code-conjure-0.0.2: conjure Haskell functions out of partial definitions
Copyright(c) 2021 Rudy Matela
License3-Clause BSD (see the file LICENSE)
MaintainerRudy Matela <rudy@matela.com.br>
Safe HaskellNone
LanguageHaskell2010

Conjure.Engine

Description

An internal module of Conjure, a library for Conjuring function implementations from tests or partial definitions. (a.k.a.: functional inductive programming)

Synopsis

Documentation

sixtuple :: Expr -> Expr -> Expr -> Expr -> Expr -> Expr -> Expr #

quintuple :: Expr -> Expr -> Expr -> Expr -> Expr -> Expr #

quadruple :: Expr -> Expr -> Expr -> Expr -> Expr #

triple :: Expr -> Expr -> Expr -> Expr #

pair :: Expr -> Expr -> Expr #

(-|-) :: Expr -> Expr -> Expr #

just :: Expr -> Expr #

if' :: Expr -> Expr -> Expr -> Expr #

A virtual function if :: Bool -> a -> a -> a lifted over the Expr type. This is displayed as an if-then-else.

> if' pp zero xx
(if p then 0 else x) :: Int
> zz -*- if' pp xx yy
z * (if p then x else y) :: Int
> if' pp false true -||- if' qq true false
(if p then False else True) || (if q then True else False) :: Bool
> evl $ if' true (val 't') (val 'f') :: Char
't'

(-<-) :: Expr -> Expr -> Expr infix 4 #

(-<=-) :: Expr -> Expr -> Expr infix 4 #

(-/=-) :: Expr -> Expr -> Expr infix 4 #

(-$-) :: Expr -> Expr -> Expr infixl 6 #

elem' :: Expr -> Expr -> Expr #

length' :: Expr -> Expr #

List length lifted over the Expr type. Works for the element types Int, Char and Bool.

> length' $ unit one
length [1] :: Int
> length' $ unit bee
length "b" :: Int
> length' $ zero -:- unit two
length [0,2] :: Int
> evl $ length' $ unit one :: Int
1

null' :: Expr -> Expr #

List null lifted over the Expr type. Works for the element types Int, Char and Bool.

> null' $ unit one
null [1] :: Bool
> null' $ nil
null [] :: Bool
> evl $ null' nil :: Bool
True

tail' :: Expr -> Expr #

List tail lifted over the Expr type. Works for the element types Int, Char and Bool.

> tail' $ unit one
tail [1] :: [Int]
> tail' $ unit bee
tail "b" :: [Char]
> tail' $ zero -:- unit two
tail [0,2] :: [Int]
> evl $ tail' $ zero -:- unit two :: [Int]
[2]

head' :: Expr -> Expr #

List head lifted over the Expr type. Works for the element types Int, Char and Bool.

> head' $ unit one
head [1] :: Int
> head' $ unit bee
head "b" :: Char
> head' $ zero -:- unit two
head [0,2] :: Int
> evl $ head' $ unit one :: Int
1

(-++-) :: Expr -> Expr -> Expr infixr 5 #

List concatenation lifted over the Expr type. Works for the element types Int, Char and Bool.

> (zero -:- one -:- nil) -:- (two -:- three -:- nil)
[0,1] -++- [2,3] :: [Int]
> (bee -:- unit cee) -:- unit dee
"bc" -++- "c" :: [Char]

(-:-) :: Expr -> Expr -> Expr infixr 5 #

The list constructor lifted over the Expr type. Works for the element types Int, Char and Bool.

> zero -:- one -:- unit two
[0,1,2] :: [Int]
> zero -:- one -:- two -:- nil
[0,1,2] :: [Int]
> bee -:- unit cee
"bc" :: [Char]

unit :: Expr -> Expr #

unit constructs a list with a single element. This works for elements of type Int, Char and Bool.

> unit one
[1]
> unit false
[False]

consChar :: Expr #

The list constructor : encoded as an Expr.

consBool :: Expr #

The list constructor : encoded as an Expr.

consInt :: Expr #

The list constructor : encoded as an Expr.

cons :: Expr #

The list constructor with Int as element type encoded as an Expr.

> cons
(:) :: Int -> [Int] -> [Int]
> cons :$ one :$ nil
[1] :: [Int]

Consider using -:- and unit when building lists of Expr.

nilChar :: Expr #

The empty list '[]' encoded as an Expr.

nilBool :: Expr #

The empty list '[]' encoded as an Expr.

nilInt :: Expr #

The empty list '[]' encoded as an Expr.

emptyString :: Expr #

An empty String encoded as an Expr.

> emptyString
"" :: String

nil :: Expr #

An empty list of type [Int] encoded as an Expr.

> nil
[] :: [Int]

yys :: Expr #

A variable named ys of type [Int] encoded as an Expr.

> yys
ys :: [Int]

xxs :: Expr #

A variable named xs of type [Int] encoded as an Expr.

> xxs
xs :: [Int]

is_ :: Expr #

A typed hole of [Int] type encoded as an Expr.

> is_
_ :: [Int]

ord' :: Expr -> Expr #

dee :: Expr #

The character 'd' encoded as an Expr

> dee
'd' :: Char
> evl dee :: Char
'd'

cee :: Expr #

The character 'c' encoded as an Expr

> cee
'c' :: Char
> evl cee :: Char
'c'

bee :: Expr #

The character 'b' encoded as an Expr

> bee
'b' :: Char
> evl bee :: Char
'b'

ae :: Expr #

dd :: Expr #

cc :: Expr #

c_ :: Expr #

A hole of Char type encoded as an Expr.

> c_
_ :: Char

odd' :: Expr -> Expr #

absE :: Expr #

abs over the Int type encoded as an Expr.

> absE
abs :: Int -> Int

abs' :: Expr -> Expr #

abs over the Int type lifted over the Expr type.

> abs' xx'
abs x' :: Int
> evl (abs' minusTwo) :: Int
2

negateE :: Expr #

negate over the Int type encoded as an Expr

> negateE
negate :: Int -> Int

negate' :: Expr -> Expr #

negate over the Int type lifted over the Expr type.

> negate' xx
negate x :: Int
> evl (negate' one) :: Int
-1

const' :: Expr -> Expr -> Expr #

idString :: Expr #

The function id encoded as an Expr. (cf. id')

idBools :: Expr #

The function id encoded as an Expr. (cf. id')

idInts :: Expr #

The function id encoded as an Expr. (cf. id')

idChar :: Expr #

The function id encoded as an Expr. (cf. id')

idBool :: Expr #

The function id encoded as an Expr. (cf. id')

idInt :: Expr #

The function id encoded as an Expr. (cf. id')

idE :: Expr #

The function id for the Int type encoded as an Expr. (See also id'.)

> idE :$ xx
id x :: Int
> idE :$ zero
id 0 :: Int
> evaluate $ idE :$ zero :: Maybe Int
Just 0

id' :: Expr -> Expr #

Constructs an application of id as an Expr. Only works for Int, Bool, Char, String, [Int], [Bool].

> id' yy
id yy :: Int
> id' one
id 1 :: Int
> evl (id' one) :: Int
1
> id' pp
id p :: Bool
> id' false
id' False :: Bool
> evl (id' true) :: Bool
True :: Bool

times :: Expr #

The operator * for the Int type. (See also -*-.)

> times
(*) :: Int -> Int -> Int
> times :$ two
(2 *) :: Int -> Int
> times :$ xx :$ yy
x * y :: Int

(-*-) :: Expr -> Expr -> Expr infixl 7 #

The operator * for the Int type lifted over the Expr type. (See also times.)

