C) -> C -> Int #

unsafeIndex :: (C, C) -> C -> Int #

inRange :: (C, C) -> C -> Bool #

rangeSize :: (C, C) -> Int #

unsafeRangeSize :: (C, C) -> Int #

Num C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

(+) :: C -> C -> C #

(-) :: C -> C -> C #

(*) :: C -> C -> C #

negate :: C -> C #

abs :: C -> C #

signum :: C -> C #

fromInteger :: Integer -> C #

Read C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Integral C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

quot :: C -> C -> C #

rem :: C -> C -> C #

div :: C -> C -> C #

mod :: C -> C -> C #

quotRem :: C -> C -> (C, C) #

divMod :: C -> C -> (C, C) #

toInteger :: C -> Integer #

Real C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

toRational :: C -> Rational #

Show C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

showsPrec :: Int -> C -> ShowS #

show :: C -> String #

showList :: [C] -> ShowS #

Conjurable C Source # 
Instance details

Defined in Conjure.Conjurable

Express C Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: C -> Expr #

Name C Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: C -> String #

Eq C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

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

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

Ord C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

compare :: C -> C -> Ordering #

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

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

(>) :: C -> C -> Bool #

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

max :: C -> C -> C #

min :: C -> C -> C #

Listable C 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

tiers :: [[C]] #

list :: [C] #

data D #

Generic type D.

Can be used to test polymorphic functions with four type variables.

This type is homomorphic to A, B, C, Nat6, E and F.

Instances

Instances details
Bounded D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

minBound :: D #

maxBound :: D #

Enum D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

succ :: D -> D #

pred :: D -> D #

toEnum :: Int -> D #

fromEnum :: D -> Int #

enumFrom :: D -> [D] #

enumFromThen :: D -> D -> [D] #

enumFromTo :: D -> D -> [D] #

enumFromThenTo :: D -> D -> D -> [D] #

Ix D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

range :: (D, D) -> [D] #

index :: (D, D) -> D -> Int #

unsafeIndex :: (D, D) -> D -> Int #

inRange :: (D, D) -> D -> Bool #

rangeSize :: (D, D) -> Int #

unsafeRangeSize :: (D, D) -> Int #

Num D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

(+) :: D -> D -> D #

(-) :: D -> D -> D #

(*) :: D -> D -> D #

negate :: D -> D #

abs :: D -> D #

signum :: D -> D #

fromInteger :: Integer -> D #

Read D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Integral D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

quot :: D -> D -> D #

rem :: D -> D -> D #

div :: D -> D -> D #

mod :: D -> D -> D #

quotRem :: D -> D -> (D, D) #

divMod :: D -> D -> (D, D) #

toInteger :: D -> Integer #

Real D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

toRational :: D -> Rational #

Show D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

showsPrec :: Int -> D -> ShowS #

show :: D -> String #

showList :: [D] -> ShowS #

Conjurable D Source # 
Instance details

Defined in Conjure.Conjurable

Express D Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: D -> Expr #

Name D Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: D -> String #

Eq D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

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

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

Ord D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

compare :: D -> D -> Ordering #

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

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

(>) :: D -> D -> Bool #

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

max :: D -> D -> D #

min :: D -> D -> D #

Listable D 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

tiers :: [[D]] #

list :: [D] #

data E #

Generic type E.

Can be used to test polymorphic functions with five type variables.

This type is homomorphic to A, B, C, D, Nat6 and F.

Instances

Instances details
Bounded E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

minBound :: E #

maxBound :: E #

Enum E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

succ :: E -> E #

pred :: E -> E #

toEnum :: Int -> E #

fromEnum :: E -> Int #

enumFrom :: E -> [E] #

enumFromThen :: E -> E -> [E] #

enumFromTo :: E -> E -> [E] #

enumFromThenTo :: E -> E -> E -> [E] #

Ix E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

range :: (E, E) -> [E] #

index :: (E, E) -> E -> Int #

unsafeIndex :: (E, E) -> E -> Int #

inRange :: (E, E) -> E -> Bool #

rangeSize :: (E, E) -> Int #

unsafeRangeSize :: (E, E) -> Int #

Num E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

(+) :: E -> E -> E #

(-) :: E -> E -> E #

(*) :: E -> E -> E #

negate :: E -> E #

abs :: E -> E #

signum :: E -> E #

fromInteger :: Integer -> E #

Read E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Integral E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

quot :: E -> E -> E #

rem :: E -> E -> E #

div :: E -> E -> E #

mod :: E -> E -> E #

quotRem :: E -> E -> (E, E) #

divMod :: E -> E -> (E, E) #

toInteger :: E -> Integer #

Real E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

toRational :: E -> Rational #

Show E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

showsPrec :: Int -> E -> ShowS #

show :: E -> String #

showList :: [E] -> ShowS #

Conjurable E Source # 
Instance details

Defined in Conjure.Conjurable

Express E Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: E -> Expr #

Name E Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: E -> String #

Eq E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

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

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

Ord E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

compare :: E -> E -> Ordering #

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

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

(>) :: E -> E -> Bool #

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

max :: E -> E -> E #

min :: E -> E -> E #

Listable E 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

tiers :: [[E]] #

list :: [E] #

data F #

Generic type F.

Can be used to test polymorphic functions with five type variables.

This type is homomorphic to A, B, C, D, E and Nat6.

Instances

Instances details
Bounded F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

minBound :: F #

maxBound :: F #

Enum F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

succ :: F -> F #

pred :: F -> F #

toEnum :: Int -> F #

fromEnum :: F -> Int #

enumFrom :: F -> [F] #

enumFromThen :: F -> F -> [F] #

enumFromTo :: F -> F -> [F] #

enumFromThenTo :: F -> F -> F -> [F] #

Ix F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

range :: (F, F) -> [F] #

index :: (F, F) -> F -> Int #

unsafeIndex :: (F, F) -> F -> Int #

inRange :: (F, F) -> F -> Bool #

rangeSize :: (F, F) -> Int #

unsafeRangeSize :: (F, F) -> Int #

Num F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

(+) :: F -> F -> F #

(-) :: F -> F -> F #

(*) :: F -> F -> F #

negate :: F -> F #

abs :: F -> F #

signum :: F -> F #

fromInteger :: Integer -> F #

Read F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Integral F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

quot :: F -> F -> F #

rem :: F -> F -> F #

div :: F -> F -> F #

mod :: F -> F -> F #

quotRem :: F -> F -> (F, F) #

divMod :: F -> F -> (F, F) #

toInteger :: F -> Integer #

Real F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

toRational :: F -> Rational #

Show F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

showsPrec :: Int -> F -> ShowS #

show :: F -> String #

showList :: [F] -> ShowS #

Conjurable F Source # 
Instance details

Defined in Conjure.Conjurable

Express F Source # 
Instance details

Defined in Conjure.Expr

Methods

expr :: F -> Expr #

Name F Source # 
Instance details

Defined in Conjure.Conjurable

Methods

name :: F -> String #

Eq F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

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

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

Ord F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

compare :: F -> F -> Ordering #

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

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

(>) :: F -> F -> Bool #

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

max :: F -> F -> F #

min :: F -> F -> F #

Listable F 
Instance details

Defined in Test.LeanCheck.Utils.Types

Methods

tiers :: [[F]] #

list :: [F] #