implement a basic brush store

* each stroke stores the brushes it uses by reference,
    so that one can interactively edit brushes
    and see the strokes be updated in real-time
  * when writing to a file, we retrive the brush code
    from the reference, and include that information statically

MetaBrush.cabal

@@ -122,6 +122,7 @@ executable MetaBrush
       , MetaBrush.Asset.TickBox
       , MetaBrush.Asset.Tools
       , MetaBrush.Asset.WindowIcons
+      , MetaBrush.Brush
       , MetaBrush.Context
       , MetaBrush.Document
       , MetaBrush.Document.Draw
@@ -175,6 +176,10 @@ executable MetaBrush
           ^>= 1.4.2.1
       , ghc-typelits-knownnat
           ^>= 0.7.3
+      , gi-cairo-render
+          ^>= 0.0.1
+      , gi-cairo-connector
+          ^>= 0.0.1
       , gi-gdk
           >= 3.0.22 && < 3.1
       , gi-gio
@@ -185,10 +190,10 @@ executable MetaBrush
           ^>= 2.0.24
       , gi-gtk
           >= 3.0.35 && < 3.1
-      , gi-cairo-render
+      , gi-gtksource
-          ^>= 0.0.1
+          >= 3.0.23 && < 3.1
-      , gi-cairo-connector
+      , hashable
-          ^>= 0.0.1
+          ^>= 1.3.0.0
       , haskell-gi-base
           ^>= 0.24.3
       , lens
@@ -207,5 +212,7 @@ executable MetaBrush
           >= 1.2.3.1 && < 1.2.5
       , tree-view
           ^>= 0.5
+      , unordered-containers
+          >= 0.2.11 && < 0.2.14
       , waargonaut
           ^>= 0.8.0.1

app/Main.hs

@@ -65,6 +65,8 @@ import qualified GI.Gtk as GTK
 -- lens
 import Control.Lens
   ( (.~), set )
+import Control.Lens.At
+  ( at )
 
 -- stm
 import qualified Control.Concurrent.STM as STM
@@ -82,6 +84,16 @@ import qualified SuperRecord
 import qualified Data.Text as Text
   ( pack )
 
+-- transformers
+import Control.Monad.Trans.Reader
+  ( runReaderT )
+
+-- unordered-containers
+import Data.HashMap.Strict
+  ( HashMap )
+import qualified Data.HashMap.Strict as HashMap
+  ( fromList )
+
 -- MetaBrush
 import Math.Bezier.Cubic.Fit
   ( FitParameters(..) )
@@ -99,6 +111,8 @@ import MetaBrush.Asset.Colours
   ( getColours )
 import MetaBrush.Asset.Logo
   ( drawLogo )
+import MetaBrush.Brush
+  ( Brush, newBrushReference )
 import MetaBrush.Context
   ( UIElements(..), Variables(..)
   , Modifier(..)
@@ -133,7 +147,7 @@ import MetaBrush.UI.Viewport
   ( Viewport(..), Ruler(..), createViewport )
 import MetaBrush.Unique
   ( newUniqueSupply
-  , Unique, unsafeUnique
+  , Unique, freshUnique
   , uniqueMapFromList
   )
 import MetaBrush.Util
@@ -164,18 +178,26 @@ main = do
   uniqueSupply <- newUniqueSupply
 
   circleBrush <- Asset.Brushes.circle uniqueSupply
+  circleBrushUnique <- runReaderT freshUnique uniqueSupply
+  docUnique         <- runReaderT freshUnique uniqueSupply
+  strokeUnique      <- runReaderT freshUnique uniqueSupply
 
   let
+
+    testBrushes :: HashMap Brush Unique
+    testBrushes = HashMap.fromList
+      [ ( circleBrush, circleBrushUnique ) ]
+
     testDocuments :: Map Unique DocumentHistory
     testDocuments = fmap newHistory $ uniqueMapFromList
-      [ emptyDocument "Test" ( unsafeUnique 0 )
+      [ emptyDocument "Test" docUnique
       & ( field' @"documentContent" . field' @"strokes" ) .~
         [ Stroke
-          { strokeName    = "Stroke 1"
+          { strokeName     = "Stroke 1"
-          , strokeVisible = True
+          , strokeVisible  = True
-          , strokeUnique  = unsafeUnique 10
+          , strokeUnique   = strokeUnique
-          , strokeBrush   = circleBrush
+          , strokeBrushRef = newBrushReference @'[ "r" SuperRecord.:= Double ] circleBrushUnique
-          , strokeSpline  =
+          , strokeSpline   =
             Spline
               { splineStart  = mkPoint ( Point2D 10 -20 ) 2
               , splineCurves = OpenCurves $ Seq.fromList
@@ -186,6 +208,7 @@ main = do
               }
           }
         ]
+      & ( field' @"documentBrushes" . at circleBrushUnique ) .~ ( Just circleBrush )
       ]
         where
           mkPoint :: Point2D Double -> Double -> PointData ( Super.Rec '[ "r" SuperRecord.:= Double ] )
@@ -193,6 +216,7 @@ main = do
 
   activeDocumentTVar <- STM.newTVarIO @( Maybe Unique )                            Nothing
   openDocumentsTVar  <- STM.newTVarIO @( Map Unique DocumentHistory )              testDocuments
+  brushesTVar        <- STM.newTVarIO @( HashMap Brush Unique )                    testBrushes
   mousePosTVar       <- STM.newTVarIO @( Maybe ( Point2D Double ) )                Nothing
   mouseHoldTVar      <- STM.newTVarIO @( Maybe HoldAction )                        Nothing
   modifiersTVar      <- STM.newTVarIO @( Set Modifier )                            Set.empty
@@ -204,14 +228,14 @@ main = do
   showGuidesTVar     <- STM.newTVarIO @Bool                                        True
   maxHistorySizeTVar <- STM.newTVarIO @Int                                         1000
   fitParametersTVar  <- STM.newTVarIO @FitParameters
-    ( FitParameters
+                          ( FitParameters
-      { maxSubdiv  = 6
+                            { maxSubdiv  = 6
-      , nbSegments = 12
+                            , nbSegments = 12
-      , dist_tol   = 5e-3
+                            , dist_tol   = 5e-3
-      , t_tol      = 1e-4
+                            , t_tol      = 1e-4
-      , maxIters   = 100
+                            , maxIters   = 100
-      }
+                            }
-    )
+                          )
 
   -- Put all these stateful variables in a record for conciseness.
   let

src/app/MetaBrush/Action.hs

@@ -184,7 +184,9 @@ instance HandleAction OpenFile where
     void $ GTK.nativeDialogRun fileChooser
     filePaths <- GTK.fileChooserGetFilenames fileChooser
     for_ filePaths \ filePath -> do
-      mbDoc <- loadDocument uniqueSupply filePath
+      knownBrushes <- STM.atomically $ STM.readTVar brushesTVar
+      ( mbDoc, knownBrushes' ) <- loadDocument uniqueSupply knownBrushes filePath
+      STM.atomically ( STM.writeTVar brushesTVar knownBrushes' )
       case mbDoc of
         Left errMessage -> warningDialog window filePath errMessage
         Right doc -> do
@@ -233,7 +235,9 @@ instance HandleAction OpenFolder where
       when exists do
         filePaths <- listDirectory folderPath
         for_ filePaths \ filePath -> when ( takeExtension filePath == ".mb" ) do
-          mbDoc <- loadDocument uniqueSupply ( folderPath </> filePath )
+          knownBrushes <- STM.atomically $ STM.readTVar brushesTVar
+          ( mbDoc, knownBrushes' ) <- loadDocument uniqueSupply knownBrushes ( folderPath </> filePath )
+          STM.atomically ( STM.writeTVar brushesTVar knownBrushes' )
           case mbDoc of
             Left errMessage -> warningDialog window filePath errMessage
             Right doc -> do

src/app/MetaBrush/Asset/Brushes.hs

@@ -9,16 +9,6 @@
 
 module MetaBrush.Asset.Brushes where
 
--- base
-import Data.Kind
-  ( Type )
-import Data.Type.Equality
-  ( (:~:)(Refl) )
-
--- superrecord
-import qualified SuperRecord
-  ( (:=) )
-
 -- text
 import Data.Text
   ( Text )
@@ -26,10 +16,8 @@ import qualified Data.Text as Text
   ( unpack )
 
 -- MetaBrush
-import MetaBrush.Document
+import MetaBrush.Brush
   ( Brush(..) )
-import MetaBrush.MetaParameter.AST
-  ( BrushFunction, STypesI(sTypesI), eqTys )
 import MetaBrush.MetaParameter.Driver
   ( SomeBrushFunction(..), interpretBrush )
 import MetaBrush.Unique
@@ -37,11 +25,8 @@ import MetaBrush.Unique
 
 --------------------------------------------------------------------------------
 
-circle
+circle :: UniqueSupply -> IO Brush
-  :: forall circleBrushFields
+circle uniqueSupply = mkBrush uniqueSupply name code
-  .  ( circleBrushFields ~ '[ "r" SuperRecord.:= Double ] )
-  => UniqueSupply -> IO ( Brush circleBrushFields )
-circle uniqueSupply = mkBrush @circleBrushFields uniqueSupply name code
   where
     name, code :: Text
     name = "Circle"
@@ -57,11 +42,8 @@ circle uniqueSupply = mkBrush @circleBrushFields uniqueSupply name code
      \          -- (-r  ,-r*c) -- (-r*c,-r  ) -> ( 0,-r)\n\
      \          -- ( r*c,-r  ) -- ( r  ,-r*c) ->   .   ]"
 
-rounded
+rounded :: UniqueSupply -> IO Brush
-  :: forall roundedBrushFields
+rounded uniqueSupply = mkBrush uniqueSupply name code
-  .  ( roundedBrushFields ~ '[ ] ) -- TODO
-  => UniqueSupply -> IO ( Brush roundedBrushFields )
-rounded uniqueSupply = mkBrush @roundedBrushFields uniqueSupply name code
   where
     name, code :: Text
     name = "Rounded quadrilateral"
@@ -88,21 +70,11 @@ rounded uniqueSupply = mkBrush @roundedBrushFields uniqueSupply name code
 