> three -*- three
9 :: Int
> one -*- two -*- three
(1 * 2) * 3 :: Int
> two -*- xx
2 * x :: Int

plus :: Expr #

The operator + for the Int type. (See also -+-.)

> plus
(+) :: Int -> Int -> Int
> plus :$ one
(1 +) :: Int -> Int
> plus :$ xx :$ yy
x + y :: Int

(-+-) :: Expr -> Expr -> Expr infixl 6 #

The operator + for the Int type for use on Exprs. (See also plus.)

> two -+- three
2 + 3 :: Int
> minusOne -+- minusTwo -+- zero
((-1) + (-2)) + 0 :: Int
> xx -+- (yy -+- zz)
x + (y + z) :: Int

ggE :: Expr #

A variable g of 'Int -> Int' type encoded as an Expr.

> ggE
g :: Int -> Int

(-?-) :: Expr -> Expr -> Expr #

A variable binary operator ? lifted over the Expr type. Works for Int, Bool, Char, [Int] and String.

> xx -?- yy
x ? y :: Int
> pp -?- qq
p ? q :: Bool
> xx -?- qq
*** Exception: (-?-): cannot apply `(?) :: * -> * -> *` to `x :: Int' and `q :: Bool'.  Unhandled types?

gg :: Expr -> Expr #

A variable function g of 'Int -> Int' type lifted over the Expr type.

> gg yy
g y :: Int
> gg minusTwo
gg (-2) :: Int

ffE :: Expr #

A variable f of 'Int -> Int' type encoded as an Expr.

> ffE
f :: Int -> Int

ff :: Expr -> Expr #

A variable function f of 'Int -> Int' type lifted over the Expr type.

> ff xx
f x :: Int
> ff one
f 1 :: Int

minusTwo :: Expr #

The value -2 bound to the Int type encoded as an Expr.

> minusOne
-2 :: Int

minusOne :: Expr #

The value -1 bound to the Int type encoded as an Expr.

> minusOne
-1 :: Int

three :: Expr #

The value 3 bound to the Int type encoded as an Expr.

> three
3 :: Int

two :: Expr #

The value 2 bound to the Int type encoded as an Expr.

> two
2 :: Int

one :: Expr #

The value 1 bound to the Int type encoded as an Expr.

> one
1 :: Int

zero :: Expr #

The value 0 bound to the Int type encoded as an Expr.

> zero
0 :: Int

kk :: Expr #

jj :: Expr #

ii :: Expr #

xx' :: Expr #

A variable x' of Int type.

> xx'
x' :: Int

zz :: Expr #

A variable z of Int type.

> zz
z :: Int

yy :: Expr #

A variable y of Int type.

> yy
y :: Int

xx :: Expr #

A variable x of Int type.

> xx
x :: Int

i_ :: Expr #

A typed hole of Int type.

> i_
_ :: Int

(-||-) :: Expr -> Expr -> Expr infixr 2 #

The function || lifted over the Expr type.

> pp -||- qq
p || q :: Bool
> false -||- true
False || True :: Bool
> evalBool $ false -||- true
True

(-&&-) :: Expr -> Expr -> Expr infixr 3 #

The function && lifted over the Expr type.

> pp -&&- qq
p && q :: Bool
> false -&&- true
False && True :: Bool
> evalBool $ false -&&- true
False

not' :: Expr -> Expr #

The function not lifted over the Expr type.

> not' false
not False :: Bool
> evalBool $ not' false
True
> not' pp
not p :: Bool

(-==>-) :: Expr -> Expr -> Expr infixr 0 #

orE :: Expr #

The function or encoded as an Expr.

> orE
(||) :: Bool -> Bool -> Bool

andE :: Expr #

The function and encoded as an Expr.

> andE
(&&) :: Bool -> Bool -> Bool

notE :: Expr #

The function not encoded as an Expr.

> notE
not :: Bool -> Bool

true :: Expr #

True encoded as an Expr.

> true
True :: Bool

false :: Expr #

False encoded as an Expr.

> false
False :: Bool

pp' :: Expr #

Expr representing a variable p' :: Bool.

> pp'
p' :: Bool

rr :: Expr #

Expr representing a variable r :: Bool.

> rr
r :: Bool

qq :: Expr #

Expr representing a variable q :: Bool.

> qq
q :: Bool

pp :: Expr #

Expr representing a variable p :: Bool.

> pp
p :: Bool

b_ :: Expr #

Expr representing a hole of Bool type.

> b_
_ :: Bool

fastMostSpecificVariation :: Expr -> Expr #

A faster version of mostSpecificCanonicalVariation that disregards name clashes across different types. Consider using mostSpecificCanonicalVariation instead.

The same caveats of fastCanonicalVariations do apply here.

fastMostGeneralVariation :: Expr -> Expr #

A faster version of mostGeneralCanonicalVariation that disregards name clashes across different types. Consider using mostGeneralCanonicalVariation instead.

The same caveats of fastCanonicalVariations do apply here.

fastCanonicalVariations :: Expr -> [Expr] #

A faster version of canonicalVariations that disregards name clashes across different types. Results are confusing to the user but fine for Express which differentiates between variables with the same name but different types.

Without applying canonicalize, the following Expr may seem to have only one variable:

> fastCanonicalVariations $ i_ -+- ord' c_
[x + ord x :: Int]

Where in fact it has two, as the second x has a different type. Applying canonicalize disambiguates:

> map canonicalize . fastCanonicalVariations $ i_ -+- ord' c_
[x + ord c :: Int]

This function is useful when resulting Exprs are not intended to be presented to the user but instead to be used by another function. It is simply faster to skip the step where clashes are resolved.

mostSpecificCanonicalVariation :: Expr -> Expr #

Returns the most specific canonical variation of an Expr by filling holes with variables.

> mostSpecificCanonicalVariation $ i_
x :: Int
> mostSpecificCanonicalVariation $ i_ -+- i_
x + x :: Int
> mostSpecificCanonicalVariation $ i_ -+- i_ -+- i_
(x + x) + x :: Int
> mostSpecificCanonicalVariation $ i_ -+- ord' c_
x + ord c :: Int
> mostSpecificCanonicalVariation $ i_ -+- i_ -+- ord' c_
(x + x) + ord c :: Int
> mostSpecificCanonicalVariation $ i_ -+- i_ -+- length' (c_ -:- unit c_)
(x + x) + length (c:c:"") :: Int

In an expression without holes this functions just returns the given expression itself:

> mostSpecificCanonicalVariation $ val (0 :: Int)
0 :: Int
> mostSpecificCanonicalVariation $ ord' bee
ord 'b' :: Int

This function is the same as taking the last of canonicalVariations but a bit faster.

mostGeneralCanonicalVariation :: Expr -> Expr #

Returns the most general canonical variation of an Expr by filling holes with variables.

> mostGeneralCanonicalVariation $ i_
x :: Int
> mostGeneralCanonicalVariation $ i_ -+- i_
x + y :: Int
> mostGeneralCanonicalVariation $ i_ -+- i_ -+- i_
(x + y) + z :: Int
> mostGeneralCanonicalVariation $ i_ -+- ord' c_
x + ord c :: Int
> mostGeneralCanonicalVariation $ i_ -+- i_ -+- ord' c_
(x + y) + ord c :: Int
> mostGeneralCanonicalVariation $ i_ -+- i_ -+- length' (c_ -:- unit c_)
(x + y) + length (c:d:"") :: Int

In an expression without holes this functions just returns the given expression itself:

> mostGeneralCanonicalVariation $ val (0 :: Int)
0 :: Int
> mostGeneralCanonicalVariation $ ord' bee
ord 'b' :: Int

This function is the same as taking the head of canonicalVariations but a bit faster.

canonicalVariations :: Expr -> [Expr] #

Returns all canonical variations of an Expr by filling holes with variables. Where possible, variations are listed from most general to least general.

