| Copyright | (c) 2021-2025 Rudy Matela |
|---|---|
| License | 3-Clause BSD (see the file LICENSE) |
| Maintainer | Rudy Matela <rudy@matela.com.br> |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Conjure
Description
A library for Conjuring function implementations from tests or partial definitions. (a.k.a.: functional inductive programming)
Step 1: declare your partial function
factorial :: Int -> Int factorial 2 = 2 factorial 3 = 6 factorial 4 = 24
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) , prim "-" ((-) :: Int -> Int -> Int) ]
Step 3: call conjure and see your generated function:
> conjure "factorial" factorial primitives factorial :: Int -> Int -- testing 3 combinations of argument values -- pruning with 27/65 rules -- looking through 3 candidates of size 1 -- looking through 3 candidates of size 2 -- looking through 9 candidates of size 3 -- looking through 10 candidates of size 4 -- looking through 32 candidates of size 5 -- looking through 39 candidates of size 6 -- looking through 185 candidates of size 7 -- tested 107 candidates factorial 0 = 1 factorial x = x * factorial (x - 1)
The above example takes less than a second to run in a modern laptop.
Factorial is discovered from scratch through a search. We prune the search space using properties discovered from the results of testing.
Conjure is not limited to integers, it works for functions over algebraic data types too. See:
take' :: Int -> [a] -> [a] take' 0 [x] = [] take' 1 [x] = [x] take' 0 [x,y] = [] take' 1 [x,y] = [x] take' 2 [x,y] = [x,y] take' 3 [x,y] = [x,y]
> conjure "take" (take' :: Int -> [A] -> [A]) > [ pr (0 :: Int) > , pr (1 :: Int) > , pr ([] :: [A]) > , prim ":" ((:) :: A -> [A] -> [A]) > , prim "-" ((-) :: Int -> Int -> Int) > ] take :: Int -> [A] -> [A] -- testing 153 combinations of argument values -- pruning with 4/7 rules -- ... ... ... -- looking through 58 candidates of size 9 -- tested 104 candidates take 0 xs = [] take x [] = [] take x (y:xs) = y:take (x - 1) xs
The above example also takes less than a second to run in a modern laptop. The selection of functions in the list of primitives was minimized to what was absolutely needed here. With a larger collection as primitives YMMV.
Conjure works for user-defined algebraic data types too,
given that they are made instances of the Conjurable typeclass.
For types without data invariants,
it should be enough to call deriveConjurable
to create an instance using TH.
Synopsis
- conjure :: Conjurable f => String -> f -> [Prim] -> IO ()
- type Prim = (Expr, Reification)
- pr :: (Conjurable a, Show a) => a -> Prim
- prim :: Conjurable a => String -> a -> Prim
- prif :: Conjurable a => a -> Prim
- primOrdCaseFor :: Conjurable a => a -> Prim
- conjureWithMaxSize :: Conjurable f => Int -> String -> f -> [Prim] -> IO ()
- conjureWith :: Conjurable f => Args -> String -> f -> [Prim] -> IO ()
- data Args = Args {
- maxTests :: Int
- maxSize :: Int
- maxEvalRecursions :: Int
- maxEquationSize :: Int
- maxSearchTests :: Int
- maxDeconstructionSize :: Int
- maxConstantSize :: Int
- carryOn :: Bool
- showTheory :: Bool
- usePatterns :: Bool
- showCandidates :: Bool
- showTests :: Bool
- showPatterns :: Bool
- showDeconstructions :: Bool
- rewriting :: Bool
- requireDescent :: Bool
- adHocRedundancy :: Bool
- copyBindings :: Bool
- atomicNumbers :: Bool
- requireZero :: Bool
- uniqueCandidates :: Bool
- args :: Args
- conjureFromSpec :: Conjurable f => String -> (f -> Bool) -> [Prim] -> IO ()
- conjureFromSpecWith :: Conjurable f => Args -> String -> (f -> Bool) -> [Prim] -> IO ()
- class (Typeable a, Name a) => Conjurable a where
- conjureEquality :: a -> Maybe Expr
- conjureTiers :: a -> Maybe [[Expr]]
- conjureSubTypes :: a -> Reification
- conjureCases :: a -> [Expr]
- conjureSize :: a -> Int
- conjureExpress :: a -> Expr -> Expr
- data Expr
- val :: (Typeable a, Show a) => a -> Expr
- value :: Typeable a => String -> a -> Expr
- reifyExpress :: (Express a, Show a) => a -> Expr -> Expr
- reifyEquality :: (Eq a, Typeable a) => a -> Maybe Expr
- reifyTiers :: (Listable a, Show a, Typeable a) => a -> Maybe [[Expr]]
- conjureType :: Conjurable a => a -> Reification