 --------------------------------------------------------------------------------
 
-mkBrush
+mkBrush :: UniqueSupply -> Text -> Text -> IO Brush
-  :: forall ( givenBrushFields :: [ Type ] )
-  .  STypesI givenBrushFields
-  => UniqueSupply -> Text -> Text
-  -> IO ( Brush  givenBrushFields )
 mkBrush uniqSupply brushName brushCode = do
   ( mbBrush, _ ) <- interpretBrush uniqSupply brushCode
   case mbBrush of
-    Left err -> error ( "Could not interpret '" <> Text.unpack brushName <> "' brush:\n" <> show err )
+    Left err ->
-    Right ( SomeBrushFunction ( brushFunction :: BrushFunction inferredBrushFields ) ) ->
+      error ( "Could not interpret '" <> Text.unpack brushName <> "' brush:\n" <> show err )
-      case eqTys @givenBrushFields @inferredBrushFields of
+    Right ( SomeBrushFunction brushFunction ) ->
-        Just Refl -> pure ( BrushData { brushName, brushCode, brushFunction } )
+      pure ( BrushData { brushName, brushCode, brushFunction } )
-        Nothing   ->
-          error
-            ( "Incorrect record type for '" <> Text.unpack brushName <> "' brush:\n\
-              \Expected: " <> show ( sTypesI @givenBrushFields ) <> "\n\
-              \  Actual: " <> show ( sTypesI @inferredBrushFields )
-            )