> canonicalVariations $ i_
[x :: Int]
> canonicalVariations $ i_ -+- i_
[ x + y :: Int
, x + x :: Int ]
> canonicalVariations $ i_ -+- i_ -+- i_
[ (x + y) + z :: Int
, (x + y) + x :: Int
, (x + y) + y :: Int
, (x + x) + y :: Int
, (x + x) + x :: Int ]
> canonicalVariations $ i_ -+- ord' c_
[x + ord c :: Int]
> canonicalVariations $ i_ -+- i_ -+- ord' c_
[ (x + y) + ord c :: Int
, (x + x) + ord c :: Int ]
> canonicalVariations $ i_ -+- i_ -+- length' (c_ -:- unit c_)
[ (x + y) + length (c:d:"") :: Int
, (x + y) + length (c:c:"") :: Int
, (x + x) + length (c:d:"") :: Int
, (x + x) + length (c:c:"") :: Int ]

In an expression without holes this functions just returns a singleton list with the expression itself:

> canonicalVariations $ val (0 :: Int)
[0 :: Int]
> canonicalVariations $ ord' bee
[ord 'b' :: Int]

When applying this to expressions already containing variables new variables are introduced so name clashes are avoided:

> canonicalVariations $ i_ -+- ii -+- jj -+- i_
[ x + y + z + x' :: Int
, x + y + z + x :: Int ]
> canonicalVariations $ ii -+- jj
[x + y :: Int]
> canonicalVariations $ xx -+- i_ -+- i_ -+- length' (c_ -:- unit c_) -+- yy
[ (((x + y) + z) + length (c:d:"")) + x' :: Int
, (((x + y) + z) + length (c:c:"")) + x' :: Int
, (((x + y) + y) + length (c:d:"")) + z :: Int
, (((x + y) + y) + length (c:c:"")) + z :: Int
]

isCanonical :: Expr -> Bool #

Returns whether an Expr is canonical: if applying canonicalize is an identity using names as provided by preludeNameInstances.

canonicalization :: Expr -> [(Expr, Expr)] #

Return a canonicalization of an Expr that makes variable names appear in order using names as provided by preludeNameInstances. By using //- it can canonicalize Exprs.

> canonicalization (gg yy -+- ff xx -+- gg xx)
[ (x :: Int,        y :: Int)
, (f :: Int -> Int, g :: Int -> Int)
, (y :: Int,        x :: Int)
, (g :: Int -> Int, f :: Int -> Int) ]
> canonicalization (yy -+- xx -+- yy)
[ (x :: Int, y :: Int)
, (y :: Int, x :: Int) ]

canonicalize :: Expr -> Expr #

Canonicalizes an Expr so that variable names appear in order. Variable names are taken from the preludeNameInstances.

> canonicalize (xx -+- yy)
x + y :: Int
> canonicalize (yy -+- xx)
x + y :: Int
> canonicalize (xx -+- xx)
x + x :: Int
> canonicalize (yy -+- yy)
x + x :: Int

Constants are untouched:

> canonicalize (jj -+- (zero -+- abs' ii))
x + (y + abs y) :: Int

This also works for variable functions:

> canonicalize (gg yy -+- ff xx -+- gg xx)
(f x + g y) + f y :: Int

isCanonicalWith :: (Expr -> [String]) -> Expr -> Bool #

Like isCanonical but allows specifying the list of variable names.

canonicalizationWith :: (Expr -> [String]) -> Expr -> [(Expr, Expr)] #

Like canonicalization but allows customization of the list of variable names. (cf. lookupNames, variableNamesFromTemplate)

canonicalizeWith :: (Expr -> [String]) -> Expr -> Expr #

Like canonicalize but allows customization of the list of variable names. (cf. lookupNames, variableNamesFromTemplate)

> canonicalizeWith (const ["i","j","k","l",...]) (xx -+- yy)
i + j :: Int

The argument Expr of the argument function allows to provide a different list of names for different types:

> let namesFor e
>   | typ e == typeOf (undefined::Char) = variableNamesFromTemplate "c1"
>   | typ e == typeOf (undefined::Int)  = variableNamesFromTemplate "i"
>   | otherwise                         = variableNamesFromTemplate "x"
> canonicalizeWith namesFor ((xx -+- ord' dd) -+- (ord' cc -+- yy))
(i + ord c1) + (ord c2 + j) :: Int

validApps :: [Expr] -> Expr -> [Expr] #

listVarsWith :: [Expr] -> Expr -> [Expr] #

mkEquation :: [Expr] -> Expr -> Expr -> Expr #

isEqOrd :: [Expr] -> Expr -> Bool #

O(n+m). Returns whether both Eq and Ord instance exist in the given list for the given Expr.

Given that the instances list has length m and that the given Expr has size n, this function is O(n+m).

isOrd :: [Expr] -> Expr -> Bool #

O(n+m). Returns whether an Ord instance exists in the given instances list for the given Expr.

> isOrd (reifyEqOrd (undefined :: Int)) (val (0::Int))
True
> isOrd (reifyEqOrd (undefined :: Int)) (val ([[[0::Int]]]))
False

Given that the instances list has length m and that the given Expr has size n, this function is O(n+m).

isEq :: [Expr] -> Expr -> Bool #

O(n+m). Returns whether an Eq instance exists in the given instances list for the given Expr.

> isEq (reifyEqOrd (undefined :: Int)) (val (0::Int))
True
> isEq (reifyEqOrd (undefined :: Int)) (val ([[[0::Int]]]))
False

Given that the instances list has length m and that the given Expr has size n, this function is O(n+m).

isEqOrdT :: [Expr] -> TypeRep -> Bool #

O(n). Returns whether both Eq and Ord instance exist in the given list for the given TypeRep.

Given that the instances list has length n, this function is O(n).

isOrdT :: [Expr] -> TypeRep -> Bool #

O(n). Returns whether an Ord instance exists in the given instances list for the given TypeRep.

> isOrdT (reifyEqOrd (undefined :: Int)) (typeOf (undefined :: Int))
True
> isOrdT (reifyEqOrd (undefined :: Int)) (typeOf (undefined :: [[[Int]]]))
False

Given that the instances list has length n, this function is O(n).

isEqT :: [Expr] -> TypeRep -> Bool #

O(n). Returns whether an Eq instance exists in the given instances list for the given TypeRep.

> isEqT (reifyEqOrd (undefined :: Int)) (typeOf (undefined :: Int))
True
> isEqT (reifyEqOrd (undefined :: Int)) (typeOf (undefined :: [[[Int]]]))
False

Given that the instances list has length n, this function is O(n).

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

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

mkName :: Typeable a => (a -> String) -> [Expr] #

O(1). Builds a reified Name instance from the given name function. (cf. reifyName, mkNameWith)

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

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

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

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

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 ]

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]]

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

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

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 ]

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 ]

isSubexprOf :: Expr -> Expr -> Bool #

O(n^2). Checks if an Expr is a subexpression of another.

