> {-# LANGUAGE NoMonomorphismRestriction #-}
> import Diagrams.Prelude
> import Data.List
> import Data.Ord (comparing)
> import Data.Function (on)
> import Data.Maybe (fromMaybe)
> import Data.Colour.SRGB (sRGB24read)
>
> colors = map sRGB24read["#000000", "#D1DBBD", "#91AA9D", "#3E606F", "#193441", "#000000"]
A subset is represented by the size of the parent set paired with the
list of elements in the subset. `isSubset` tests whether one set is a
subset of another; `subsetsBySize` lists all the subsets of a set of
size `n`, grouped according to size.
> data Subset = Subset Int [Int]
>
> (Subset _ elts1) `isSubset` (Subset _ elts2) = all (`elem` elts2) elts1
>
> subsetsBySize :: Int -> [[Subset]]
> subsetsBySize n = map (map (Subset n))
> . groupBy ((==) `on` length)
> . sortBy (comparing length)
> . subsequences
> $ [1..n]
Draw the elements of a subset, by drawing a colored square for each
element present, and leaving a blank space for absent elements.
> drawElts n elts = hcat
> . map (\i -> if i `elem` elts
> then drawElt i
> else strutX 1
> )
> $ [1..n]
>
> drawElt e = unitSquare # fc (colors !! e) # lw thin
Draw a subset by drawing a dashed rectangle around the elements. Note
that we also assign a name to the rectangle, corresponding to the
elements it contains, which we use to draw connections between subsets
later.
> drawSet (Subset n elts) = ( drawElts n elts # centerXY
> <> rect (fromIntegral n + 0.5) 1.5
> # dashingG [0.2,0.2] 0
> # lw thin
> # named elts
> )
Draw a Hasse diagram by drawing subsets grouped by size in rows, and
connecting each set to its subsets in the row below. [See the user
manual](http://projects.haskell.org/diagrams/manual/diagrams-manual.html#named-subdiagrams)
for a more in-depth explanation of how names are used to connect subsets.
> hasseRow = centerX . hcat' (with & sep .~ 2) . map drawSet
>
> hasseDiagram n = setsD # drawConnections # centerXY
> where setsD = vcat' (with & sep .~ fromIntegral n)
> . map hasseRow
> . reverse
> $ subsets
> subsets = subsetsBySize n
> drawConnections = applyAll connections
To generate all the connections, we apply `connectSome` to each pair
of adjacent rows, which calls `connect` on those pairs where one is a
subset of the other.
> connections = concat $ zipWith connectSome subsets (tail subsets)
> connectSome subs1 subs2 = [ connect s1 s2 | s1 <- subs1
> , s2 <- subs2
> , s1 `isSubset` s2 ]
Connect two subsets by looking up the subdiagrams named with their
elements, and drawing a line from the upper boundary of one to the
lower boundary of the other.
> connect (Subset _ elts1) (Subset _ elts2) =
> withNames [elts1, elts2] $ \[b1, b2] ->
> beneath ((boundaryFrom b1 unitY ~~ boundaryFrom b2 unit_Y) # lw thin)
>
> example = pad 1.1 $ hasseDiagram 4