src/app/MetaBrush/Brush.hs

@@ -0,0 +1,370 @@
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE ConstraintKinds     #-}
+{-# LANGUAGE DataKinds           #-}
+{-# LANGUAGE FlexibleContexts    #-}
+{-# LANGUAGE FlexibleInstances   #-}
+{-# LANGUAGE GADTs               #-}
+{-# LANGUAGE MagicHash           #-}
+{-# LANGUAGE NamedFieldPuns      #-}
+{-# LANGUAGE PolyKinds           #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications    #-}
+{-# LANGUAGE TypeOperators       #-}
+
+{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
+
+module MetaBrush.Brush
+  ( Brush(..), BrushReference(..), newBrushReference
+  , SomeBrushFields(..), SomeFieldSType(..), reflectBrushFieldsNoDups
+  )
+  where
+
+-- base
+import Data.Kind
+  ( Type )
+import Data.List
+  ( intersect )
+import Data.Proxy
+  ( Proxy )
+import Data.Type.Equality
+  ( (:~:)(Refl) )
+import GHC.Exts
+  ( Proxy#, proxy# )
+import GHC.TypeLits
+  ( KnownSymbol, SomeSymbol(..)
+  , someSymbolVal, symbolVal'
+  )
+import GHC.TypeNats
+  ( KnownNat, SomeNat(..), someNatVal, type (-) )
+import Unsafe.Coerce
+  ( unsafeCoerce )
+
+-- deepseq
+import Control.DeepSeq
+  ( NFData(..), deepseq )
+
+-- groups
+import Data.Group
+  ( Group )
+
+-- hashable
+import Data.Hashable
+  ( Hashable(..) )
+
+-- superrecord
+import qualified SuperRecord as Super
+  ( Rec )
+import qualified SuperRecord
+  ( Has, RecTy, (:=)
+  , RecSize, RecApply(..), RecVecIdxPos, UnsafeRecBuild(..)
+  , TraversalCHelper, RemoveAccessTo, Intersect
+  )
+import SuperRecord
+  ( ConstC, Tuple22C )
+
+-- text
+import Data.Text
+  ( Text )
+import qualified Data.Text as Text
+  ( pack, unpack )
+
+-- unordered-containers
+import Data.HashMap.Strict
+  ( HashMap )
+import qualified Data.HashMap.Strict as HashMap
+  ( fromList, lookup )
+
+-- MetaBrush
+import Math.Module
+  ( Module )
+import Math.Vector2D
+  ( Point2D )
+import {-# SOURCE #-} MetaBrush.Document.Serialise
+  ( Serialisable )
+import MetaBrush.MetaParameter.AST
+  ( SType(..), STypeI(..), SomeSType(..), STypes(..), STypesI(..), someSTypes
+  , Adapted, BrushFunction
+  , MapFields, UniqueField, UseFieldsInBrush
+  )
+import MetaBrush.MetaParameter.Interpolation
+  ( Interpolatable(..), MapDiff, HasDiff', HasTorsor )
+import MetaBrush.Unique
+  ( Unique )
+
+--------------------------------------------------------------------------------
+
+data Brush where
+  BrushData
+    :: forall brushFields
+    .  ( STypesI brushFields )
+    =>
+      { brushName     :: !Text
+      , brushCode     :: !Text
+      , brushFunction :: !( BrushFunction brushFields )
+      }
+    -> Brush
+
+instance Show Brush where
+  show ( BrushData { brushName } ) = Text.unpack brushName
+instance NFData Brush where
+  rnf ( BrushData { brushName, brushCode } )
+    = deepseq brushCode
+    $ rnf brushName
+instance Eq Brush where
+  BrushData name1 code1 _ == BrushData name2 code2 _ = name1 == name2 && code1 == code2
+instance Ord Brush where
+  compare ( BrushData name1 code1 _ ) ( BrushData name2 code2 _ ) = compare ( name1, code1 ) ( name2, code2 )
+instance Hashable Brush where
+  hashWithSalt salt ( BrushData { brushName, brushCode } ) =
+    hashWithSalt ( hashWithSalt salt brushName ) brushCode
+
+data BrushReference pointFields where
+  NoBrush :: BrushReference pointFields
+  BrushReference
+    :: forall brushFields pointFields usedFields brushParams usedParams
+    .  ( brushParams ~ Super.Rec brushFields, STypesI brushFields
+       , usedParams  ~ Super.Rec usedFields
+       , Interpolatable usedParams
+       , Adapted brushFields pointFields usedFields
+       )
+    => Proxy# brushFields
+    -> Unique
+    -> BrushReference pointFields
+instance Show ( BrushReference pointFields ) where
+  show NoBrush = "NoBrush"
+  show ( BrushReference ( _ :: Proxy# brushFields ) uniq ) =
+    "BrushReference @(" <> show ( sTypesI @brushFields ) <> ") " <> show uniq
+instance NFData ( BrushReference pointFields ) where
+  rnf NoBrush = ()
+  rnf ( BrushReference _ unique ) = rnf unique
+
+
+newBrushReference
+  :: forall brushFields pointFields
+  .  ( STypesI brushFields, STypesI pointFields )
+  => Unique
+  -> BrushReference pointFields
+newBrushReference uniq = case proveAdapted @brushFields @pointFields of
+  Dict -> BrushReference ( proxy# :: Proxy# brushFields ) uniq
+
+--------------------------------------------------------------------------------
+-- Instance dictionary passing machinery.
+
+data Dict c where
+  Dict :: c => Dict c
+
+proveAdapted
+  :: forall brushFields givenFields usedFields drts_used
+  .  ( STypesI brushFields, STypesI givenFields
+     , usedFields ~ ( brushFields `SuperRecord.Intersect` givenFields )
+     , drts_used ~ MapDiff usedFields
+     )
+  => Dict ( Adapted brushFields givenFields usedFields
+          , Interpolatable ( Super.Rec usedFields )
+          )
+proveAdapted = case go ( sTypesI @brushFields ) of { Dict -> Dict }
+  where
+
+    brushFields, givenFields, usedFields :: [ ( Text, SomeSType ) ]
+    brushFields = someSTypes @brushFields
+    givenFields = someSTypes @givenFields
+    usedFields  = intersect brushFields givenFields
+
+    nbUsedFields :: Int
+    nbUsedFields = length usedFields
+
+    givenIxFieldsMap, usedIxFieldsMap :: HashMap Text Int
+    givenIxFieldsMap = listToEndIndexMap givenFields
+    usedIxFieldsMap  = listToEndIndexMap usedFields
+
+    go :: forall lts_brush lts_used dlts_used
+       .  ( lts_used ~ ( lts_brush `SuperRecord.Intersect` givenFields )
+          , dlts_used ~ MapDiff lts_used
+          )
+       => STypes lts_brush
+       -> Dict 
+            ( SuperRecord.UnsafeRecBuild usedFields lts_used ( SuperRecord.Has givenFields )
+            , SuperRecord.RecApply ( MapFields UniqueField brushFields ) ( MapFields UniqueField lts_brush ) ( UseFieldsInBrush usedFields )
+            , SuperRecord.UnsafeRecBuild drts_used dlts_used ( ConstC Monoid )
+            , SuperRecord.UnsafeRecBuild drts_used dlts_used ( ConstC ( Module Double ) )
+            , SuperRecord.RecApply drts_used dlts_used ( Tuple22C ( ConstC ( Module Double ) ) ( SuperRecord.Has drts_used ) )
+            , SuperRecord.RecApply drts_used dlts_used ( Tuple22C ( ConstC Semigroup )         ( SuperRecord.Has drts_used ) )
+            , SuperRecord.RecApply drts_used dlts_used ( Tuple22C ( ConstC Group )             ( SuperRecord.Has drts_used ) )
+            , SuperRecord.RecApply drts_used dlts_used ( HasDiff' usedFields )
+            , SuperRecord.TraversalCHelper dlts_used usedFields drts_used ( HasTorsor usedFields )
+            )
+    go STyNil
+      | SomeNat ( _ :: Proxy nbUsedFields ) <- someNatVal ( fromIntegral nbUsedFields )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize usedFields :~: nbUsedFields )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize drts_used  :~: nbUsedFields )
+      = Dict
+    go sTyCons@STyCons
+      | SomeNat ( _ :: Proxy nbUsedFields ) <- someNatVal ( fromIntegral nbUsedFields )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize usedFields :~: nbUsedFields )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize drts_used  :~: nbUsedFields )
+      , ( _ :: STypes ( ( k SuperRecord.:= v ) ': tail_lts_brush ) ) <- sTyCons
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize ( MapFields UniqueField brushFields ) :~: SuperRecord.RecSize brushFields )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k ( MapFields UniqueField brushFields ) :~: Just ( UniqueField v ) )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k ( MapFields UniqueField tail_lts_brush ) :~: MapFields UniqueField tail_lts_brush )
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k ( MapFields UniqueField brushFields ) :~: SuperRecord.RecSize tail_lts_brush )
+      , let
+          k :: Text
+          k = Text.pack ( symbolVal' ( proxy# :: Proxy# k ) )
+      = case HashMap.lookup k usedIxFieldsMap of
+          Just k_used_indexFromEnd
+            | SomeNat ( _ :: Proxy k_used_indexFromEnd ) <- someNatVal ( fromIntegral k_used_indexFromEnd )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k lts_used   :~: k_used_indexFromEnd )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k usedFields :~: k_used_indexFromEnd )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k drts_used  :~: k_used_indexFromEnd )
+            , Just k_given_indexFromEnd <- HashMap.lookup k givenIxFieldsMap
+            , SomeNat ( _ :: Proxy k_given_indexFromEnd ) <- someNatVal ( fromIntegral k_given_indexFromEnd )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k givenFields :~: k_given_indexFromEnd )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k lts_used    :~: Just v )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k usedFields  :~: Just v )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k givenFields :~: Just v )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k drts_used   :~: Just ( Diff v ) )
+            , ( _ :: Proxy# tail_lts_used  ) <- ( proxy# :: Proxy# ( tail_lts_brush `SuperRecord.Intersect` givenFields ) )
+            , ( _ :: Proxy# tail_dlts_used ) <- ( proxy# :: Proxy# ( MapDiff tail_lts_used ) )
+            , Refl <- ( unsafeCoerce Refl :: lts_used :~: ( ( k SuperRecord.:= v ) ': tail_lts_used ) )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize tail_lts_used :~: ( SuperRecord.RecSize lts_used - 1 ) )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize tail_dlts_used :~: SuperRecord.RecSize tail_lts_used )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k tail_dlts_used :~: tail_dlts_used )
+            , Just Dict <- interpolatableDict @v
+            -> case go ( sTypesI @tail_lts_brush ) of { Dict -> Dict }
+          _
+            | Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k lts_used   :~: Nothing )
+            , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k usedFields :~: Nothing )
+            , Refl <- ( unsafeCoerce Refl :: lts_used :~: ( tail_lts_brush `SuperRecord.Intersect` givenFields ) )
+            -> case go ( sTypesI @tail_lts_brush ) of { Dict -> Dict }
+
+interpolatableDict :: forall t. STypeI t => Maybe ( Dict ( Interpolatable t ) )
+interpolatableDict =
+  case sTypeI @t of
+    STyDouble -> Just Dict
+    sTyPoint@STyPoint
+      | ( _ :: SType ( Point2D c ) ) <- sTyPoint
+      , STyDouble <- sTypeI @c
+      -> Just Dict
+    _ -> Nothing
+
+listToEndIndexMap :: ( Eq k, Hashable k ) => [ ( k, v ) ] -> HashMap k Int
+listToEndIndexMap kvs =
+  HashMap.fromList
+    $ zipWith ( \ ( fieldName, _ ) index -> ( fieldName, lg - index - 1 ) )
+        kvs
+        [ 0 .. ]
+  where
+    lg :: Int
+    lg = length kvs
+
+-- | Reflects a list of brush fields to the type level.
+--
+-- Assumes the input list has no duplicate field names,
+-- but they don't have to be sorted.
+reflectBrushFieldsNoDups :: [ ( Text, SomeFieldSType ) ] -> SomeBrushFields
+reflectBrushFieldsNoDups = fromSomeBrushFieldsList . mkBrushFieldsList
+  where
+    mkBrushFieldsList :: [ ( Text, SomeFieldSType ) ] -> SomeBrushFieldsList
+    mkBrushFieldsList [] = SomeBrushFieldsList NilFields
+    mkBrushFieldsList ( ( k, SomeFieldSType ( _ :: Proxy# v ) ) : kvs )
+      | SomeBrushFieldsList ( kvs_list :: BrushFieldsList kvs ) <- mkBrushFieldsList kvs
+      , SomeSymbol ( _ :: Proxy k ) <- someSymbolVal ( Text.unpack k )
+      -- deduce RecSize ( MapDiff kvs ) ~ RecSize kvs
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize ( MapDiff kvs ) :~: SuperRecord.RecSize kvs )
+      -- compute indexing into record list (with SuperRecord, the index is the number of fields remaining)
+      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k ( ( k SuperRecord.:= v ) : kvs ) :~: SuperRecord.RecSize kvs )
+      = SomeBrushFieldsList ( ConsFields ( proxy# :: Proxy# k ) ( proxy# :: Proxy# v ) kvs_list )
+
+    fromSomeBrushFieldsList :: SomeBrushFieldsList -> SomeBrushFields
+    fromSomeBrushFieldsList ( SomeBrushFieldsList ( kvs :: BrushFieldsList kvs ) ) = case go @kvs kvs of
+      SomeClassyBrushFieldsList ( _ :: Proxy# kvs ) ( _ :: Proxy# kvs ) ->
+        SomeBrushFields ( proxy# :: Proxy# kvs )
+      where
+        go :: forall ( rts :: [ Type ] ) ( lts :: [ Type ] )
+           .  ( STypesI rts, KnownNat ( SuperRecord.RecSize rts ), KnownNat ( SuperRecord.RecSize ( MapDiff rts ) ) )
+           => BrushFieldsList lts -> SomeClassyBrushFieldsList rts lts
+        go NilFields =
+          SomeClassyBrushFieldsList ( proxy# :: Proxy# rts ) ( proxy# :: Proxy# '[] )
+        go ( ConsFields ( _ :: Proxy# k ) ( _ :: Proxy# a ) kvs' )
+          | ( SomeClassyBrushFieldsList _ ( _ :: Proxy# lts' ) ) <- go @rts kvs'
+          -- Assert some facts that result from the field names being distinct:
+          --   - current field name does not re-occur later on
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k lts' :~: lts' )
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k ( MapDiff lts' ) :~: MapDiff lts' )
+          --   - looking up the type associated with the current field name returns the current type
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k rts :~: Just a )
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k ( MapDiff rts ) :~: Just ( Diff a ) )
+          --   - MapDiff preserves length
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize ( MapDiff lts' ) :~: SuperRecord.RecSize lts' )
+          --   - compute the index (which is the number of fields remaining, i.e. the indexing starts counting from 0 from the right)
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k rts :~: SuperRecord.RecSize lts' )
+          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k ( MapDiff rts ) :~: SuperRecord.RecSize lts' )
+          = SomeClassyBrushFieldsList ( proxy# :: Proxy# rts ) ( proxy# :: Proxy# ( ( k SuperRecord.:= a ) ': lts' ) )
+
+
+-- | Existential type over an allowed record field type used in brushes, such as Double and Point2D Double.
+data SomeFieldSType where
+  SomeFieldSType
+    :: ( STypeI a, Show a, NFData a, Serialisable a, Interpolatable a )
+    => Proxy# a -> SomeFieldSType
+
+-- | Existential type for allowed fields of a brush record.
+data SomeBrushFields where
+  SomeBrushFields
+    :: forall kvs rec
+    . ( STypesI kvs
+      , rec ~ Super.Rec kvs
+      , Show rec, NFData rec
+      , Interpolatable rec
+      , Serialisable rec
+      )
+    => Proxy# kvs -> SomeBrushFields
+
+instance Show SomeBrushFields where
+  show ( SomeBrushFields ( _ :: Proxy# kvs ) ) = show ( sTypesI @kvs )
+
+-- | Auxiliary datatype used to create a proof that record fields have the required instances.
+data BrushFieldsList kvs where
+  NilFields  :: BrushFieldsList '[]
+  ConsFields
+    ::
+      ( KnownSymbol k
+      , Show a, NFData a, Serialisable a
+      , Interpolatable a
+      , STypesI kvs
+      , KnownNat ( SuperRecord.RecSize kvs )
+      , SuperRecord.Has ( k SuperRecord.:= a ': kvs ) k a
+      )
+    => Proxy# k -> Proxy# a -> BrushFieldsList kvs -> BrushFieldsList ( k SuperRecord.:= a ': kvs )
+
+-- | Existential type used in the process of proving that record fields have the required instances.
+data SomeBrushFieldsList where
+  SomeBrushFieldsList
+    :: ( STypesI kvs
+       , KnownNat ( SuperRecord.RecSize kvs )
+       , KnownNat ( SuperRecord.RecSize ( MapDiff kvs ) )
+       )
+    => BrushFieldsList kvs -> SomeBrushFieldsList
+
+-- | Type used to backtrack instance resolution in the SuperRecord library,
+-- to witness the required typeclass instances by induction on the record fields.
+data SomeClassyBrushFieldsList rts lts where
+  SomeClassyBrushFieldsList
+    :: forall rts lts drts dlts
+    . ( drts ~ MapDiff rts
+      , dlts ~ MapDiff lts
+      , KnownNat ( SuperRecord.RecSize rts )
+      , KnownNat ( SuperRecord.RecSize drts )
+      , SuperRecord.UnsafeRecBuild rts lts ( ConstC Serialisable )
+      , SuperRecord.UnsafeRecBuild drts dlts ( ConstC ( Module Double ) )
+      , SuperRecord.UnsafeRecBuild drts dlts ( ConstC Monoid )
+      , SuperRecord.RecApply rts lts ( ConstC Show )
+      , SuperRecord.RecApply rts lts ( ConstC NFData )
+      , SuperRecord.RecApply rts lts ( ConstC Serialisable )
+      , SuperRecord.RecApply drts dlts ( Tuple22C ( ConstC ( Module Double ) ) ( SuperRecord.Has drts ) )
+      , SuperRecord.RecApply drts dlts ( Tuple22C ( ConstC Semigroup )         ( SuperRecord.Has drts ) )
+      , SuperRecord.RecApply drts dlts ( Tuple22C ( ConstC Group )             ( SuperRecord.Has drts ) )
+      , SuperRecord.RecApply drts dlts ( HasDiff' rts )
+      , SuperRecord.TraversalCHelper dlts rts drts ( HasTorsor rts )
+      )
+    => Proxy# rts -> Proxy# lts -> SomeClassyBrushFieldsList rts lts

src/app/MetaBrush/Context.hs

@@ -28,6 +28,10 @@ import qualified GI.Gtk as GTK
 import qualified Control.Concurrent.STM.TVar as STM
   ( TVar )
 