> (xx -+- yy) `isSubexprOf` (zz -+- (xx -+- yy))
True
> (xx -+- yy) `isSubexprOf` abs' (yy -+- xx)
False
> xx `isSubexprOf` yy
False

hasInstanceOf :: Expr -> Expr -> Bool #

Checks if any of the subexpressions of the first argument Expr is an instance of the second argument Expr.

isInstanceOf :: Expr -> Expr -> Bool #

Given two Exprs, checks if the first expression is an instance of the second in terms of variables. (cf. hasInstanceOf)

> let zero = val (0::Int)
> let one  = val (1::Int)
> let xx   = var "x" (undefined :: Int)
> let yy   = var "y" (undefined :: Int)
> let e1 -+- e2  =  value "+" ((+)::Int->Int->Int) :$ e1 :$ e2
 one `isInstanceOf` one   =  True
  xx `isInstanceOf` xx    =  True
  yy `isInstanceOf` xx    =  True
zero `isInstanceOf` xx    =  True
  xx `isInstanceOf` zero  =  False
 one `isInstanceOf` zero  =  False
  (xx -+- (yy -+- xx)) `isInstanceOf`   (xx -+- yy)  =  True
  (yy -+- (yy -+- xx)) `isInstanceOf`   (xx -+- yy)  =  True
(zero -+- (yy -+- xx)) `isInstanceOf` (zero -+- yy)  =  True
 (one -+- (yy -+- xx)) `isInstanceOf` (zero -+- yy)  =  False

matchWith :: [(Expr, Expr)] -> Expr -> Expr -> Maybe [(Expr, Expr)] #

Like match but allowing predefined bindings.

matchWith [(xx,zero)] (zero -+- one) (xx -+- yy)  =  Just [(xx,zero), (yy,one)]
matchWith [(xx,one)]  (zero -+- one) (xx -+- yy)  =  Nothing

match :: Expr -> Expr -> Maybe [(Expr, Expr)] #

Given two expressions, returns a Just list of matches of subexpressions of the first expressions to variables in the second expression. Returns Nothing when there is no match.

> let zero = val (0::Int)
> let one  = val (1::Int)
> let xx   = var "x" (undefined :: Int)
> let yy   = var "y" (undefined :: Int)
> let e1 -+- e2  =  value "+" ((+)::Int->Int->Int) :$ e1 :$ e2
> (zero -+- one) `match` (xx -+- yy)
Just [(y :: Int,1 :: Int),(x :: Int,0 :: Int)]
> (zero -+- (one -+- two)) `match` (xx -+- yy)
Just [(y :: Int,1 + 2 :: Int),(x :: Int,0 :: Int)]
> (zero -+- (one -+- two)) `match` (xx -+- (yy -+- yy))
Nothing

In short:

          (zero -+- one) `match` (xx -+- yy)           =  Just [(xx,zero), (yy,one)]
(zero -+- (one -+- two)) `match` (xx -+- yy)           =  Just [(xx,zero), (yy,one-+-two)]
(zero -+- (one -+- two)) `match` (xx -+- (yy -+- yy))  =  Nothing

deriveExpressCascading :: Name -> DecsQ #

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

deriveExpressIfNeeded :: Name -> DecsQ #

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

deriveExpress :: Name -> DecsQ #

Derives an Express instance for the given type Name.

This function needs the TemplateHaskell extension.

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

class 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 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 Int 
Instance details

Defined in Data.Express.Express

Methods

expr :: Int -> Expr #

Express Integer 
Instance details

Defined in Data.Express.Express

Methods

expr :: Integer -> Expr #

Express Ordering 
Instance details

Defined in Data.Express.Express

Methods

expr :: Ordering -> Expr #

Express () 
Instance details

Defined in Data.Express.Express

Methods

expr :: () -> Expr #

Express a => Express [a] 
Instance details

Defined in Data.Express.Express

Methods

expr :: [a] -> Expr #

Express a => Express (Maybe a) 
Instance details

Defined in Data.Express.Express

Methods

expr :: Maybe a -> Expr #

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

Defined in Data.Express.Express

Methods

expr :: Ratio 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 #

unfold :: Expr -> [Expr] #

O(n). Unfolds an Expr representing a list into a list of Exprs. This reverses the effect of fold.

> expr [1,2,3::Int]
[1,2,3] :: [Int]
> unfold $ expr [1,2,3::Int]
[1 :: Int,2 :: Int,3 :: Int]

fold :: [Expr] -> Expr #

O(n). Folds a list of Exprs into a single Expr. (cf. unfold)

This always generates an ill-typed expression.

fold [val False, val True, val (1::Int)]
[False,True,1] :: ill-typed # ExprList $ Bool #

This is useful when applying transformations on lists of Exprs, such as canonicalize, mapValues or canonicalVariations.

> let ii = var "i" (undefined::Int)
> let kk = var "k" (undefined::Int)
> let qq = var "q" (undefined::Bool)
> let notE = value "not" not
> unfold . canonicalize . fold $ [ii,kk,notE :$ qq, notE :$ val False]
[x :: Int,y :: Int,not p :: Bool,not False :: Bool]

unfoldPair :: Expr -> (Expr, Expr) #

O(1). Unfolds an Expr representing a pair. This reverses the effect of foldPair.

> value "," ((,) :: Bool->Bool->(Bool,Bool)) :$ val True :$ val False
(True,False) :: (Bool,Bool)
> unfoldPair $ value "," ((,) :: Bool->Bool->(Bool,Bool)) :$ val True :$ val False
(True :: Bool,False :: Bool)

foldPair :: (Expr, Expr) -> Expr #

O(1). Folds a pair of Expr values into a single Expr. (cf. unfoldPair)

This always generates an ill-typed expression.

> foldPair (val False, val (1::Int))
(False,1) :: ill-typed # ExprPair $ Bool #
> foldPair (val (0::Int), val True)
(0,True) :: ill-typed # ExprPair $ Int #

This is useful when applying transformations on pairs of Exprs, such as canonicalize, mapValues or canonicalVariations.

> let ii = var "i" (undefined::Int)
> let kk = var "k" (undefined::Int)
> unfoldPair $ canonicalize $ foldPair (ii,kk)
(x :: Int,y :: Int)

foldApp :: [Expr] -> Expr #

O(n). Folds a list of Expr with function application (:$). This reverses the effect of unfoldApp.

foldApp [e0]           =  e0
foldApp [e0,e1]        =  e0 :$ e1
foldApp [e0,e1,e2]     =  e0 :$ e1 :$ e2
foldApp [e0,e1,e2,e3]  =  e0 :$ e1 :$ e2 :$ e3

Remember :$ is left-associative, so:

foldApp [e0]           =    e0
foldApp [e0,e1]        =   (e0 :$ e1)
foldApp [e0,e1,e2]     =  ((e0 :$ e1) :$ e2)
foldApp [e0,e1,e2,e3]  = (((e0 :$ e1) :$ e2) :$ e3)

This function may produce an ill-typed expression.

fill :: Expr -> [Expr] -> Expr #

Fill holes in an expression with the given list.

