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Damian Ferencz Cohn
seminatio-type-level-programming
Commits
c6ae388f
Commit
c6ae388f
authored
5 years ago
by
Marcos Viera
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sinonimos asociados
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src/associated-type-synonyms.hs
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c6ae388f
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TypeFamilies #-}
-- type functions
-- study on C++, Standard ML, Haskell, Eiffel, Java, Generic C
class
CollectionFD
c
e
|
c
->
e
where
emptyFD
::
c
insertFD
::
e
->
c
->
c
toListFD
::
c
->
[
e
]
instance
CollectionFD
[
a
]
a
where
emptyFD
=
[]
insertFD
=
(
:
)
toListFD
=
id
class
Collection
c
where
type
Elem
c
empty
::
c
insert
::
Elem
c
->
c
->
c
toList
::
c
->
[
Elem
c
]
-- ZipWith
data
Zero
=
Zero
data
Suc
n
=
Suc
n
type
N3
=
Suc
(
Suc
(
Suc
Zero
))
n3
::
N3
n3
=
Suc
(
Suc
(
Suc
Zero
))
data
VNil
a
=
VNil
data
VCons
v
a
=
VCons
a
(
v
a
)
type
Vector4
=
VCons
(
VCons
(
VCons
(
VCons
VNil
)))
::
*
->
*
class
VRepeat
v
where
vRepeat
::
a
->
v
a
instance
VRepeat
VNil
where
vRepeat
_
=
VNil
instance
VRepeat
v
=>
VRepeat
(
VCons
v
)
where
vRepeat
a
=
VCons
a
(
vRepeat
a
)
class
VList
v
where
vToList
::
v
a
->
[
a
]
instance
VList
VNil
where
vToList
VNil
=
[]
instance
VList
v
=>
VList
(
VCons
v
)
where
vToList
(
VCons
a
v
)
=
a
:
vToList
v
class
VApply
v
where
vApply
::
v
(
a
->
b
)
->
v
a
->
v
b
instance
VApply
VNil
where
vApply
VNil
VNil
=
VNil
instance
VApply
v
=>
VApply
(
VCons
v
)
where
vApply
(
VCons
f
vf
)
(
VCons
a
va
)
=
VCons
(
f
a
)
(
vApply
vf
va
)
-- class Applicative f where
-- <*> :: f (a -> b) -> f a -> f b
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
-- zipWith :: (a -> b -> c -> d) -> v a -> v b -> v c -> v d
-- | @VZipWithFD n v s t@ is satisfyiable only for
-- types @s@ of the form @a1 -> a2 -> ... -> an -> r@
-- and @t@ of the form
--
-- > v a1 -> v a2 -> ... -> v an -> v r
--
-- where @v@ is some type of vector.
--
class
VZipWithFD
n
v
s
t
|
n
t
->
v
-- , n v s -> t
where
vManyApp
::
n
->
v
s
->
t
vZipWith
::
n
->
s
->
t
instance
VRepeat
v
=>
VZipWithFD
Zero
v
t
(
v
t
)
where
vManyApp
Zero
fs
=
fs
vZipWith
Zero
a
=
vRepeat
a
instance
(
VRepeat
v
,
VApply
v
,
VZipWithFD
n
v
t
ts
)
=>
VZipWithFD
(
Suc
n
)
v
(
s
->
t
)
(
v
s
->
ts
)
where
-- v (a -> ... -> z) -> v a -> ... -> v z
vManyApp
(
Suc
n
)
fs
ss
=
vManyApp
n
(
vApply
fs
ss
{- :: v (b -> .. -> z) -> v b -> ... -> v z-}
)
vZipWith
n
f
=
vManyApp
n
(
vRepeat
f
)
testVZipWithFD
::
Vector4
Int
testVZipWithFD
=
vZipWith
n3
(
\
a
b
c
->
a
*
b
+
c
::
Int
)
(
VCons
1
$
VCons
2
$
VCons
3
$
VCons
4
VNil
::
Vector4
Int
)
(
VCons
5
$
VCons
6
$
VCons
7
$
VCons
8
VNil
::
Vector4
Int
)
(
VCons
(
-
1
)
$
VCons
(
-
2
)
$
VCons
(
-
3
)
$
VCons
(
-
4
)
VNil
::
Vector4
Int
)
vZipWithFD3
::
VZipWithFD
N3
Vector4
(
a
->
b
->
c
->
d
)
(
Vector4
a
->
Vector4
b
->
Vector4
c
->
Vector4
d
)
=>
(
a
->
b
->
c
->
d
)
->
Vector4
a
->
Vector4
b
->
Vector4
c
->
Vector4
d
vZipWithFD3
=
vZipWith
n3
testVZipWithFD3
::
Vector4
Int
testVZipWithFD3
=
vZipWithFD3
(
\
a
b
c
->
a
*
b
+
c
)
(
VCons
1
$
VCons
2
$
VCons
3
$
VCons
4
VNil
)
(
VCons
5
$
VCons
6
$
VCons
7
$
VCons
8
VNil
)
(
VCons
(
-
1
)
$
VCons
(
-
2
)
$
VCons
(
-
3
)
$
VCons
(
-
4
)
VNil
)
-- | @VZipWith n t@ is satisfyiable only for types @t@
-- of the form
--
-- > v a1 -> v a2 -> ... -> v an -> v r
--
-- where @v ~ Vec n t@ is some type of vector.