+-- unordered-containers
+import Data.HashMap.Strict
+  ( HashMap )
+
 -- MetaBrush
 import Math.Bezier.Cubic.Fit
   ( FitParameters )
@@ -35,6 +39,8 @@ import Math.Vector2D
   ( Point2D )
 import MetaBrush.Asset.Colours
   ( Colours )
+import MetaBrush.Brush
+  ( Brush )
 import MetaBrush.Document.Draw
   ( DrawAnchor )
 import MetaBrush.Document.History
@@ -73,6 +79,7 @@ data Variables
   { uniqueSupply       :: !UniqueSupply
   , activeDocumentTVar :: !( STM.TVar ( Maybe Unique )                            )
   , openDocumentsTVar  :: !( STM.TVar ( Map Unique DocumentHistory )              )
+  , brushesTVar        :: !( STM.TVar ( HashMap Brush Unique )                    )
   , mousePosTVar       :: !( STM.TVar ( Maybe ( Point2D Double ) )                )
   , mouseHoldTVar      :: !( STM.TVar ( Maybe HoldAction )                        )
   , modifiersTVar      :: !( STM.TVar ( Set Modifier )                            )

src/app/MetaBrush/Document.hs

@@ -8,6 +8,7 @@
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE GADTs                 #-}
 {-# LANGUAGE LambdaCase            #-}
+{-# LANGUAGE MagicHash             #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE NamedFieldPuns        #-}
 {-# LANGUAGE OverloadedStrings     #-}
@@ -26,7 +27,6 @@ module MetaBrush.Document
   , emptyDocument
   , Stroke(..), StrokeSpline, _strokeSpline, overStrokeSpline
   , PointData(..), BrushPointData(..), DiffPointData(..)
-  , Brush(..), emptyBrush
   , FocusState(..), Hoverable(..), HoverContext(..)
   , Guide(..)
   , _selection, _coords, coords
@@ -39,8 +39,6 @@ import Data.Coerce
   ( coerce )
 import Data.Functor.Identity
   ( Identity(..) )
-import Data.Kind
-  ( Type )
 import Data.Semigroup
   ( Arg(..), Min(..), ArgMin )
 import GHC.Generics
@@ -81,14 +79,10 @@ import Control.Concurrent.STM
 -- superrecord
 import qualified SuperRecord as Super
   ( Rec )
-import qualified SuperRecord
-  ( Intersect, rnil )
 
 -- text
 import Data.Text
   ( Text )
-import qualified Data.Text as Text
-  ( unpack )
 
 -- transformers
 import Control.Monad.Trans.Reader
@@ -96,7 +90,7 @@ import Control.Monad.Trans.Reader
 
 -- MetaBrush
 import Math.Bezier.Spline
-  ( Spline(..), KnownSplineType, Curves(..) )
+  ( Spline(..), KnownSplineType )
 import Math.Bezier.Stroke
   ( CachedStroke )
 import Math.Module
@@ -107,10 +101,12 @@ import Math.Module
   )
 import Math.Vector2D
   ( Point2D(..), Vector2D(..) )
+import MetaBrush.Brush
+  ( Brush, BrushReference )
 import {-# SOURCE #-} MetaBrush.Document.Serialise
   ( Serialisable(..) )
 import MetaBrush.MetaParameter.AST
-  ( STypesI, Adapted, AdaptableFunction(..), BrushFunction )
+  ( STypesI(..) )
 import MetaBrush.MetaParameter.Interpolation
   ( Interpolatable(..) ) -- + orphan instances
 import MetaBrush.UI.Viewport
@@ -145,6 +141,7 @@ data Document
   , zoomFactor      :: !Double
   , documentUnique  :: Unique
   , documentContent :: !DocumentContent
+  , documentBrushes :: !( Map Unique Brush )
   }
   deriving stock    ( Show, Generic )
   deriving anyclass NFData
@@ -166,28 +163,23 @@ data Stroke where
   Stroke
     :: ( KnownSplineType clo
        , pointParams ~ Super.Rec pointFields, STypesI pointFields
-       , brushParams ~ Super.Rec brushFields, STypesI brushFields
-       , usedParams  ~ Super.Rec usedFields , STypesI usedFields
-       , usedFields  ~ ( brushFields `SuperRecord.Intersect` pointFields )
-       , Show brushParams, NFData brushParams
        , Show pointParams, NFData pointParams
        , Interpolatable pointParams
-       , Interpolatable usedParams
        , Serialisable pointParams
-       , Adapted brushFields pointFields usedFields
        )
     =>
-      { strokeName    :: Text
+      { strokeName     :: !Text
-      , strokeVisible :: !Bool
+      , strokeVisible  :: !Bool
-      , strokeUnique  :: Unique
+      , strokeUnique   :: Unique
-      , strokeBrush   :: Brush brushFields
+      , strokeBrushRef :: !( BrushReference pointFields )
-      , strokeSpline  :: !( StrokeSpline clo pointParams )
+      , strokeSpline   :: !( StrokeSpline clo pointParams )
       }
     -> Stroke
 deriving stock instance Show Stroke
 instance NFData Stroke where
-  rnf ( Stroke { strokeName, strokeVisible, strokeUnique, strokeSpline } )
+  rnf ( Stroke { strokeName, strokeVisible, strokeUnique, strokeBrushRef, strokeSpline } )
     = deepseq strokeSpline
+    . deepseq strokeBrushRef
     . deepseq strokeUnique
     . deepseq strokeVisible
     $ rnf strokeName
@@ -224,21 +216,6 @@ overStrokeSpline
 overStrokeSpline f = coerce ( _strokeSpline @Identity ( coerce . f ) )
 
 
-data Brush ( brushFields :: [ Type ] )
-  = BrushData
-  { brushName     :: !Text
-  , brushCode     :: !Text
-  , brushFunction :: !( BrushFunction brushFields )
-  }
-
-instance Show ( Brush brushFields ) where
-  show ( BrushData { brushName } ) = Text.unpack brushName
-
--- Brush parameters using open records.
-emptyBrush :: Brush '[]
-emptyBrush = BrushData "Empty brush" ""
-  ( AdaptableFunction ( const SuperRecord.rnil, const $ Spline ( Point2D 0 0 ) NoCurves ) )
-
 data PointData params
   = PointData
   { pointCoords :: !( Point2D Double )
@@ -285,6 +262,7 @@ emptyDocument docName unique =
       , strokes        = []
       , guides         = Map.empty
       }
+    , documentBrushes = Map.empty
     }
 
 --------------------------------------------------------------------------------

src/app/MetaBrush/Document/Draw.hs

@@ -65,10 +65,11 @@ import Math.Module
   ( squaredNorm )
 import Math.Vector2D
   ( Point2D(..), Vector2D(..) )
+import MetaBrush.Brush
+  ( BrushReference(NoBrush) )
 import MetaBrush.Document
   ( Document(..), Stroke(..), StrokeSpline
   , FocusState(..), PointData(..)
-  , emptyBrush
   , _selection, _strokeSpline
   , coords, overStrokeSpline
   )
@@ -118,11 +119,11 @@ getOrCreateDrawAnchor uniqueSupply c doc@( Document { zoomFactor } ) =
         newStroke :: Stroke
         newStroke =
           Stroke
-            { strokeName    = "Stroke " <> uniqueText uniq
+            { strokeName     = "Stroke " <> uniqueText uniq
-            , strokeVisible = True
+            , strokeVisible  = True
-            , strokeUnique  = uniq
+            , strokeUnique   = uniq
-            , strokeSpline  = newSpline
+            , strokeSpline   = newSpline
-            , strokeBrush   = emptyBrush
+            , strokeBrushRef = NoBrush
             }
         newDoc' :: Document
         newDoc'

src/app/MetaBrush/Document/Serialise.hs

@@ -1,6 +1,4 @@
-{-# LANGUAGE AllowAmbiguousTypes  #-}
 {-# LANGUAGE BlockArguments       #-}
-{-# LANGUAGE ConstraintKinds      #-}
 {-# LANGUAGE DataKinds            #-}
 {-# LANGUAGE FlexibleContexts     #-}
 {-# LANGUAGE GADTs                #-}
@@ -12,12 +10,9 @@
 {-# LANGUAGE PolyKinds            #-}
 {-# LANGUAGE ScopedTypeVariables  #-}
 {-# LANGUAGE TypeApplications     #-}
-{-# LANGUAGE TypeFamilies         #-}
 {-# LANGUAGE TypeOperators        #-}
 {-# LANGUAGE UndecidableInstances #-}
 
-{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
-
 module MetaBrush.Document.Serialise
   ( Serialisable(..)
   , documentToJSON, documentFromJSON
@@ -27,7 +22,7 @@ module MetaBrush.Document.Serialise
 
 -- base
 import Control.Arrow
-  ( (&&&) )
+  ( (&&&), first )
 import Control.Monad
   ( unless )
 import qualified Data.Bifunctor as Bifunctor
@@ -38,22 +33,12 @@ import Data.Functor.Contravariant
   ( contramap )
 import Data.Functor.Identity
   ( Identity(..) )
-import Data.Kind
-  ( Type )
-import Data.List
-  ( sortBy )
-import Data.Ord
-  ( comparing )
-import Data.Proxy
-  ( Proxy(Proxy) )
 import Data.Type.Equality
   ( (:~:)(Refl) )
-import Data.Typeable
-  ( Typeable, eqT )
 import GHC.Exts
   ( Proxy#, proxy# )
 import GHC.TypeLits
-  ( symbolVal', KnownSymbol, SomeSymbol(..), someSymbolVal, sameSymbol )
+  ( symbolVal', KnownSymbol )
 import GHC.TypeNats
   ( KnownNat )
 import Unsafe.Coerce
@@ -77,16 +62,12 @@ import qualified Data.ByteString.Lazy.Builder as Lazy.ByteString.Builder
 import Data.Map.Strict
   ( Map )
 import qualified Data.Map.Strict as Map
-  ( fromList, elems )
+  ( elems, empty, fromList, insert, lookup )
 import Data.Sequence
   ( Seq )
 import qualified Data.Sequence as Seq
   ( fromList )
 