> let i_  =  hole (undefined :: Int)
> let e1 -+- e2  =  value "+" ((+) :: Int -> Int -> Int) :$ e1 :$ e2
> let xx  =  var "x" (undefined :: Int)
> let yy  =  var "y" (undefined :: Int)
> fill (i_ -+- i_) [xx, yy]
x + y :: Int
> fill (i_ -+- i_) [xx, xx]
x + x :: Int
> let one  =  val (1::Int)
> fill (i_ -+- i_) [one, one -+- one]
1 + (1 + 1) :: Int

This function silently remaining expressions:

> fill i_ [xx, yy]
x :: Int

This function silently keeps remaining holes:

> fill (i_ -+- i_ -+- i_) [xx, yy]
(x + y) + _ :: Int

This function silently skips remaining holes if one is not of the right type:

> fill (i_ -+- i_ -+- i_) [xx, val 'c', yy]
(x + _) + _ :: Int

listVarsAsTypeOf :: String -> Expr -> [Expr] #

Generate an infinite list of variables based on a template and the type of a given Expr. (cf. listVars)

> let one = val (1::Int)
> putL 10 $ "x" `listVarsAsTypeOf` one
[ x :: Int
, y :: Int
, z :: Int
, x' :: Int
, ...
]
> let false = val False
> putL 10 $ "p" `listVarsAsTypeOf` false
[ p :: Bool
, q :: Bool
, r :: Bool
, p' :: Bool
, ...
]

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

Generate an infinite list of variables based on a template and a given type. (cf. listVarsAsTypeOf)

> putL 10 $ listVars "x" (undefined :: Int)
[ x :: Int
, y :: Int
, z :: Int
, x' :: Int
, y' :: Int
, z' :: Int
, x'' :: Int
, ...
]
> putL 10 $ listVars "p" (undefined :: Bool)
[ p :: Bool
, q :: Bool
, r :: Bool
, p' :: Bool
, q' :: Bool
, r' :: Bool
, p'' :: Bool
, ...
]

nubHoles :: Expr -> [Expr] #

O(n^2). Lists all holes in an expression without repetitions. (cf. holes)

> nubHoles $ hole (undefined :: Bool)
[_ :: Bool]
> nubHoles $ value "&&" (&&) :$ hole (undefined :: Bool) :$ hole (undefined :: Bool)
[_ :: Bool]
> nubHoles $ hole (undefined :: Bool->Bool) :$ hole (undefined::Bool)
[_ :: Bool,_ :: Bool -> Bool]

Runtime averages to O(n log n) on evenly distributed expressions such as (f x + g y) + (h z + f w); and to O(n^2) on deep expressions such as f (g (h (f (g (h x))))).

holes :: Expr -> [Expr] #

O(n). Lists all holes in an expression, in order and with repetitions. (cf. nubHoles)

> holes $ hole (undefined :: Bool)
[_ :: Bool]
> holes $ value "&&" (&&) :$ hole (undefined :: Bool) :$ hole (undefined :: Bool)
[_ :: Bool,_ :: Bool]
> holes $ hole (undefined :: Bool->Bool) :$ hole (undefined::Bool)
[_ :: Bool -> Bool,_ :: Bool]

isHole :: Expr -> Bool #

O(1). Checks if an Expr represents a typed hole. (cf. hole)

> isHole $ hole (undefined :: Int)
True
> isHole $ value "not" not :$ val True
False
> isHole $ val 'a'
False

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

holeAsTypeOf :: Expr -> Expr #

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

> val (1::Int)
1 :: Int
> holeAsTypeOf $ val (1::Int)
_ :: Int

varAsTypeOf :: String -> Expr -> Expr #

O(1). Creates a variable with the same type as the given Expr.

> let one = val (1::Int)
> "x" `varAsTypeOf` one
x :: Int
> "p" `varAsTypeOf` val False
p :: Bool

renameVarsBy :: (String -> String) -> Expr -> Expr #

Rename variables in an Expr.

> renameVarsBy (++ "'") (xx -+- yy)
x' + y' :: Int
> renameVarsBy (++ "'") (yy -+- (zz -+- xx))
(y' + (z' + x')) :: Int
> renameVarsBy (++ "1") (abs' xx)
abs x1 :: Int
> renameVarsBy (++ "2") $ abs' (xx -+- yy)
abs (x2 + y2) :: Int

NOTE: this will affect holes!

(//) :: Expr -> [(Expr, Expr)] -> Expr #

O(n*n*m). Substitute subexpressions in an expression from the given list of substitutions. (cf. mapSubexprs).

Please consider using //- if you are replacing just terminal values as it is faster.

Given that:

> let xx = var "x" (undefined :: Int)
> let yy = var "y" (undefined :: Int)
> let zz = var "z" (undefined :: Int)
> let xx -+- yy = value "+" ((+) :: Int->Int->Int) :$ xx :$ yy

Then:

> ((xx -+- yy) -+- (yy -+- zz)) // [(xx -+- yy, yy), (yy -+- zz, yy)]
y + y :: Int
> ((xx -+- yy) -+- zz) // [(xx -+- yy, zz), (zz, xx -+- yy)]
z + (x + y) :: Int

Replacement happens only once with outer expressions having more precedence than inner expressions.

> (xx -+- yy) // [(yy,xx), (xx -+- yy,zz), (zz,xx)]
z :: Int

Given that the argument list has length m, this function is O(n*n*m). Remember that since n is the size of an expression, comparing two expressions is O(n) in the worst case, and we may need to compare with n subexpressions in the worst case.

(//-) :: Expr -> [(Expr, Expr)] -> Expr #

O(n*m). Substitute occurrences of values in an expression from the given list of substitutions. (cf. mapValues)

Given that:

> let xx = var "x" (undefined :: Int)
> let yy = var "y" (undefined :: Int)
> let zz = var "z" (undefined :: Int)
> let xx -+- yy = value "+" ((+) :: Int->Int->Int) :$ xx :$ yy

Then:

> ((xx -+- yy) -+- (yy -+- zz)) //- [(xx, yy), (zz, yy)]
(y + y) + (y + y) :: Int
> ((xx -+- yy) -+- (yy -+- zz)) //- [(yy, yy -+- zz)]
(x + (y + z)) + ((y + z) + z) :: Int

This function does not work for substituting non-terminal subexpressions:

> (xx -+- yy) //- [(xx -+- yy, zz)]
x + y :: Int

Please use the slower // if you want the above replacement to work.

Replacement happens only once:

> xx //- [(xx,yy), (yy,zz)]
y :: Int

Given that the argument list has length m, this function is O(n*m).

mapSubexprs :: (Expr -> Maybe Expr) -> Expr -> Expr #

O(n*m). Substitute subexpressions of an expression using the given function. Outer expressions have more precedence than inner expressions. (cf. //)

With:

> let xx = var "x" (undefined :: Int)
> let yy = var "y" (undefined :: Int)
> let zz = var "z" (undefined :: Int)
> let plus = value "+" ((+) :: Int->Int->Int)
> let times = value "*" ((*) :: Int->Int->Int)
> let xx -+- yy = plus :$ xx :$ yy
> let xx -*- yy = times :$ xx :$ yy
> let pluswap (o :$ xx :$ yy) | o == plus = Just $ o :$ yy :$ xx
|     pluswap _                           = Nothing

Then:

> mapSubexprs pluswap $ (xx -*- yy) -+- (yy -*- zz)
y * z + x * y :: Int
> mapSubexprs pluswap $ (xx -+- yy) -*- (yy -+- zz)
(y + x) * (z + y) :: Int

Substitutions do not stack, in other words a replaced expression or its subexpressions are not further replaced:

> mapSubexprs pluswap $ (xx -+- yy) -+- (yy -+- zz)
(y + z) + (x + y) :: Int

Given that the argument function is O(m), this function is O(n*m).

mapConsts :: (Expr -> Expr) -> Expr -> Expr #

O(n*m). Applies a function to all terminal constants in an expression.

