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module Complex where
data Repr = Normal | Polar
data Complex :: Repr -> Type where
Complex :: forall r . Float -> Float -> Complex r
repr :: forall r . Complex r -> Repr
repr @r _ = r
normal :: Float -> Float -> Complex Normal
normal a b = Complex a b
polar :: Float -> Float -> Complex Polar
polar a b = Complex a b
-- TODO: Write tests that checks if the derived type is the same as the given
cabs :: forall r . Complex r -> Float
cabs @'Normal (Complex a b) = sqrt (a*a + b*b)
cabs @'Polar (Complex r _phi) = r
toPolar :: Complex Normal -> Complex Polar
toPolar (Complex x y) =
if x > 0.0 then polar r (atan (y / x))
else if x < 0.0 && y >= 0.0 then polar r (atan (y / x) + pi)
else if x < 0.0 && y < 0.0 then polar r (atan (y / x) - pi)
else if x == 0.0 && y >= 0.0 then polar r ( pi / 2.0)
else if x == 0.0 && y < 0.0 then polar r (-pi / 2.0)
else undefined -- x == 0.0 && y == 0.0
where
r = sqrt (x*x + y*y)
{- TODO:
if x > 0.0 then polar r (arctan (y / x))
if x < 0.0 && y >= 0.0 then polar r (arctan (y / x) + pi)
!Failed complex
"./testdata/accept/complex.lc" (line 32, column 10):
unexpected reserved word "if"
expecting lowercase ident or uppercase ident
-}
{- TODO:
!Failed complex
can't find: error in "./testdata/accept/complex.lc" (line 33, column 9):
else (error "indeterminate polar complex number")
^^^^^
-}
{-
toPolar (Complex x y)
| x > 0.0 && y >= 0.0 = polar r 0
| x > 0.0 && y < 0.0 = polar r 0
where
r = sqrt (x*x + y*y)
!Failed complex
"./testdata/accept/complex.lc" (line 26, column 4):
unexpected reserved operator "|"
expecting symbols
-}
{-
toPolar c@(Complex a b) = undefined
!Crashed mandel
../src/LambdaCube/Compiler/Infer.hs:(1162,1)-(1164,98): Non-exhaustive patterns in function addLams'
-}
toNormal :: Complex Polar -> Complex Normal
toNormal (Complex r phi) = Complex (r * cos phi) (r * sin phi)
{-
convert :: forall r0 . forall r1 . Complex r0 -> Complex r1
convert @'Normal @'Normal c = c
convert @'Polar @'Polar c = c
convert @'Normal @'Polar c = toPolar c
convert @'Polar @'Normal c = toNormal c
!Failed mandel
checkMetas lam: \(a : V0~Polar) (b : Normal~V1) (c : 'Num ('MatVecElem 'Float)) (d : 'Num ('MatVecElem
'Float)) (e : Polar~V4) (f : Normal~V5) (g : V6~Normal) {h:'Repr} (i : h~V8) (j : 'Complex V9) ->
'ReprCase (\'Repr -> 'Complex V11) ('ReprCase (\'Repr -> 'Complex V11) (labend j) (labend (toPolar j))
h) ('ReprCase (\'Repr -> 'Complex Normal) (labend (toNormal c d j)) (labend j) h) V10
-}
{-
convert :: forall r0 . forall r1 . Complex r0 -> Complex r1
convert @'Normal @'Normal = id
convert @'Polar @'Polar = id
convert @'Normal @'Polar = toPolar
convert @'Polar @'Normal = toNormal
!Failed mandel
type error: can not unify
Polar
with
Normal
in "./testdata/accept/mandel.lc" (line 51, column 27):
convert @'Normal @'Polar = toPolar
^^^^^^^
-}
{- ISSUE: Which is expected, which is found???
crepr :: forall r . Complex r -> r
crepr @r (Complex _ _) = r
!Failed mandel
type error: can not unify
Type
with
'Repr
r should have type X, but it has Y
-}
-- ISSUE: It compiles
it_should_fail (Complex r _ _ _ _) = r
add :: forall r0 . forall r1 . Complex r0 -> Complex r1 -> Complex r0
add @'Normal @'Normal (Complex a b) (Complex c d) = Complex (a + c) (b + d)
{-
add @'Polar @'Polar c0 c1 = toPolar (add (toNormal c0) (toNormal c1))
!Failed mandel
checkMetas lam: \(a : Polar~V0) (b : 'Num ('MatVecElem 'Float)) (c : 'Num ('MatVecElem 'Float))
{d:'Repr} (e : Polar~d) (f : V5~Polar) (g : 'Complex V6) (h : 'Complex d) -> 'ReprCase (\'Repr ->
'Complex Polar) ('ReprCase (\'Repr -> 'Complex Polar) ('ComplexCase (\'Repr 'Complex k -> 'Complex
Polar) (\{m:'Repr} n:'Float o:'Float -> 'ComplexCase (\'Repr 'Complex p -> 'Complex Polar) (\{r:'Repr}
s:'Float t:'Float -> labend (Complex Polar (PrimAdd 'Float V19 n s) (PrimAdd 'Float V18 o t))) d h) V8
g) (labend (undefined ('Complex Polar))) d) ('ReprCase (\'Repr -> 'Complex Polar) (labend (undefined
('Complex Polar))) (labend (toPolar (V9 Normal Normal (toNormal V11 V10 g) (toNormal b c h)))) d) V8
-}
mul :: forall r0 r1 . Complex r0 -> Complex r1 -> Complex r0
mul @'Normal @'Normal (Complex a b) (Complex c d) = Complex (a*c - b*d) (b*c + a*d)
{- TODO: The hidden parameters should not be shown... or a configuration level...
{a : 'Num ('MatVecElem 'Float)} -> {b : 'Num ('MatVecElem 'Float)} -> {c : 'Num ('MatVecElem 'Float)} ->
{d : 'Num ('MatVecElem 'Float)} -> {e : 'Num ('MatVecElem 'Float)} -> {f : 'Num ('MatVecElem 'Float)} ->
'Complex Normal -> 'Complex Normal -> 'Complex Normal
-}
s :: Complex r -> Complex r
s c = (mul c c) `add` c
-- ISSUE: More application consumes lot of memory
s4 c = s (s (s (s c)))
iter = s4
mandel c = cabs (iter c) < 2.0
{- PROPOSAL:
main should be called screenOut
main :: Output
main = ...
-}
|