--- deepseq
-import Control.DeepSeq
-  ( NFData(..) )
-
 -- directory
 import System.Directory
   ( canonicalizePath, createDirectoryIfMissing, doesFileExist )
@@ -99,10 +80,6 @@ import System.FilePath
 import Data.Generics.Product.Typed
   ( HasType(typed) )
 
--- groups
-import Data.Group
-  ( Group )
-
 -- lens
 import Control.Lens
   ( view )
@@ -123,13 +100,12 @@ import qualified Control.Concurrent.STM as STM
 import qualified SuperRecord as Super
   ( Rec )
 import qualified SuperRecord
-  ( Has, RecTy, (:=), FldProxy(..)
+  ( FldProxy(..)
-  , RecSize, RecApply(..), RecVecIdxPos, UnsafeRecBuild(..)
+  , RecSize, RecApply(..), UnsafeRecBuild(..)
-  , TraversalCHelper, RemoveAccessTo, Intersect
   , reflectRec
   )
 import SuperRecord
-  ( ConstC, Tuple22C )
+  ( ConstC )
 
 -- text
 import Data.Text
@@ -140,10 +116,18 @@ import qualified Data.Text as Text
 -- transformers
 import Control.Monad.IO.Class
   ( MonadIO(liftIO) )
-import Control.Monad.Trans.Reader
-  ( runReaderT )
 import Control.Monad.Trans.Class
   ( MonadTrans(lift) )
+import Control.Monad.Trans.Reader
+  ( runReaderT )
+import Control.Monad.Trans.State.Strict
+  ( StateT, runStateT, get, put )
+
+-- unordered-containers
+import Data.HashMap.Strict
+  ( HashMap )
+import qualified Data.HashMap.Strict as HashMap
+  ( foldrWithKey', insert, lookup )
 
 -- waargonaut
 import qualified Waargonaut.Attoparsec as JSON.Decoder
@@ -172,8 +156,12 @@ import qualified Waargonaut.Prettier as JSON
   ( prettyJson )
 import qualified Waargonaut.Prettier as TonyMorris
   ( Natural )
+import qualified Waargonaut.Types.JObject as JSON
+  ( MapLikeObj )
 import Waargonaut.Types.Json
   ( Json )
+import qualified Waargonaut.Types.Whitespace as JSON
+  ( WS )
 
 -- MetaBrush
 import qualified Math.Bezier.Cubic as Cubic
@@ -186,26 +174,25 @@ import Math.Bezier.Spline
   )
 import Math.Bezier.Stroke
   ( CachedStroke(..) )
-import Math.Module
-  ( Module )
 import Math.Vector2D
   ( Point2D(..), Vector2D(..), Segment )
+import MetaBrush.Brush
+  ( Brush(..), BrushReference(..), newBrushReference
+  , SomeBrushFields(..), SomeFieldSType(..), reflectBrushFieldsNoDups
+  )
 import MetaBrush.Document
   ( Document(..), DocumentContent(..), Guide(..)
   , Stroke(..), StrokeSpline
-  , PointData(..), Brush(..) , FocusState(..)
+  , PointData(..), FocusState(..)
   )
 import MetaBrush.MetaParameter.AST
-  ( SType(..), STypeI(..), STypes(..), STypesI(..)
+  ( SType(..), STypeI(..), STypesI(..)
   , SomeSType(..), someSTypes
-  , Adapted, AdaptableFunction(..), BrushFunction
+  , AdaptableFunction(..), BrushFunction
-  , MapFields, UniqueField, UseFieldsInBrush
   , eqTy, eqTys
   )
 import MetaBrush.MetaParameter.Driver
   ( SomeBrushFunction(..), interpretBrush )
-import MetaBrush.MetaParameter.Interpolation
-  ( Interpolatable(..), MapDiff, HasDiff', HasTorsor )
 import MetaBrush.Unique
   ( Unique, UniqueSupply, freshUnique )
 
@@ -226,9 +213,16 @@ documentToJSON
       four = unsafeCoerce ( 4 :: Integer )
 
 -- | Parse a document from JSON (given by a strict bytestring).
-documentFromJSON :: UniqueSupply -> Maybe FilePath -> Strict.ByteString -> IO ( Either JSON.DecodeError Document )
+--
-documentFromJSON uniqueSupply mfp
+-- Updates the store of brushes by adding any new brushes contained in the document.
-  = fmap ( Bifunctor.first fst )
+documentFromJSON
+  :: UniqueSupply -> HashMap Brush Unique
+  -> Maybe FilePath
+  -> Strict.ByteString
+  -> IO ( Either JSON.DecodeError Document, HashMap Brush Unique )
+documentFromJSON uniqueSupply brushUniques mfp
+  = fmap ( first $ Bifunctor.first fst )
+  . ( `runStateT` brushUniques )
   . JSON.Decoder.decodeAttoparsecByteString ( decodeDocument uniqueSupply mfp )
 
 --------------------------------------------------------------------------------
@@ -247,12 +241,14 @@ saveDocument path doc = do
   atomicReplaceFile Nothing path' ( documentToJSON doc )
 
 -- | Load a MetaBrush document.
-loadDocument :: UniqueSupply -> FilePath -> IO ( Either String Document )
+--
-loadDocument uniqueSupply fp = do
+-- Updates the store of brushes by adding any new brushes contained in the document.
+loadDocument :: UniqueSupply -> HashMap Brush Unique -> FilePath -> IO ( Either String Document, HashMap Brush Unique )
+loadDocument uniqueSupply brushUniques fp = do
   exists <- doesFileExist fp
   if exists
-  then Bifunctor.first show <$> ( documentFromJSON uniqueSupply ( Just fp ) =<< Strict.ByteString.readFile fp )
+  then first ( Bifunctor.first show ) <$> ( documentFromJSON uniqueSupply brushUniques ( Just fp ) =<< Strict.ByteString.readFile fp )
-  else pure ( Left $ "No file at " <> fp )
+  else pure ( Left $ "No file at " <> fp, brushUniques )
 
 --------------------------------------------------------------------------------
 
@@ -348,21 +344,21 @@ encodeCurve
 encodeCurve  encodePtData = case ssplineType @clo of
   SOpen   -> JSON.Encoder.mapLikeObj \case
     LineTo          ( NextPoint p1 ) _ ->
-        JSON.Encoder.atKey' "p1"     encodePtData p1
+        JSON.Encoder.atKey' "p1" encodePtData p1
     Bezier2To    p1 ( NextPoint p2 ) _ ->
-        JSON.Encoder.atKey' "p1"     encodePtData p1
+        JSON.Encoder.atKey' "p1" encodePtData p1
-      . JSON.Encoder.atKey' "p2"     encodePtData p2
+      . JSON.Encoder.atKey' "p2" encodePtData p2
     Bezier3To p1 p2 ( NextPoint p3 ) _ ->
-        JSON.Encoder.atKey' "p1"     encodePtData p1
+        JSON.Encoder.atKey' "p1" encodePtData p1
-      . JSON.Encoder.atKey' "p2"     encodePtData p2
+      . JSON.Encoder.atKey' "p2" encodePtData p2
-      . JSON.Encoder.atKey' "p3"     encodePtData p3
+      . JSON.Encoder.atKey' "p3" encodePtData p3
   SClosed -> JSON.Encoder.mapLikeObj \case
     LineTo          BackToStart _ -> id
     Bezier2To    p1 BackToStart _ ->
-        JSON.Encoder.atKey' "p1"     encodePtData p1
+        JSON.Encoder.atKey' "p1" encodePtData p1
     Bezier3To p1 p2 BackToStart _ ->
-        JSON.Encoder.atKey' "p1"     encodePtData p1
+        JSON.Encoder.atKey' "p1" encodePtData p1
-      . JSON.Encoder.atKey' "p2"     encodePtData p2
+      . JSON.Encoder.atKey' "p2" encodePtData p2
 
 decodeCurve
   :: forall clo ptData m
@@ -551,6 +547,7 @@ encodeSomeSType = JSON.Encoder.mapLikeObj \ ( SomeSType ( _ :: Proxy# ty ) ) ->
       -> JSON.Encoder.atKey' "tag" JSON.Encoder.text "adaptableFun"
        . JSON.Encoder.atKey' "fields" encodeFieldTypes ( someSTypes @kvs )
        . JSON.Encoder.atKey' "res"    encodeSomeSType  ( SomeSType ( proxy# :: Proxy# res ) )
+
 {-
 decodeSomeSType :: Monad m => JSON.Decoder m SomeSType
 decodeSomeSType = do
@@ -583,32 +580,33 @@ decodeSomeSType = do
       ( SomeBrushFields ( _ :: Proxy# kvs ) ) <- JSON.Decoder.atKey "fields" decodeFieldTypes
       ( SomeSType       ( _ :: Proxy# a   ) ) <- JSON.Decoder.atKey "res"    decodeSomeSType
       pure ( SomeSType ( proxy# :: Proxy# ( AdaptableFunction kvs a ) ) )
+    _ -> throwError ( JSON.ParseFailed $ "Unsupported record field type with tag " <> tag )
 -}
+
 decodeSomeFieldSType :: Monad m => JSON.Decoder m SomeFieldSType
 decodeSomeFieldSType = do
-  tag <- JSON.Decoder.atKey "tag" JSON.Decoder.text
+  tag   <- JSON.Decoder.atKey "tag" JSON.Decoder.text
   case tag of
     "double" -> pure ( SomeFieldSType ( proxy# :: Proxy# Double ) )
     "point"  -> do
       ( SomeFieldSType ( _ :: Proxy# a ) ) <- JSON.Decoder.atKey "coords" decodeSomeFieldSType
-      case eqT @a @Double of
+      case eqTy @a @Double of
         Just Refl -> pure ( SomeFieldSType ( proxy# :: Proxy# ( Point2D Double ) ) )
         Nothing   -> throwError ( JSON.ParseFailed "Point2D: non-Double coordinate type" )
     _ -> throwError ( JSON.ParseFailed $ "Unsupported record field type with tag " <> tag )
 