Given that:

> let one   = val (1 :: Int)
> let two   = val (2 :: Int)
> let xx -+- yy = value "+" ((+) :: Int->Int->Int) :$ xx :$ yy
> let intToZero e = if typ e == typ zero then zero else e

Then:

> one -+- (two -+- xx)
1 + (2 + x) :: Int
> mapConsts intToZero (one -+- (two -+- xx))
0 + (0 + x) :: Integer

Given that the argument function is O(m), this function is O(n*m).

mapVars :: (Expr -> Expr) -> Expr -> Expr #

O(n*m). Applies a function to all variables in an expression.

Given that:

> let primeify e = if isVar e
|                  then case e of (Value n d) -> Value (n ++ "'") d
|                  else e
> let xx = var "x" (undefined :: Int)
> let yy = var "y" (undefined :: Int)
> let xx -+- yy = value "+" ((+) :: Int->Int->Int) :$ xx :$ yy

Then:

> xx -+- yy
x + y :: Int
> primeify xx
x' :: Int
> mapVars primeify $ xx -+- yy
x' + y' :: Int
> mapVars (primeify . primeify) $ xx -+- yy
x'' + y'' :: Int

Given that the argument function is O(m), this function is O(n*m).

mapValues :: (Expr -> Expr) -> Expr -> Expr #

O(n*m). Applies a function to all terminal values in an expression. (cf. //-)

Given that:

> let zero  = val (0 :: Int)
> let one   = val (1 :: Int)
> let two   = val (2 :: Int)
> let three = val (3 :: Int)
> let xx -+- yy = value "+" ((+) :: Int->Int->Int) :$ xx :$ yy
> let intToZero e = if typ e == typ zero then zero else e

Then:

> one -+- (two -+- three)
1 + (2 + 3) :: Int
> mapValues intToZero $ one -+- (two -+- three)
0 + (0 + 0) :: Integer

Given that the argument function is O(m), this function is O(n*m).

height :: Expr -> Int #

O(n). Returns the maximum height of a given expression given by the maximum number of nested function applications. Curried function application is counted each time, i.e. the application of a two argument function increases the depth of its first argument by two and of its second argument by one. (cf. depth)

With:

zero          =  val (0 :: Int)
one           =  val (1 :: Int)
two           =  val (2 :: Int)
const' xx yy  =  value "const" (const :: Int->Int->Int) :$ xx :$ yy
abs' xx       =  value "abs" (abs :: Int->Int) :$ xx

Then:

> height zero
1
> height (abs' one)
2
> height ((const' one) two)
3
> height ((const' (abs' one)) two)
4
> height ((const' one) (abs' two))
3

Flipping arguments of applications in subterms may change the result of the function.

depth :: Expr -> Int #

O(n). Returns the maximum depth of a given expression given by the maximum number of nested function applications. Curried function application is counted only once, i.e. the application of a two argument function increases the depth of both its arguments by one. (cf. height)

With

zero       =  val (0 :: Int)
one        =  val (1 :: Int)
two        =  val (2 :: Int)
xx -+- yy  =  value "+" ((+) :: Int->Int->Int) :$ xx :$ yy
abs' xx    =  value "abs" (abs :: Int->Int) :$ xx
> depth zero
1
> depth (one -+- two)
2
> depth (abs' one -+- two)
3

Flipping arguments of applications in any of the subterms does not affect the result.

size :: Expr -> Int #

O(n). Returns the size of the given expression, i.e. the number of terminal values in it.

zero       =  val (0 :: Int)
one        =  val (1 :: Int)
two        =  val (2 :: Int)
xx -+- yy  =  value "+" ((+) :: Int->Int->Int) :$ xx :$ yy
abs' xx    =  value "abs" (abs :: Int->Int) :$ xx
> size zero
1
> size (one -+- two)
3
> size (abs' one)
2

arity :: Expr -> Int #

O(n). Return the arity of the given expression, i.e. the number of arguments that its type takes.

> arity (val (0::Int))
0
> arity (val False)
0
> arity (value "id" (id :: Int -> Int))
1
> arity (value "const" (const :: Int -> Int -> Int))
2
> arity (one -+- two)
0

nubVars :: Expr -> [Expr] #

O(n^2). Lists all variables in an expression without repetitions. (cf. vars)

> nubVars (yy -+- xx)
[ x :: Int
, y :: Int
]
> nubVars (xx -+- (yy -+- xx))
[ x :: Int
, y :: Int
]
> nubVars (zero -+- (one -*- two))
[]
> nubVars (pp -&&- true)
[p :: Bool]

Runtime averages to O(n log n) on evenly distributed expressions such as (f x + g y) + (h z + f w); and to O(n^2) on deep expressions such as f (g (h (f (g (h x))))).

vars :: Expr -> [Expr] #

O(n). Lists all variables in an expression in order and with repetitions. (cf. nubVars)

> vars (xx -+- yy)
[ x :: Int
, y :: Int
]
> vars (xx -+- (yy -+- xx))
[ x :: Int
, y :: Int
, x :: Int
]
> vars (zero -+- (one -*- two))
[]
> vars (pp -&&- true)
[p :: Bool]

nubConsts :: Expr -> [Expr] #

O(n^2). List terminal constants in an expression without repetitions. (cf. consts)

> nubConsts (xx -+- yy)
[ (+) :: Int -> Int -> Int ]
> nubConsts (xx -+- (yy -+- zz))
[ (+) :: Int -> Int -> Int ]
> nubConsts (pp -&&- true)
[ True :: Bool
, (&&) :: Bool -> Bool -> Bool
]

Runtime averages to O(n log n) on evenly distributed expressions such as (f x + g y) + (h z + f w); and to O(n^2) on deep expressions such as f (g (h (f (g (h x))))).

consts :: Expr -> [Expr] #

O(n). List terminal constants in an expression in order and with repetitions. (cf. nubConsts)

> consts (xx -+- yy)
[ (+) :: Int -> Int -> Int ]
> consts (xx -+- (yy -+- zz))
[ (+) :: Int -> Int -> Int
, (+) :: Int -> Int -> Int
]
> consts (zero -+- (one -*- two))
[ (+) :: Int -> Int -> Int
, 0 :: Int
, (*) :: Int -> Int -> Int
, 1 :: Int
, 2 :: Int
]
> consts (pp -&&- true)
[ (&&) :: Bool -> Bool -> Bool
, True :: Bool
]

nubValues :: Expr -> [Expr] #

O(n^2). Lists all terminal values in an expression without repetitions. (cf. values)

> nubValues (xx -+- yy)
[ x :: Int
, y :: Int
, (+) :: Int -> Int -> Int

]

> nubValues (xx -+- (yy -+- zz))
[ x :: Int
, y :: Int
, z :: Int
, (+) :: Int -> Int -> Int
]
> nubValues (zero -+- (one -*- two))
[ 0 :: Int
, 1 :: Int
, 2 :: Int
, (*) :: Int -> Int -> Int
, (+) :: Int -> Int -> Int
]
> nubValues (pp -&&- pp)
[ p :: Bool
, (&&) :: Bool -> Bool -> Bool
]

Runtime averages to O(n log n) on evenly distributed expressions such as (f x + g y) + (h z + f w); and to O(n^2) on deep expressions such as f (g (h (f (g (h x))))).

values :: Expr -> [Expr] #

O(n). Lists all terminal values in an expression in order and with repetitions. (cf. nubValues)