- class Name a where
- class (Show a, Typeable a) => Express a where
- deriveConjurable :: Name -> DecsQ
- deriveConjurableIfNeeded :: Name -> DecsQ
- deriveConjurableCascading :: Name -> DecsQ
- data Results = Results {
- implementationss :: [[Defn]]
- candidatess :: [[Defn]]
- bindings :: [Expr]
- theory :: Thy
- patternss :: [[Defn]]
- deconstructions :: [Expr]
- conjpure :: Conjurable f => String -> f -> [Prim] -> Results
- conjpureWith :: Conjurable f => Args -> String -> f -> [Prim] -> Results
- data A
- data B
- data C
- data D
- data E
- data F
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:
factorial :: Int -> Int factorial 2 = 2 factorial 3 = 6 factorial 4 = 24 primitives :: [Prim] primitives = [ pr (0::Int) , pr (1::Int) , prim "+" ((+) :: Int -> Int -> Int) , prim "*" ((*) :: Int -> Int -> Int) , prim "-" ((-) :: Int -> Int -> Int) ]
The conjure function does the following:
> conjure "factorial" factorial primitives factorial :: Int -> Int -- testing 3 combinations of argument values -- pruning with 27/65 rules -- ... ... ... -- looking through 185 candidates of size 7 -- tested 107 candidates factorial 0 = 1 factorial x = x * factorial (x - 1)
type Prim = (Expr, Reification) Source #
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)
conjure "fun" fun [ ...
, prim "&&" (&&)
, prim "||" (||)
, prim "+" ((+) :: Int -> Int -> Int)
, prim "*" ((*) :: Int -> Int -> Int)
, prim "-" ((-) :: Int -> Int -> Int)
, ...
]Argument types have to be monomorphized, so use type bindings when applicable.
prif :: Conjurable a => a -> Prim Source #
Provides an if condition bound to the given return type.
This should be used when one wants Conjure to consider if-expressions at all:
last' :: [Int] -> Int last' [x] = x last' [x,y] = y last' [x,y,z] = z
> conjure "last" last' [ pr ([] :: [Int])
> , prim ":" ((:) :: Int -> [Int] -> [Int])
> , prim "null" (null :: [Int] -> Bool)
> , prif (undefined :: Int)
> , prim "undefined" (undefined :: Int)
> ]
last :: [Int] -> Int
-- ... ... ...
-- looking through 4 candidates of size 7
-- tested 5 candidates
last [] = undefined
last (x:xs) = if null xs
then x
else last xsprimOrdCaseFor :: Conjurable a => a -> Prim Source #
Provides a case condition bound to the given return type.
This should be used when one wants Conjure to consider ord-case expressions:
> conjure "mem" mem
> [ pr False
> , pr True
> , prim "`compare`" (compare :: Int -> Int -> Ordering)
> , primOrdCaseFor (undefined :: Bool)
> ]
mem :: Int -> Tree -> Bool
-- ... ... ...
-- looking through 384 candidates of size 12
-- tested 371 candidates
mem x Leaf = False
mem x (Node t1 y t2) = case x `compare` y of
LT -> mem x t1
EQ -> True
GT -> mem x t2Advanced 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 18 "function" function [...]
For example, given the following partial definition for insert:
insert' :: Int -> [Int] -> [Int] insert' 0 [] = [0] insert' 0 [1,2] = [0,1,2] insert' 1 [0,2] = [0,1,2] insert' 2 [0,1] = [0,1,2]
Conjure is able to find an appropriate definition at size 17 with the following primitives:
> conjureWithMaxSize 18 "insert" insert'
> [ prim "[]" ([] :: [Int])
> , prim ":" ((:) :: Int -> [Int] -> [Int])
> , prim "<=" ((<=) :: Int -> Int -> Bool)
> , prif (undefined :: [Int])
> ]
insert :: Int -> [Int] -> [Int]
-- testing 4 combinations of argument values
-- pruning with 4/4 rules
-- ... ... ...
-- looking through 14550 candidates of size 17
-- tested 14943 candidates
insert x [] = [x]
insert x (y:xs) = if x <= y
then x:insert y xs
else y:insert x xsThe default maximum size of 12 would not be enough for the above definition.
conjureWith :: Conjurable f => Args -> String -> f -> [Prim] -> IO () Source #
Arguments to be passed to conjureWith or conjpureWith.
See args for the defaults.
Constructors
| Args | |
Fields
| |
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 show tested candidates
- do not make candidates unique module testing
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 == 4Then:
> 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 = 18} "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 ...) = xAbove 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.
