Well I figured out that I should be using the State monad, but it seems not
to be behaving like most of the tutorials on the web. Did the syntax
change? ....
type SankeyState = (P2,CircleFrac,Double)
type SankeyPic = (Trail R2, Trail R2)
type Sankey = State SankeyState SankeyPic
saBlank :: Sankey
saBlank = return (mempty, mempty)
saVia :: Double -> Sankey
saVia l = state (
\(p,a,w) ->
(
( hrule l # translateX 0.5 # translateY (w/2) # rotate a
, hrule (-l) # translateX 0.5 # translateY (-w/2) # rotate a
)
, (p .+^ (unitX # scale l # rotate a),a,w)
)
)
saTo :: Sankey
saTo = state (
\(p,a,w) ->
(
( hrule w # translateX (w/2) # translateY (w/2) # rotate
(-1/8::CircleFrac) # scale (0.7071) # rotate a # translate (origin .-. p)
, hrule (-w) # translateX (w/2) # translateY (-w/2) # rotate
(1/8::CircleFrac) # scale (0.7071) # rotate a # translate (origin .-. p)
)
, (p,a,w)
)
)
x :: SankeyPic
x = evalState ( saTo ) (origin, 0, 5) -- works and looks nice
--x = evalState ( saVia 10 ) (origin, 0, 5) -- works but not much
to see
--x = evalState ( saVia 10 >>= saTo ) (origin, 0, 5) -- barfs with
something unintelligible
pic3 = strokeT ( close ( fst x <> snd x)) # fc red
The unintelligible bit is:
Couldn't match expected type `SankeyPic
-> StateT SankeyState
Data.Functor.Identity.Identity SankeyPic'
with actual type `Sankey'
In the second argument of `(>>=)', namely `saTo'
In the first argument of `evalState', namely `(saVia 10 >>= saTo)'
In the expression: evalState (saVia 10 >>= saTo) (origin, 0, 5)
TIA,
Adrian.
On 31 May 2013 21:16, Adrian May
Hi all,
Take a look at this disaster area, or just scroll down to where I come to the point...
=======================
type SankeyBrain = (P2,CircleFrac,Double) -- like a turtle plus width data SankeyWorld tb = SankeyWorld ((Trail R2,Trail R2),tb) --outgoing and returning trails, plus brain
emptySankey :: SankeyWorld SankeyBrain emptySankey = SankeyWorld ((mempty,mempty),(origin,0,0))
sankeyFrom:: CircleFrac -> Double -> SankeyWorld SankeyBrain sankeyFrom a w = SankeyWorld ((mempty,mempty),(p2 (0,0),a,w)) -- kick off with an angle and width
instance Monad SankeyWorld where return a = SankeyWorld ((mempty,mempty), a) --never use this (SankeyWorld l) >>= f = let (SankeyWorld r) = f (snd l) in -- out = left then right, return = right then left SankeyWorld ( (((fst.fst) l <> (fst.fst) r),((snd.fst) r <> (snd.fst) l)),(snd r) )
sankeyVia :: Double -> SankeyBrain -> SankeyWorld SankeyBrain sankeyVia d (p,a,w) = let -- draw parallel lines and move them into place l1 = hrule 1 # scaleX d # translateX (d/2) # translateY (w/2) # rotate a # translate (origin .-. p) l2 = hrule 1 # scaleX (-d) # translateX (d/2) # translateY (-w/2) # rotate a # translate (origin .-. p) in SankeyWorld ( ( l1 , l2 ) , ( p .+^ (unitX # scale d # rotate a), a, w) )
sankeyTo :: SankeyBrain -> SankeyWorld SankeyBrain sankeyTo (p,a,w) = SankeyWorld ( --arrow at the end of the flow ( hrule w # translateX (w/2) # translateY (w/2) # rotate (-1/8::CircleFrac) # scale (0.7071) # rotate a # translate (origin .-. p) , hrule (-w) # translateX (w/2) # translateY (-w/2) # rotate (1/8::CircleFrac) # scale (0.7071) # rotate a # translate (origin .-. p) ), (p,a,w))
sankeyTurn r a' (p,a,w) = let (outr, inr, qu) = if a'>=0 then (r, -w-r, -0.25::CircleFrac) else (-w-r, r, 0.25::CircleFrac) in SankeyWorld ( -- turn a corner with nice round edges ( arc' outr (a+qu) (a+a'+qu) # translate (unitY # rotate (a+a' )# scale w) , arc' inr (a+a'+qu) (a+qu) # translate (unitY # rotate (a+a' )# scale w) ),(p,a+a',w))
-- bump... sankeySplit :: [(Double, SankeyBrain -> SankeyWorld SankeyBrain)] -> SankeyBrain -> SankeyWorld SankeyBrain sankeySplit fs (p,a,w) = let (placed,_) = ( foldl ( \(l,t) -> \(i,c) -> ( l++[( ( p .+^ (unitY # rotate a # scale (((t+i/2)-0.5)*w)), a, w*i) ,c )],t+i) ) ([],0) fs ) in foldl (\(SankeyWorld ((lo,lr),lb)) -> \(SankeyWorld ((ro,rr),rb)) -> SankeyWorld ( ( lo <> ro , rr <> lr ), rb ) ) emptySankey $ map (\(b,f)-> f b) placed
SankeyWorld ((turtb,turta),_) = {- This is the bit that fails: sankeyFrom 0 5 >>= sankeyVia 5 >>= sankeySplit [ (0.3, sankeyVia 10 ) , (0.7, sankeyVia 15 ) ] -} sankeyFrom 0 5 >>= sankeyVia 5 >>= sankeyTurn 1 (-0.125) >>= sankeyVia 10
= sankeyTurn 1 (0.25) >>= sankeyTo -- >>= turn 0.25 >>= forward 10 >>= turn 0.25 >>= forward 20 >>= turn 0.25 >>= forward 10
pic3 = (strokeT (close ( turtb<>turta) )) # fc red
======================
The idea is that SankeyWorld is a monad containing two trails (outbound and inbound) and a turtle-like state. I bind it onto functions like SankeyBrain -> SankeyWorld, whereby >>= passes the state across. >>= draws the left hand outward trail, then the right hand outward trail, then the right hand inward trail, then the left hand inward trail, so it all makes a nice polygon and I can colour it in.
sankeyFrom angle width is already a monad, sankeyVia length is such a function and I could have sankeyTo contain () in place of the brain (i.e. state) cos you're not supposed to continue from it.
The tricky bit is splitting the flow. I want a function that takes the brain, splits the width according to named shares and shoves each share into a function SankeyBrain -> SankeyWorld that might have lots more stages and splits downwind.
It was all going fine until I discovered that if I can say m >>= f, then I can't say f >>= f. So I don't know how to write the bits after the split. Silly me. But what should I do instead to model Sankey diagrams splitting? Is MonadPlus the trick? If so, am I gonna have to make [SankeyWorld] a monad as well?
TIA, Adrian.
PS: I rarely have any use for the polymorphism of the parameter to Monad. In this case, it's a SankeyBrain, end of story. Is there a simpler kind of monad that doesn't throw this complication at me?