--
-- > ZippedFun n (v a1 -> v a2 -> ... -> v an -> v r)
-- > = a1 -> a2 -> ... -> an -> r
--
class
VZipWith
n
t
where
type
Vec
n
t
::
*
->
*
type
ZippedFun
n
t
vManyApp'
::
n
->
Vec
n
t
(
ZippedFun
n
t
)
->
t
vZipWith'
::
n
->
ZippedFun
n
t
->
t
instance
VRepeat
v
=>
VZipWith
Zero
(
v
t
)
where
type
Vec
Zero
(
v
t
)
=
v
type
ZippedFun
Zero
(
v
t
)
=
t
vManyApp'
Zero
fs
=
fs
vZipWith'
Zero
a
=
vRepeat
a
instance
(
VRepeat
v
,
VApply
v
,
VZipWith
n
ts
,
Vec
n
ts
~
v
)
=>
VZipWith
(
Suc
n
)
(
v
s
->
ts
)
where
type
Vec
(
Suc
n
)
(
v
s
->
ts
)
=
v
type
ZippedFun
(
Suc
n
)
(
v
s
->
ts
)
=
s
->
ZippedFun
n
ts
vManyApp'
(
Suc
n
)
fs
ss
=
vManyApp'
n
(
vApply
fs
ss
)
vZipWith'
n
f
=
vManyApp'
n
(
vRepeat
f
)
testVZipWith
::
Vector4
Int
testVZipWith
=
vZipWith'
n3
(
\
a
b
c
->
a
*
b
+
c
)
(
VCons
1
$
VCons
2
$
VCons
3
$
VCons
4
VNil
)
(
VCons
5
$
VCons
6
$
VCons
7
$
VCons
8
VNil
)
(
VCons
(
-
1
)
$
VCons
(
-
2
)
$
VCons
(
-
3
)
$
VCons
(
-
4
)
VNil
)
vZipWith3
::
(
VZipWith
N3
t
,
t
~
(
Vector4
a
->
Vector4
b
->
Vector4
c
->
Vector4
d
)
)
=>
ZippedFun
N3
t
->
t
vZipWith3
=
vZipWith'
n3
testVZipWith3
::
Vector4
Int
testVZipWith3
=
vZipWith3
(
\
a
b
c
->
a
*
b
+
c
)
(
VCons
1
$
VCons
2
$
VCons
3
$
VCons
4
VNil
)
(
VCons
5
$
VCons
6
$
VCons
7
$
VCons
8
VNil
)
(
VCons
(
-
1
)
$
VCons
(
-
2
)
$
VCons
(
-
3
)
$
VCons
(
-
4
)
VNil
)
-- (1) restricted to type constructors and variables
-- (2) specific
-- (3) non-overlapping
-- (4) Smaller context
instance
Collection
[
a
]
where
type
Elem
[
a
]
=
a
empty
=
[]
insert
=
(
:
)
toList
=
id
-- wrt FD
-- * type checking limitations
-- * readability
-- * expressiveness
class
C
a
b
|
a
->
b
where
foo
::
a
->
b
instance
C
Bool
Int
where
foo
False
=
0
foo
True
=
1
-- bar :: C a b => a -> b
bar
::
C
Bool
b
=>
Bool
->
b
bar
=
foo
data
T
=
T
deriving
Show
baz
::
Show
T
=>
T
->
String
baz
=
show
{-
class Zip a b c | a c -> b, b c -> a
class Zip1 a b c | a c -> b
class Zip2 a b c | b c -> a
class (Zip1 a b c, Zip2 a b c) => Zip3 a b c
f :: Zip3 a b c => a -> b -- qué instancia?
f = undefined
-}
-- open vs closed
class
Nat
n
where
type
Add
n
m
instance
Nat
Zero
where
type
Add
Zero
m
=
m
instance
Nat
n
=>
Nat
(
Suc
n
)
where
type
Add
(
Suc
n
)
m
=
Suc
(
Add
n
m
)
class
Nat
n
=>
VecBound
n
where
data
NVec
n
a
appVec
::
NVec
n
a
->
NVec
m
a
->
NVec
(
Add
n
m
)
a
instance
VecBound
Zero
where
data
NVec
Zero
a
=
Nil
appVec
Nil
ys
=
ys
instance
VecBound
n
=>
VecBound
(
Suc
n
)
where
data
NVec
(
Suc
n
)
a
=
Cons
a
(
NVec
n
a
)
appVec
(
Cons
x
xs
)
ys
=
Cons
x
(
appVec
xs
ys
)
-- data types vs type synonyms
merge
::
(
Collection
c1
,
Collection
c2
,
Elem
c1
~
Elem
c2
)
=>
c1
->
c2
->
c2
merge
=
undefined
-- index :: Array e -> Int -> e
-- index = undefined
-- typechecking with equalities
-- and type synonyms
-- f :: c ~ Int => Elem c -> c -> Int
-- f _ _ = 0
--
-- main = print (f undefined [])
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