Conjurable instances can be derived automatically using
deriveConjurable.
(cf. reifyTiers, reifyEquality, conjureType)
Minimal complete definition
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
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 areShowinstances;value, for values that are notShowinstances, like functions;:$, for applications betweenExprs.
> val False False :: Bool
> value "not" not :$ 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
(:$, var).
The var underscore convention:
Functions that manipulate Exprs usually follow the convention
where a value whose String representation starts with '_'
represents a variable.
Instances
| Show Expr | Shows > show (value "not" not :$ val False) "not False :: Bool" |
| 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. |
| 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 ( |
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]
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)
...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
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
| Name Int16 | |
Defined in Data.Express.Name | |
| Name Int32 | |
Defined in Data.Express.Name | |
| Name Int64 | |
Defined in Data.Express.Name | |
| Name Int8 | |
Defined in Data.Express.Name | |
| Name GeneralCategory | |
Defined in Data.Express.Name Methods name :: GeneralCategory -> String # | |
| Name Word16 | |
Defined in Data.Express.Name | |
| Name Word32 | |
Defined in Data.Express.Name | |
| Name Word64 | |
Defined in Data.Express.Name | |
| Name Word8 | |
Defined in Data.Express.Name | |
| Name Ordering | name (undefined :: Ordering) = "o" names (undefined :: Ordering) = ["o", "p", "q", "o'", ...] |
Defined in Data.Express.Name | |
| Name A Source # | |
Defined in Conjure.Conjurable | |
| Name B Source # | |
Defined in Conjure.Conjurable | |
| Name C Source # | |
Defined in Conjure.Conjurable | |
| Name D Source # | |
Defined in Conjure.Conjurable | |
| Name E Source # | |
Defined in Conjure.Conjurable | |
| Name F Source # | |
Defined in Conjure.Conjurable | |
| Name Integer | name (undefined :: Integer) = "x" names (undefined :: Integer) = ["x", "y", "z", "x'", ...] |
Defined in Data.Express.Name | |
| Name () | name (undefined :: ()) = "u" names (undefined :: ()) = ["u", "v", "w", "u'", "v'", ...] |
Defined in Data.Express.Name | |
| Name Bool | name (undefined :: Bool) = "p" names (undefined :: Bool) = ["p", "q", "r", "p'", "q'", ...] |
Defined in Data.Express.Name | |
| Name Char | name (undefined :: Char) = "c" names (undefined :: Char) = ["c", "d", "e", "c'", "d'", ...] |
Defined in Data.Express.Name | |
| Name Double | name (undefined :: Double) = "x" names (undefined :: Double) = ["x", "y", "z", "x'", ...] |
Defined in Data.Express.Name | |
| Name Float | name (undefined :: Float) = "x" names (undefined :: Float) = ["x", "y", "z", "x'", ...] |
Defined in Data.Express.Name | |
| Name Int | name (undefined :: Int) = "x" names (undefined :: Int) = ["x", "y", "z", "x'", "y'", ...] |
Defined in Data.Express.Name | |
| Name Word | |
Defined in Data.Express.Name | |
| Name (Complex a) | name (undefined :: Complex) = "x" names (undefined :: Complex) = ["x", "y", "z", "x'", ...] |
Defined in Data.Express.Name | |
| Name (Ratio a) | name (undefined :: Rational) = "q" names (undefined :: Rational) = ["q", "r", "s", "q'", ...] |
Defined in Data.Express.Name | |
| Name a => Name (Maybe a) | names (undefined :: Maybe Int) = ["mx", "mx1", "mx2", ...] nemes (undefined :: Maybe Bool) = ["mp", "mp1", "mp2", ...] |
Defined in Data.Express.Name | |
| Name a => Name [a] | names (undefined :: [Int]) = ["xs", "ys", "zs", "xs'", ...] names (undefined :: [Bool]) = ["ps", "qs", "rs", "ps'", ...] |
Defined in Data.Express.Name | |
| (Name a, Name b) => Name (Either a b) | names (undefined :: Either Int Int) = ["exy", "exy1", ...] names (undefined :: Either Int Bool) = ["exp", "exp1", ...] |
Defined in Data.Express.Name | |
| (Name a, Name b) => Name (a, b) | names (undefined :: (Int,Int)) = ["xy", "zw", "xy'", ...] names (undefined :: (Bool,Bool)) = ["pq", "rs", "pq'", ...] |
Defined in Data.Express.Name | |
| Name (a -> b) | names (undefined :: ()->()) = ["f", "g", "h", "f'", ...] names (undefined :: Int->Int) = ["f", "g", "h", ...] |
Defined in Data.Express.Name | |
| (Name a, Name b, Name c) => Name (a, b, c) | names (undefined :: (Int,Int,Int)) = ["xyz","uvw", ...] names (undefined :: (Int,Bool,Char)) = ["xpc", "xpc1", ...] |
Defined in Data.Express.Name | |
| (Name a, Name b, Name c, Name d) => Name (a, b, c, d) | names (undefined :: ((),(),(),())) = ["uuuu", "uuuu1", ...] names (undefined :: (Int,Int,Int,Int)) = ["xxxx", ...] |
Defined in Data.Express.Name | |
| (Name a, Name b, Name c, Name d, Name e) => Name (a, b, c, d, e) | |
Defined in Data.Express.Name | |
| (Name a, Name b, Name c, Name d, Name e, Name f) => Name (a, b, c, d, e, f) | |
Defined in Data.Express.Name | |
| (Name a, Name b, Name c, Name d, Name e, Name f, Name g) => Name (a, b, c, d, e, f, g) | |