> values (xx -+- yy)
[ (+) :: Int -> Int -> Int
, x :: Int
, y :: Int
]
> values (xx -+- (yy -+- zz))
[ (+) :: Int -> Int -> Int
, x :: Int
, (+) :: Int -> Int -> Int
, y :: Int
, z :: Int
]
> values (zero -+- (one -*- two))
[ (+) :: Int -> Int -> Int
, 0 :: Int
, (*) :: Int -> Int -> Int
, 1 :: Int
, 2 :: Int
]
> values (pp -&&- true)
[ (&&) :: Bool -> Bool -> Bool
, p :: Bool
, True :: Bool
]

nubSubexprs :: Expr -> [Expr] #

O(n^3) for full evaluation. Lists all subexpressions of a given expression without repetitions. This includes the expression itself and partial function applications. (cf. subexprs)

> nubSubexprs (xx -+- yy)
[ x :: Int
, y :: Int
, (+) :: Int -> Int -> Int
, (x +) :: Int -> Int
, x + y :: Int
]
> nubSubexprs (pp -&&- (pp -&&- true))
[ p :: Bool
, True :: Bool
, (&&) :: Bool -> Bool -> Bool
, (p &&) :: Bool -> Bool
, p && True :: Bool
, p && (p && True) :: Bool
]

Runtime averages to O(n^2 log n) on evenly distributed expressions such as (f x + g y) + (h z + f w); and to O(n^3) on deep expressions such as f (g (h (f (g (h x))))).

subexprs :: Expr -> [Expr] #

O(n) for the spine, O(n^2) for full evaluation. Lists subexpressions of a given expression in order and with repetitions. This includes the expression itself and partial function applications. (cf. nubSubexprs)

> subexprs (xx -+- yy)
[ x + y :: Int
, (x +) :: Int -> Int
, (+) :: Int -> Int -> Int
, x :: Int
, y :: Int
]
> subexprs (pp -&&- (pp -&&- true))
[ p && (p && True) :: Bool
, (p &&) :: Bool -> Bool
, (&&) :: Bool -> Bool -> Bool
, p :: Bool
, p && True :: Bool
, (p &&) :: Bool -> Bool
, (&&) :: Bool -> Bool -> Bool
, p :: Bool
, True :: Bool
]

isApp :: Expr -> Bool #

O(1). Returns whether an Expr is an application (:$).

> isApp $ var "x" (undefined :: Int)
False
> isApp $ val False
False
> isApp $ value "not" not :$ var "p" (undefined :: Bool)
True

This is equivalent to pattern matching the :$ constructor.

Properties:

  •  isApp (e1 :$ e2)  =  True
  •  isApp (Value e)  =  False
  •  isApp  =  not . isValue
  •  isApp e  =  not (isVar e) && not (isConst e)

isValue :: Expr -> Bool #

O(1). Returns whether an Expr is a terminal value (Value).

> isValue $ var "x" (undefined :: Int)
True
> isValue $ val False
True
> isValue $ value "not" not :$ var "p" (undefined :: Bool)
False

This is equivalent to pattern matching the Value constructor.

Properties:

  •  isValue (Value e)  =  True
  •  isValue (e1 :$ e2)  =  False
  •  isValue  =  not . isApp
  •  isValue e  =  isVar e || isConst e

isVar :: Expr -> Bool #

O(1). Returns whether an Expr is a terminal variable (var). (cf. hasVar).

> isVar $ var "x" (undefined :: Int)
True
> isVar $ val False
False
> isVar $ value "not" not :$ var "p" (undefined :: Bool)
False

isConst :: Expr -> Bool #

O(1). Returns whether an Expr is a terminal constant. (cf. isGround).

> isConst $ var "x" (undefined :: Int)
False
> isConst $ val False
True
> isConst $ value "not" not :$ val False
False

isGround :: Expr -> Bool #

O(n). Returns whether a Expr has no variables. This is equivalent to "not . hasVar".

The name "ground" comes from term rewriting.

> isGround $ value "not" not :$ val True
True
> isGround $ value "&&" (&&) :$ var "p" (undefined :: Bool) :$ val True
False

hasVar :: Expr -> Bool #

O(n). Check if an Expr has a variable. (By convention, any value whose String representation starts with '_'.)

> hasVar $ value "not" not :$ val True
False
> hasVar $ value "&&" (&&) :$ var "p" (undefined :: Bool) :$ val True
True

unfoldApp :: Expr -> [Expr] #

O(n). Unfold a function application Expr into a list of function and arguments.

unfoldApp $ e0                    =  [e0]
unfoldApp $ e0 :$ e1              =  [e0,e1]
unfoldApp $ e0 :$ e1 :$ e2        =  [e0,e1,e2]
unfoldApp $ e0 :$ e1 :$ e2 :$ e3  =  [e0,e1,e2,e3]

Remember :$ is left-associative, so:

unfoldApp e0                          =  [e0]
unfoldApp (e0 :$ e1)                  =  [e0,e1]
unfoldApp ((e0 :$ e1) :$ e2)          =  [e0,e1,e2]
unfoldApp (((e0 :$ e1) :$ e2) :$ e3)  =  [e0,e1,e2,e3]

compareQuickly :: Expr -> Expr -> Ordering #

O(n). A fast total order between Exprs that can be used when sorting Expr values.

This is lazier than its counterparts compareComplexity and compareLexicographically and tries to evaluate the given Exprs as least as possible.

compareLexicographically :: Expr -> Expr -> Ordering #

O(n). Lexicographical structural comparison of Exprs where variables < constants < applications then types are compared before string representations.

> compareLexicographically one (one -+- one)
LT
> compareLexicographically one zero
GT
> compareLexicographically (xx -+- zero) (zero -+- xx)
LT
> compareLexicographically (zero -+- xx) (zero -+- xx)
EQ

(cf. compareTy)

This comparison is a total order.

compareComplexity :: Expr -> Expr -> Ordering #

O(n). Compares the complexity of two Exprs. An expression e1 is strictly simpler than another expression e2 if the first of the following conditions to distingish between them is:

  1. e1 is smaller in size/length than e2, e.g.: x + y < x + (y + z);
  2. or, e1 has more distinct variables than e2, e.g.: x + y < x + x;
  3. or, e1 has more variable occurrences than e2, e.g.: x + x < 1 + x;
  4. or, e1 has fewer distinct constants than e2, e.g.: 1 + 1 < 0 + 1.

They're otherwise considered of equal complexity, e.g.: x + y and y + z.

> (xx -+- yy) `compareComplexity` (xx -+- (yy -+- zz))
LT
> (xx -+- yy) `compareComplexity` (xx -+- xx)
LT
> (xx -+- xx) `compareComplexity` (one -+- xx)
LT
> (one -+- one) `compareComplexity` (zero -+- one)
LT
> (xx -+- yy) `compareComplexity` (yy -+- zz)
EQ
> (zero -+- one) `compareComplexity` (one -+- zero)
EQ

This comparison is not a total order.

showExpr :: Expr -> String #

O(n). Returns a string representation of an expression. Differently from show (:: Expr -> String) this function does not include the type in the output.

> putStrLn $ showExpr (one -+- two)
1 + 2
> putStrLn $ showExpr $ (pp -||- true) -&&- (qq -||- false)
(p || True) && (q || False)

toDynamic :: Expr -> Maybe Dynamic #

O(n). Evaluates an expression to a terminal Dynamic value when possible. Returns Nothing otherwise.

> toDynamic $ val (123 :: Int) :: Maybe Dynamic
Just <<Int>>
> toDynamic $ value "abs" (abs :: Int -> Int) :$ val (-1 :: Int)
Just <<Int>>
> toDynamic $ value "abs" (abs :: Int -> Int) :$ val 'a'
Nothing

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

O(n). Evaluates an expression when possible (correct type). Raises an error otherwise.