 
-encodeFieldTypes :: Monad f => JSON.Encoder f ( [ ( Text, SomeSType ) ] )
+
+encodeFieldTypes :: Monad f => JSON.Encoder f [ ( Text, SomeSType ) ]
 encodeFieldTypes = JSON.Encoder.keyValueTupleFoldable encodeSomeSType
 
 decodeFieldTypes :: Monad m => JSON.Decoder m SomeBrushFields
 decodeFieldTypes = do
   fields <- JSON.Decoder.objectAsKeyValues JSON.Decoder.text decodeSomeFieldSType
   let
-    sortedFields :: [ ( Text, SomeFieldSType ) ]
-    sortedFields = sortBy ( comparing fst ) fields
     duplicates :: [ Text ]
-    duplicates = duplicatesAcc [] [] sortedFields
+    duplicates = duplicatesAcc [] [] fields
-    duplicatesAcc :: [ Text ] -> [ Text ] -> [ ( Text, SomeFieldSType ) ] -> [ Text ]
+    duplicatesAcc :: [ Text ] -> [ Text ] -> [ ( Text, whatever ) ] -> [ Text ]
     duplicatesAcc _    dups [] = dups
     duplicatesAcc seen dups ( ( k, _ ) : kvs )
       | k `elem` seen
@@ -616,89 +614,37 @@ decodeFieldTypes = do
       | otherwise
       = duplicatesAcc ( k : seen ) dups kvs
   case duplicates of
-    []    -> pure ( mkBrushFields sortedFields )
+    []    -> pure ( reflectBrushFieldsNoDups fields )
     [dup] -> throwError ( JSON.ParseFailed $ "Duplicate field name " <> dup <> " in brush record type" )
     dups  -> throwError ( JSON.ParseFailed $ "Duplicate field names in brush record type:\n" <> Text.unwords dups )
 
-  where
-
-    mkBrushFields :: [ ( Text, SomeFieldSType ) ] -> SomeBrushFields
-    mkBrushFields = fromSomeBrushFieldsList . mkBrushFieldsList
-
-    mkBrushFieldsList :: [ ( Text, SomeFieldSType ) ] -> SomeBrushFieldsList
-    mkBrushFieldsList [] = SomeBrushFieldsList NilFields
-    mkBrushFieldsList ( ( k, SomeFieldSType ( _ :: Proxy# v ) ) : kvs )
-      | SomeBrushFieldsList ( kvs_list :: BrushFieldsList kvs ) <- mkBrushFieldsList kvs
-      , SomeSymbol ( _ :: Proxy k ) <- someSymbolVal ( Text.unpack k )
-      -- deduce RecSize ( MapDiff kvs ) ~ RecSize kvs
-      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize ( MapDiff kvs ) :~: SuperRecord.RecSize kvs )
-      -- compute indexing into record list (with SuperRecord, the index is the number of fields remaining)
-      , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k ( ( k SuperRecord.:= v ) : kvs ) :~: SuperRecord.RecSize kvs )
-      = SomeBrushFieldsList ( ConsFields ( proxy# :: Proxy# k ) ( proxy# :: Proxy# v ) kvs_list )
-
-    fromSomeBrushFieldsList :: SomeBrushFieldsList -> SomeBrushFields
-    fromSomeBrushFieldsList ( SomeBrushFieldsList ( kvs :: BrushFieldsList kvs ) ) = case go @kvs kvs of
-      SomeClassyBrushFieldsList ( _ :: Proxy# kvs ) ( _ :: Proxy# kvs ) ->
-        SomeBrushFields ( proxy# :: Proxy# kvs )
-      where
-        go :: forall ( rts :: [ Type ] ) ( lts :: [ Type ] )
-           .  ( STypesI rts, KnownNat ( SuperRecord.RecSize rts ), KnownNat ( SuperRecord.RecSize ( MapDiff rts ) ) )
-           => BrushFieldsList lts -> SomeClassyBrushFieldsList rts lts
-        go NilFields =
-          SomeClassyBrushFieldsList ( proxy# :: Proxy# rts ) ( proxy# :: Proxy# '[] )
-        go ( ConsFields ( _ :: Proxy# k ) ( _ :: Proxy# a ) kvs' )
-          | ( SomeClassyBrushFieldsList _ ( _ :: Proxy# lts' ) ) <- go @rts kvs'
-          -- Assert some facts that result from the field names being distinct:
-          --   - current field name does not re-occur later on
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k lts' :~: lts' )
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k ( MapDiff lts' ) :~: MapDiff lts' )
-          --   - looking up the type associated with the current field name returns the current type
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k rts :~: Just a )
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k ( MapDiff rts ) :~: Just ( Diff a ) )
-          --   - MapDiff preserves length
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize ( MapDiff lts' ) :~: SuperRecord.RecSize lts' )
-          --   - compute the index (which is the number of fields remaining, i.e. the indexing starts counting from 0 from the right)
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k rts :~: SuperRecord.RecSize lts' )
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k ( MapDiff rts ) :~: SuperRecord.RecSize lts' )
-          = SomeClassyBrushFieldsList ( proxy# :: Proxy# rts ) ( proxy# :: Proxy# ( ( k SuperRecord.:= a ) ': lts' ) )
 
 
-
+encodeBrush :: Applicative f => JSON.Encoder f Brush
-encodeBrush :: Applicative f => JSON.Encoder f ( Brush brushParams )
+encodeBrush = JSON.Encoder.mapLikeObj
-encodeBrush = JSON.Encoder.mapLikeObj \ ( BrushData { brushName, brushCode } ) ->
+  \ ( BrushData { brushName, brushCode } ) ->
     JSON.Encoder.atKey' "name" JSON.Encoder.text brushName
   . JSON.Encoder.atKey' "code" JSON.Encoder.text brushCode
 
-decodeBrush
+decodeBrush :: MonadIO m => UniqueSupply -> JSON.Decoder m Brush
-  :: forall m flds. ( MonadIO m, STypesI flds )
-  => UniqueSupply
-  -> JSON.Decoder m ( Brush flds )
 decodeBrush uniqSupply = do
   brushName <- JSON.Decoder.atKey "name" JSON.Decoder.text
   brushCode <- JSON.Decoder.atKey "code" JSON.Decoder.text
   ( mbBrush, _ ) <- lift ( liftIO $ interpretBrush uniqSupply brushCode )
   case mbBrush of
     Left err -> throwError ( JSON.ParseFailed ( "Failed to interpret brush code:\n" <> ( Text.pack $ show err ) ) )
-    Right ( SomeBrushFunction ( brushFunction :: BrushFunction brushParams ) ) ->
+    Right ( SomeBrushFunction brushFunction ) ->
-      case eqTys @flds @brushParams of
+      pure ( BrushData { brushName, brushCode, brushFunction } )
-        Just Refl -> pure ( BrushData { brushName, brushCode, brushFunction } )
-        Nothing   ->
-          throwError
-            ( JSON.ParseFailed $
-                "Brush has unexpected input record type:\n\
-                \Expected: " <> Text.pack ( show ( sTypesI @flds ) ) <> "\n\
-                \  Actual: " <> Text.pack ( show ( sTypesI @brushParams ) )
-            )
 
 
 
-encodeStroke :: Monad f => JSON.Encoder f Stroke
+encodeStroke :: Monad f => Map Unique Brush -> JSON.Encoder f Stroke
-encodeStroke = JSON.Encoder.mapLikeObj 
+encodeStroke brushes = JSON.Encoder.mapLikeObj
   \ ( Stroke
       { strokeName
       , strokeVisible
       , strokeSpline = strokeSpline :: StrokeSpline clo ( Super.Rec pointFields )
-      , strokeBrush  = strokeBrush  :: Brush brushFields
+      , strokeBrushRef
       }
     ) ->
     let
@@ -706,38 +652,58 @@ encodeStroke = JSON.Encoder.mapLikeObj
       closed = case ssplineType @clo of
         SClosed -> True
         SOpen   -> False
+      mbEncodeBrush :: JSON.MapLikeObj JSON.WS Json -> JSON.MapLikeObj JSON.WS Json
+      mbEncodeBrush = case strokeBrushRef of
+        BrushReference ( _ :: Proxy# brushFields1 ) unique ->
+          case Map.lookup unique brushes of
+            Nothing -> error ( "encodeStroke: no brush with unique " <> show unique <> "in environment" )
+            Just ( brush@BrushData { brushName, brushFunction = ( _ :: BrushFunction brushFields2 ) } ) ->
+              case eqTys @brushFields1 @brushFields2 of
+                Nothing -> error
+                  ( "encodeStroke: brush '" <> Text.unpack brushName <> "' has unexpected field types.\n\
+                    \Expected: " <> show ( sTypesI @brushFields1 ) <> "\n\
+                    \  Actual: " <> show ( sTypesI @brushFields2 )
+                  )
+                Just Refl -> JSON.Encoder.atKey' "brush" encodeBrush brush
+        NoBrush -> id
     in
       JSON.Encoder.atKey' "name"        JSON.Encoder.text                strokeName
     . JSON.Encoder.atKey' "visible"     JSON.Encoder.bool                strokeVisible
     . JSON.Encoder.atKey' "closed"      JSON.Encoder.bool                closed
-    . JSON.Encoder.atKey' "brushFields" encodeFieldTypes                 ( someSTypes @brushFields )
     . JSON.Encoder.atKey' "pointFields" encodeFieldTypes                 ( someSTypes @pointFields )
-    . JSON.Encoder.atKey' "usedFields"  encodeFieldTypes                 ( someSTypes @( brushFields `SuperRecord.Intersect` pointFields ) )
+    . mbEncodeBrush
-    . JSON.Encoder.atKey' "brush"       encodeBrush                      strokeBrush
     . JSON.Encoder.atKey' "spline"      ( encodeSpline encodePointData ) strokeSpline
 