Defined in Data.Express.Name | |
| (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) | |
Defined in Data.Express.Name | |
| (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) | |
Defined in Data.Express.Name | |
| (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) | |
Defined in Data.Express.Name | |
| (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) | |
Defined in Data.Express.Name | |
| (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) | |
Defined in Data.Express.Name | |
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:
valalways encodes values as atomicValueExprs -- shallow encoding.exprideally encodes expressions as applications (:$) betweenValueExprs -- deep encoding.
Depending on the situation, one or the other may be desirable.
Instances can be automatically derived using the TH function
deriveExpress.
The following example shows a datatype and its instance:
data Stack a = Stack a (Stack a) | Empty
instance Express a => Express (Stack a) where expr s@(Stack x y) = value "Stack" (Stack ->>: s) :$ 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
Instances
deriveConjurable :: Name -> DecsQ Source #
Derives an Conjurable instance for the given type Name.
This function needs the TemplateHaskell extension.
If the Data.Express' type binding operators
(-:,
->: or
->>:)
are not in scope,
this derives them as well.
deriveConjurableIfNeeded :: Name -> DecsQ Source #
Same as deriveConjurable but does not warn when instance already exists
(deriveConjurable is preferable).
deriveConjurableCascading :: Name -> DecsQ Source #
Derives a Conjurable instance for a given type Name
cascading derivation of type arguments as well.
Pure interfaces
Results to the conjpure family of functions.
This is for advanced users.
One is probably better-off using the conjure family.
Constructors
| Results | |
Fields
| |
conjpure :: Conjurable f => String -> f -> [Prim] -> Results Source #
Like conjure but in the pure world.
The most important part of the result are the tiers of implementations however results also include candidates, tests and the underlying theory.
conjpureWith :: Conjurable f => Args -> String -> f -> [Prim] -> Results Source #
Helper test types
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
| Bounded A | |
| Enum A | |
| Ix A | |
| Num A | |
| Read A | |
| Integral A | |
| Real A | |
Defined in Test.LeanCheck.Utils.Types Methods toRational :: A -> Rational # | |
| Show A | |
| Conjurable A Source # | |
Defined in Conjure.Conjurable Methods conjureArgumentHoles :: A -> [Expr] Source # conjureEquality :: A -> Maybe Expr Source # conjureTiers :: A -> Maybe [[Expr]] Source # conjureSubTypes :: A -> Reification Source # conjureIf :: A -> Expr Source # conjureCases :: A -> [Expr] Source # conjureArgumentCases :: A -> [[Expr]] Source # conjureSize :: A -> Int Source # conjureExpress :: A -> Expr -> Expr Source # conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe A Source # | |
| Express A Source # | |
Defined in Conjure.Expr | |
| Name A Source # | |
Defined in Conjure.Conjurable | |
| Eq A | |
| Ord A | |
| Listable A | |
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
Instances
| Bounded B | |
| Enum B | |
| Ix B | |
| Num B | |
| Read B | |
| Integral B | |
| Real B | |
Defined in Test.LeanCheck.Utils.Types Methods toRational :: B -> Rational # | |
| Show B | |
| Conjurable B Source # | |
Defined in Conjure.Conjurable Methods conjureArgumentHoles :: B -> [Expr] Source # conjureEquality :: B -> Maybe Expr Source # conjureTiers :: B -> Maybe [[Expr]] Source # conjureSubTypes :: B -> Reification Source # conjureIf :: B -> Expr Source # conjureCases :: B -> [Expr] Source # conjureArgumentCases :: B -> [[Expr]] Source # conjureSize :: B -> Int Source # conjureExpress :: B -> Expr -> Expr Source # conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe B Source # | |
| Express B Source # | |
Defined in Conjure.Expr | |
| Name B Source # | |
Defined in Conjure.Conjurable | |
| Eq B | |
| Ord B | |
| Listable B | |
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]
Instances
| Bounded C | |
| Enum C | |
| Ix C | |
| Num C | |
| Read C | |
| Integral C | |
| Real C | |
Defined in Test.LeanCheck.Utils.Types Methods toRational :: C -> Rational # | |
| Show C | |
| Conjurable C Source # | |
Defined in Conjure.Conjurable Methods conjureArgumentHoles :: C -> [Expr] Source # conjureEquality :: C -> Maybe Expr Source # conjureTiers :: C -> Maybe [[Expr]] Source # conjureSubTypes :: C -> Reification Source # conjureIf :: C -> Expr Source # conjureCases :: C -> [Expr] Source # conjureArgumentCases :: C -> [[Expr]] Source # conjureSize :: C -> Int Source # conjureExpress :: C -> Expr -> Expr Source # conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe C Source # | |
| Express C Source # | |
Defined in Conjure.Expr | |
| Name C Source # | |
Defined in Conjure.Conjurable | |
| Eq C | |
| Ord C | |
| Listable C | |
Generic type D.