> evl $ two -+- three :: Int
5
> evl $ two -+- three :: Bool
*** Exception: evl: cannot evaluate Expr `2 + 3 :: Int' at the Bool type

This may raise errors, please consider using eval or evaluate.

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

O(n). Evaluates an expression when possible (correct type). Returns a default value otherwise.

> let two = val (2 :: Int)
> let three = val (3 :: Int)
> let e1 -+- e2 = value "+" ((+) :: Int->Int->Int) :$ e1 :$ e2
> eval 0 $ two -+- three :: Int
5
> eval 'z' $ two -+- three :: Char
'z'
> eval 0 $ two -+- val '3' :: Int
0

evaluate :: Typeable a => Expr -> Maybe a #

O(n). Just the value of an expression when possible (correct type), Nothing otherwise. This does not catch errors from undefined Dynamic values.

> let one = val (1 :: Int)
> let bee = val 'b'
> let negateE = value "negate" (negate :: Int -> Int)
> evaluate one :: Maybe Int
Just 1
> evaluate one :: Maybe Char
Nothing
> evaluate bee :: Maybe Int
Nothing
> evaluate bee :: Maybe Char
Just 'b'
> evaluate $ negateE :$ one :: Maybe Int
Just (-1)
> evaluate $ negateE :$ bee :: Maybe Int
Nothing

isFun :: Expr -> Bool #

O(n). Returns whether the given Expr is of a functional type. This is the same as checking if the arity of the given Expr is non-zero.

> isFun (value "abs" (abs :: Int -> Int))
True
> isFun (val (1::Int))
False
> isFun (value "const" (const :: Bool -> Bool -> Bool) :$ val False)
True

isWellTyped :: Expr -> Bool #

O(n). Returns whether the given Expr is well typed. (cf. isIllTyped)

> isWellTyped (absE :$ val (1 :: Int))
True
> isWellTyped (absE :$ val 'b')
False

isIllTyped :: Expr -> Bool #

O(n). Returns whether the given Expr is ill typed. (cf. isWellTyped)

> let one = val (1 :: Int)
> let bee = val 'b'
> let absE = value "abs" (abs :: Int -> Int)
> isIllTyped (absE :$ val (1 :: Int))
False
> isIllTyped (absE :$ val 'b')
True

mtyp :: Expr -> Maybe TypeRep #

O(n). Returns Just the type of an expression or Nothing when there is an error.

> let one = val (1 :: Int)
> let bee = val 'b'
> let absE = value "abs" (abs :: Int -> Int)
> mtyp one
Just Int
> mtyp (absE :$ bee)
Nothing

etyp :: Expr -> Either (TypeRep, TypeRep) TypeRep #

O(n). Computes the type of an expression returning either the type of the given expression when possible or when there is a type error, the pair of types which produced the error.

> let one = val (1 :: Int)
> let bee = val 'b'
> let absE = value "abs" (abs :: Int -> Int)
> etyp one
Right Int
> etyp bee
Right Char
> etyp absE
Right (Int -> Int)
> etyp (absE :$ one)
Right Int
> etyp (absE :$ bee)
Left (Int -> Int, Char)
> etyp ((absE :$ bee) :$ one)
Left (Int -> Int, Char)

typ :: Expr -> TypeRep #

O(n). Computes the type of an expression. This raises errors, but this should not happen if expressions are smart-constructed with $$.

> let one = val (1 :: Int)
> let bee = val 'b'
> let absE = value "abs" (abs :: Int -> Int)
> typ one
Int
> typ bee
Char
> typ absE
Int -> Int
> typ (absE :$ one)
Int
> typ (absE :$ bee)
*** Exception: type mismatch, cannot apply `Int -> Int' to `Char'
> typ ((absE :$ bee) :$ one)
*** Exception: type mismatch, cannot apply `Int -> Int' to `Char'

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

O(1). Creates an Expr representing a variable with the given name and argument type.

> var "x" (undefined :: Int)
x :: Int
> var "u" (undefined :: ())
u :: ()
> var "xs" (undefined :: [Int])
xs :: [Int]

This function follows the underscore convention: a variable is just a value whose string representation starts with underscore ('_').

($$) :: Expr -> Expr -> Maybe Expr #

O(n). Creates an Expr representing a function application. Just an Expr application if the types match, Nothing otherwise. (cf. :$)

> value "id" (id :: () -> ()) $$ val ()
Just (id () :: ())
> value "abs" (abs :: Int -> Int) $$ val (1337 :: Int)
Just (abs 1337 :: Int)
> value "abs" (abs :: Int -> Int) $$ val 'a'
Nothing
> value "abs" (abs :: Int -> Int) $$ val ()
Nothing

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]

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.

Constructors

Value String Dynamic

a value enconded as String and Dynamic

Expr :$ Expr

function application between expressions

Instances

Instances details
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 #

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 #

deriveNameCascading :: Name -> DecsQ #

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

deriveNameIfNeeded :: Name -> DecsQ #

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

deriveName :: Name -> DecsQ #

Derives a Name instance for the given type Name.

This function needs the TemplateHaskell extension.

names :: Name a => a -> [String] #

Returns na infinite list of variable names from the given type: the result of variableNamesFromTemplate after name.

> 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''", ...]

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

Defined in Data.Express.Name

Methods

name :: Integer -> 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 Word 
Instance details

Defined in Data.Express.Name

Methods

name :: Word -> String #

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

Defined in Data.Express.Name

Methods

name :: () -> 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 (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 (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 -> 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 (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, 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 #

variableNamesFromTemplate :: String -> [String] #

Returns an infinite list of variable names based on the given template.

> variableNamesFromTemplate "x"
["x", "y", "z", "x'", "y'", ...]
> variableNamesFromTemplate "p"
["p", "q", "r", "p'", "q'", ...]
> variableNamesFromTemplate "xy"
["xy", "zw", "xy'", "zw'", "xy''", ...]

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 9 symbols
  • pruning with equations up to size 5
  • recursion up to 60 symbols.

conjure :: Conjurable f => String -> f -> [Expr] -> 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

background :: [Expr]
background =
  [ val (0::Int)
  , val (1::Int)
  , value "+" ((+) :: Int -> Int -> Int)
  , value "*" ((*) :: Int -> Int -> Int)
  , value "==" ((==) :: Int -> Int -> Bool)
]

The conjure function does the following:

> conjure "square" square background
square :: Int -> Int
-- looking through 815 candidates, 100% match, 3/3 assignments
square x  =  x * x

The background is defined with val, value and ifFor.

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

Like conjure but allows setting options through Args and args.

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

Like conjure but in the pure world.

Returns a triple whose:

  1. first element is the number of candidates considered
  2. second element is the number of defined points in the given function
  3. third element is a list of implementations encoded as Exprs paired with the number of matching points.

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

Like conjpure but allows setting options through Args and args.

candidateExprs :: Conjurable f => String -> f -> Int -> (Expr -> Expr -> Bool) -> [[Expr]] -> [[Expr]] Source #

ifFor :: Typeable a => a -> Expr Source #

Creates an if Expr of the type of the given proxy.

> ifFor (undefined :: Int)
if :: Bool -> Int -> Int -> Int
> ifFor (undefined :: String)
if :: Bool -> [Char] -> [Char] -> [Char]

You need to provide this as part of your building blocks on the background if you want recursive functions to be considered and produced.