-
+decodeStroke :: forall m. MonadIO m => UniqueSupply -> JSON.Decoder ( StateT ( HashMap Brush Unique ) m ) Stroke
-
-decodeStroke :: forall m. MonadIO m => UniqueSupply -> JSON.Decoder m Stroke
 decodeStroke uniqueSupply = do
+  brushHashMap  <- lift get
   strokeName    <- JSON.Decoder.atKey "name"    JSON.Decoder.text
   strokeVisible <- JSON.Decoder.atKey "visible" JSON.Decoder.bool
   strokeUnique  <- lift ( liftIO . STM.atomically $ runReaderT freshUnique uniqueSupply )
   strokeClosed  <- JSON.Decoder.atKey "closed"  JSON.Decoder.bool
-  SomeBrushFields ( _ :: Proxy# brushFields ) <- JSON.Decoder.atKey "brushFields" decodeFieldTypes
   SomeBrushFields ( _ :: Proxy# pointFields ) <- JSON.Decoder.atKey "pointFields" decodeFieldTypes
-  SomeBrushFields ( _ :: Proxy# usedFields  ) <- JSON.Decoder.atKey "usedFields"  decodeFieldTypes
+  mbBrush       <- JSON.Decoder.atKeyOptional "brush" ( decodeBrush uniqueSupply )
-  strokeBrush   <- JSON.Decoder.atKey "brush"   ( decodeBrush @m @brushFields uniqueSupply )
+  strokeBrushRef <-
-  case proveAdapted @brushFields @pointFields @usedFields of
+    case mbBrush of
-    Nothing -> throwError ( JSON.ParseFailed "Stroke: 'usedFields' is not equal to 'brushFields `Intersect` pointFields'" )
+      Nothing -> pure NoBrush
-    Just Dict ->
+      Just ( brush@BrushData { brushFunction = _ :: BrushFunction brushFields } ) -> do
-      case strokeClosed of
+        brushUnique <-
-        True -> do
+          case HashMap.lookup brush brushHashMap of
-          strokeSpline  <- JSON.Decoder.atKey "spline"  ( decodeSpline @Closed @( PointData ( Super.Rec pointFields ) ) decodePointData )
+            Nothing -> do
-          pure ( Stroke { strokeName, strokeVisible, strokeUnique, strokeSpline, strokeBrush } )
+              brushUnique <- lift ( liftIO . STM.atomically $ runReaderT freshUnique uniqueSupply )
-        False -> do
+              lift $ put ( HashMap.insert brush brushUnique brushHashMap )
-          strokeSpline  <- JSON.Decoder.atKey "spline"  ( decodeSpline @Open   @( PointData ( Super.Rec pointFields ) ) decodePointData )
+              pure brushUnique
-          pure ( Stroke { strokeName, strokeVisible, strokeUnique, strokeSpline, strokeBrush } )
+            Just brushUnique -> pure brushUnique
+        pure ( newBrushReference @brushFields brushUnique )
+  if strokeClosed
+  then do
+    strokeSpline <- JSON.Decoder.atKey "spline" ( decodeSpline @Closed @( PointData ( Super.Rec pointFields ) ) decodePointData )
+    pure ( Stroke { strokeName, strokeVisible, strokeUnique, strokeSpline, strokeBrushRef } )
+  else do
+    strokeSpline <- JSON.Decoder.atKey "spline" ( decodeSpline @Open   @( PointData ( Super.Rec pointFields ) ) decodePointData )
+    pure ( Stroke { strokeName, strokeVisible, strokeUnique, strokeSpline, strokeBrushRef } )
+
+
 
 encodeGuide :: Applicative f => JSON.Encoder f Guide
 encodeGuide = JSON.Encoder.mapLikeObj \ ( Guide { guidePoint, guideNormal } ) ->
@@ -756,12 +722,15 @@ decodeGuide uniqueSupply = do
 
 
 
-encodeDocumentContent :: Applicative f => JSON.Encoder f DocumentContent
+encodeDocumentContent :: Applicative f => Map Unique Brush -> JSON.Encoder f DocumentContent
-encodeDocumentContent = JSON.Encoder.mapLikeObj \ ( Content { guides, strokes } ) ->
+encodeDocumentContent brushes = JSON.Encoder.mapLikeObj \ ( Content { guides, strokes } ) ->
-    JSON.Encoder.atKey' "guides"  ( encodeUniqueMap encodeGuide )    guides
+    JSON.Encoder.atKey' "guides"  ( encodeUniqueMap encodeGuide )              guides
-  . JSON.Encoder.atKey' "strokes" ( JSON.Encoder.list encodeStroke ) strokes
+  . JSON.Encoder.atKey' "strokes" ( JSON.Encoder.list $ encodeStroke brushes ) strokes
 
-decodeDocumentContent :: MonadIO m => UniqueSupply -> JSON.Decoder m DocumentContent
+decodeDocumentContent
+  :: MonadIO m
+  => UniqueSupply
+  -> JSON.Decoder ( StateT ( HashMap Brush Unique ) m ) DocumentContent
 decodeDocumentContent uniqueSupply = do
   let
     unsavedChanges :: Bool
@@ -775,189 +744,22 @@ decodeDocumentContent uniqueSupply = do
 
 
 encodeDocument :: Applicative f => JSON.Encoder f Document
-encodeDocument = JSON.Encoder.mapLikeObj \ ( Document { displayName, viewportCenter, zoomFactor, documentContent } ) ->
+encodeDocument = JSON.Encoder.mapLikeObj
-    JSON.Encoder.atKey' "name"    JSON.Encoder.text               displayName
+  \ ( Document { displayName, viewportCenter, zoomFactor, documentContent, documentBrushes } ) ->
-  . JSON.Encoder.atKey' "center"  ( encoder @( Point2D Double ) ) viewportCenter
+    JSON.Encoder.atKey' "name"    JSON.Encoder.text                         displayName
-  . JSON.Encoder.atKey' "zoom"    ( encoder @Double )             zoomFactor
+  . JSON.Encoder.atKey' "center"  ( encoder @( Point2D Double ) )           viewportCenter
-  . JSON.Encoder.atKey' "content" encodeDocumentContent           documentContent
+  . JSON.Encoder.atKey' "zoom"    ( encoder @Double )                       zoomFactor
+  . JSON.Encoder.atKey' "content" ( encodeDocumentContent documentBrushes ) documentContent
 