Can be used to test polymorphic functions with four type variables.
Instances
| Bounded D | |
| Enum D | |
| Ix D | |
| Num D | |
| Read D | |
| Integral D | |
| Real D | |
Defined in Test.LeanCheck.Utils.Types Methods toRational :: D -> Rational # | |
| Show D | |
| Conjurable D Source # | |
Defined in Conjure.Conjurable Methods conjureArgumentHoles :: D -> [Expr] Source # conjureEquality :: D -> Maybe Expr Source # conjureTiers :: D -> Maybe [[Expr]] Source # conjureSubTypes :: D -> Reification Source # conjureIf :: D -> Expr Source # conjureCases :: D -> [Expr] Source # conjureArgumentCases :: D -> [[Expr]] Source # conjureSize :: D -> Int Source # conjureExpress :: D -> Expr -> Expr Source # conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe D Source # | |
| Express D Source # | |
Defined in Conjure.Expr | |
| Name D Source # | |
Defined in Conjure.Conjurable | |
| Eq D | |
| Ord D | |
| Listable D | |
Generic type E.
Can be used to test polymorphic functions with five type variables.
Instances
| Bounded E | |
| Enum E | |
| Ix E | |
| Num E | |
| Read E | |
| Integral E | |
| Real E | |
Defined in Test.LeanCheck.Utils.Types Methods toRational :: E -> Rational # | |
| Show E | |
| Conjurable E Source # | |
Defined in Conjure.Conjurable Methods conjureArgumentHoles :: E -> [Expr] Source # conjureEquality :: E -> Maybe Expr Source # conjureTiers :: E -> Maybe [[Expr]] Source # conjureSubTypes :: E -> Reification Source # conjureIf :: E -> Expr Source # conjureCases :: E -> [Expr] Source # conjureArgumentCases :: E -> [[Expr]] Source # conjureSize :: E -> Int Source # conjureExpress :: E -> Expr -> Expr Source # conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe E Source # | |
| Express E Source # | |
Defined in Conjure.Expr | |
| Name E Source # | |
Defined in Conjure.Conjurable | |
| Eq E | |
| Ord E | |
| Listable E | |
Generic type F.
Can be used to test polymorphic functions with five type variables.
Instances
| Bounded F | |
| Enum F | |
| Ix F | |
| Num F | |
| Read F | |
| Integral F | |
| Real F | |
Defined in Test.LeanCheck.Utils.Types Methods toRational :: F -> Rational # | |
| Show F | |
| Conjurable F Source # | |
Defined in Conjure.Conjurable Methods conjureArgumentHoles :: F -> [Expr] Source # conjureEquality :: F -> Maybe Expr Source # conjureTiers :: F -> Maybe [[Expr]] Source # conjureSubTypes :: F -> Reification Source # conjureIf :: F -> Expr Source # conjureCases :: F -> [Expr] Source # conjureArgumentCases :: F -> [[Expr]] Source # conjureSize :: F -> Int Source # conjureExpress :: F -> Expr -> Expr Source # conjureEvaluate :: (Expr -> Expr) -> Int -> Defn -> Expr -> Maybe F Source # | |
| Express F Source # | |
Defined in Conjure.Expr | |
| Name F Source # | |
Defined in Conjure.Conjurable | |
| Eq F | |
| Ord F | |
| Listable F | |