-decodeDocument :: MonadIO m => UniqueSupply -> Maybe FilePath -> JSON.Decoder m Document
+decodeDocument :: MonadIO m => UniqueSupply -> Maybe FilePath -> JSON.Decoder ( StateT ( HashMap Brush Unique ) m ) Document
 decodeDocument uniqueSupply mbFilePath = do
   displayName     <- JSON.Decoder.atKey "name" JSON.Decoder.text
   viewportCenter  <- JSON.Decoder.atKey "center" ( decoder @( Point2D Double ) )
   zoomFactor      <- JSON.Decoder.atKey "zoom"   ( decoder @Double )
   documentUnique  <- lift ( liftIO . STM.atomically $ runReaderT freshUnique uniqueSupply )
   documentContent <- JSON.Decoder.atKey "content" ( decodeDocumentContent uniqueSupply )
-  pure ( Document { displayName, mbFilePath, viewportCenter, zoomFactor, documentUnique, documentContent } )
+  brushUniques    <- lift get
-
+  let
---------------------------------------------------------------------------------
+    documentBrushes :: Map Unique Brush
--- Various auxiliary types.
+    documentBrushes = HashMap.foldrWithKey' ( flip Map.insert ) Map.empty brushUniques
-
+  pure ( Document { displayName, mbFilePath, viewportCenter, zoomFactor, documentUnique, documentContent, documentBrushes } )
--- | Existential type over an allowed record field type used in brushes, such as Double and Point2D Double.
-data SomeFieldSType where
-  SomeFieldSType
-    :: ( STypeI a, Show a, NFData a, Serialisable a, Interpolatable a, Typeable a )
-    => Proxy# a -> SomeFieldSType
-
--- | Existential type for allowed fields of a brush record.
-data SomeBrushFields where
-  SomeBrushFields
-    :: forall kvs rec
-    . ( STypesI kvs
-      , rec ~ Super.Rec kvs
-      , Show rec, NFData rec
-      , Interpolatable rec
-      , Serialisable rec
-      )
-    => Proxy# kvs -> SomeBrushFields
-
-instance Show SomeBrushFields where
-  show ( SomeBrushFields ( _ :: Proxy# kvs ) ) = show ( sTypesI @kvs )
-
--- | Auxiliary datatype used to create a proof that record fields have the required instances.
-data BrushFieldsList kvs where
-  NilFields  :: BrushFieldsList '[]
-  ConsFields
-    ::
-      ( KnownSymbol k
-      , Show a, NFData a, Serialisable a
-      , Interpolatable a
-      , STypesI kvs
-      , KnownNat ( SuperRecord.RecSize kvs )
-      , SuperRecord.Has ( k SuperRecord.:= a ': kvs ) k a
-      )
-    => Proxy# k -> Proxy# a -> BrushFieldsList kvs -> BrushFieldsList ( k SuperRecord.:= a ': kvs )
-
--- | Existential type used in the process of proving that record fields have the required instances.
-data SomeBrushFieldsList where
-  SomeBrushFieldsList
-    :: ( STypesI kvs
-       , KnownNat ( SuperRecord.RecSize kvs )
-       , KnownNat ( SuperRecord.RecSize ( MapDiff kvs ) )
-       )
-    => BrushFieldsList kvs -> SomeBrushFieldsList
-
--- | Type used to backtrack instance resolution in the SuperRecord library,
--- to witness the required typeclass instances by induction on the record fields.
-data SomeClassyBrushFieldsList rts lts where
-  SomeClassyBrushFieldsList
-    :: forall rts lts drts dlts
-    . ( drts ~ MapDiff rts
-      , dlts ~ MapDiff lts
-      , KnownNat ( SuperRecord.RecSize rts )
-      , KnownNat ( SuperRecord.RecSize drts )
-      , SuperRecord.UnsafeRecBuild rts lts ( ConstC Serialisable )
-      , SuperRecord.UnsafeRecBuild drts dlts ( ConstC ( Module Double ) )
-      , SuperRecord.UnsafeRecBuild drts dlts ( ConstC Monoid )
-      , SuperRecord.RecApply rts lts ( ConstC Show )
-      , SuperRecord.RecApply rts lts ( ConstC NFData )
-      , SuperRecord.RecApply rts lts ( ConstC Serialisable )
-      , SuperRecord.RecApply drts dlts ( Tuple22C ( ConstC ( Module Double ) ) ( SuperRecord.Has drts ) )
-      , SuperRecord.RecApply drts dlts ( Tuple22C ( ConstC Semigroup )         ( SuperRecord.Has drts ) )
-      , SuperRecord.RecApply drts dlts ( Tuple22C ( ConstC Group )             ( SuperRecord.Has drts ) )
-      , SuperRecord.RecApply drts dlts ( HasDiff' rts )
-      , SuperRecord.TraversalCHelper dlts rts drts ( HasTorsor rts )
-      )
-    => Proxy# rts -> Proxy# lts -> SomeClassyBrushFieldsList rts lts
-
-proveAdapted
-  :: forall brushFields givenFields usedFields
-  .  ( STypesI brushFields, STypesI givenFields, STypesI usedFields )
-  => Maybe ( Dict ( Adapted brushFields givenFields usedFields ) )
-proveAdapted
-  | Just Dict <- proveUnsafeRecBuild @usedFields
-  , Just Dict <- proveRecApply       @brushFields ( size @usedFields )
-  , Refl      <- ( unsafeCoerce Refl :: usedFields :~: ( brushFields `SuperRecord.Intersect` givenFields ) )
-  = Just Dict
-  | otherwise
-  = Nothing
-  where
-    -- Provide evidence that each field of "used" appears in "given".
-    proveUnsafeRecBuild
-      :: forall lts_used 
-      .  ( STypesI lts_used )
-      => Maybe ( Dict ( SuperRecord.UnsafeRecBuild usedFields lts_used ( SuperRecord.Has givenFields ) ) )
-    proveUnsafeRecBuild = case sTypesI @lts_used of
-      STyNil -> Just Dict
-      sTyCons@STyCons
-        | ( _ :: STypes ( k SuperRecord.:= v ': tail_lts_used ) ) <- sTyCons
-        , SomeIndex ( _ :: Proxy# i ) <- lookupIndex @k @v @givenFields
-        , Just Dict <- proveUnsafeRecBuild @tail_lts_used
-        -> Just Dict
-        | otherwise
-        -> Nothing
-
-    -- Provide evidence whether each field of "brush" appears in "used" or not.
-    -- Additionally checks that "used" is a subset of "brush".
-    proveRecApply
-      :: forall lts_brush
-      .  ( STypesI lts_brush )
-      => Int 
-      -> Maybe ( Dict ( SuperRecord.RecApply ( MapFields UniqueField brushFields ) ( MapFields UniqueField lts_brush ) ( UseFieldsInBrush usedFields ) ) )
-    proveRecApply nbUnseen = case sTypesI @lts_brush of
-      STyNil -> if nbUnseen < 1 then Just Dict else Nothing
-      sTyCons@STyCons
-        | ( _ :: STypes ( k SuperRecord.:= v ': tail_lts_brush ) ) <- sTyCons
-        , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecSize ( MapFields UniqueField brushFields ) :~: SuperRecord.RecSize brushFields )
-        , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k ( MapFields UniqueField brushFields ) :~: SuperRecord.RecSize tail_lts_brush )
-        , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k ( MapFields UniqueField brushFields ) :~: Just ( UniqueField v ) )
-        , Refl <- ( unsafeCoerce Refl :: SuperRecord.RemoveAccessTo k ( MapFields UniqueField tail_lts_brush ) :~: MapFields UniqueField tail_lts_brush )
-        -> case lookupIndex @k @v @usedFields of
-              SomeIndex ( _ :: Proxy# i ) ->
-                case proveRecApply @tail_lts_brush ( nbUnseen - 1 ) of
-                  Just Dict -> Just Dict
-                  Nothing   -> Nothing
-              NoIndex ->
-                case proveRecApply @tail_lts_brush nbUnseen of
-                  Just Dict -> Just Dict
-                  Nothing   -> Nothing
-
-data LookupResult k v kvs where
-  NoIndex
-    :: forall k v kvs
-    .  ( SuperRecord.RecTy k kvs ~ Nothing )
-    => LookupResult k v kvs
-  SomeIndex
-    :: forall k v kvs i
-    .  ( SuperRecord.RecTy k kvs ~ Just v
-       , SuperRecord.RecVecIdxPos k kvs ~ i
-       , KnownNat i
-       )
-    => Proxy# i -> LookupResult k v kvs
-
-lookupIndex
-  :: forall k v kvs
-  .  ( STypesI kvs, KnownSymbol k, STypeI v )
-  => LookupResult k v kvs
-lookupIndex = case sTypesI @kvs of
-  STyNil -> NoIndex
-  sTyCons@STyCons
-    | ( _ :: STypes ( ( l SuperRecord.:= w ) ': tail_kvs ) ) <- sTyCons
-    -> case sameSymbol ( Proxy :: Proxy k ) ( Proxy :: Proxy l ) of
-        Just Refl
-          | Just Refl <- eqTy @v @w
-          , ( index_proxy :: Proxy# i ) <- ( proxy# :: Proxy# ( SuperRecord.RecSize tail_kvs ) )
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k kvs :~: i )
-          , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k kvs :~: Just v )
-          -> SomeIndex index_proxy
-        _ -> case lookupIndex @k @v @tail_kvs of
-                NoIndex
-                  | Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k kvs :~: Nothing )
-                  -> NoIndex
-                SomeIndex ( px_j :: Proxy# j )
-                  | Refl <- ( unsafeCoerce Refl :: SuperRecord.RecTy k kvs :~: Just v )
-                  , Refl <- ( unsafeCoerce Refl :: SuperRecord.RecVecIdxPos k kvs :~: j )
-                  -> SomeIndex px_j
-
-size :: forall kvs. STypesI kvs => Int
-size = case sTypesI @kvs of
-  STyNil -> 0
-  sTyCons@STyCons
-    | ( _ :: STypes ( head_kvs ': tail_kvs ) ) <- sTyCons
-    -> 1 + size @tail_kvs
-
-data Dict c where
-  Dict :: c => Dict c
-
-type family FromJust ( x :: Maybe a ) where
-  FromJust ( Just a ) = a

src/app/MetaBrush/Document/Serialise.hs-boot

@@ -1,15 +1,46 @@
+{-# LANGUAGE FlexibleContexts     #-}
+{-# LANGUAGE UndecidableInstances #-}
+
 module MetaBrush.Document.Serialise
   ( Serialisable(..) )
   where
 
+-- base
+import GHC.TypeNats
+  ( KnownNat )
+
+-- superrecord
+import qualified SuperRecord as Super
+  ( Rec )
+import qualified SuperRecord
+  ( RecApply, RecSize, UnsafeRecBuild )
+import SuperRecord
+  ( ConstC )
+
 -- waargonaut
 import qualified Waargonaut.Decode as JSON
   ( Decoder )
 import qualified Waargonaut.Encode as JSON
   ( Encoder )
 
+-- MetaBrush
+import Math.Vector2D
+  ( Point2D, Vector2D )
+
 --------------------------------------------------------------------------------
 
 class Serialisable a where
   encoder :: Monad f => JSON.Encoder f a
   decoder :: Monad m => JSON.Decoder m a
+
+instance Serialisable Double
+
+instance Serialisable a => Serialisable ( Point2D a )
+
+instance Serialisable a => Serialisable ( Vector2D a )
+
+instance ( SuperRecord.RecApply       flds flds ( ConstC Serialisable )
+         , SuperRecord.UnsafeRecBuild flds flds ( ConstC Serialisable )
+         , KnownNat ( SuperRecord.RecSize flds )
+         )
+      => Serialisable ( Super.Rec flds )

src/app/MetaBrush/MetaParameter/AST.hs

@@ -50,6 +50,8 @@ import Data.Functor.Identity
   ( Identity(..) )
 import Data.Kind
   ( Type, Constraint )
+import Data.List
+  ( intercalate )
 import Data.Proxy
   ( Proxy(..) )
 import Data.Type.Equality
@@ -178,22 +180,32 @@ instance ( STypesI kvs, STypeI a ) => STypeI ( AdaptableFunction kvs a ) where
 data STypes ( kvs :: [ Type ] ) where
   STyNil  :: STypes '[]
   STyCons :: ( kv ~ ( k SuperRecord.:= v ), KnownSymbol k, STypeI v, STypesI kvs ) => STypes ( kv ': kvs )
-deriving stock instance Show ( STypes kvs )
+instance Show ( STypes kvs ) where
+  show sTypes = "'[" <> intercalate "," ( showSTypes sTypes ) <> "]"
+showSTypes :: STypes kvs -> [ String ]
+showSTypes STyNil = []
+showSTypes sTyCons@STyCons
+  | ( _ :: STypes ( ( k SuperRecord.:= v ) ': tail_kvs ) ) <- sTyCons
+  = ( symbolVal' ( proxy# :: Proxy# k ) <> " := " <> show ( sTypeI @v ) ) : showSTypes ( sTypesI @tail_kvs )
 
 class KnownNat ( SuperRecord.RecSize kvs ) => STypesI kvs where
   sTypesI :: STypes kvs
 
 instance STypesI '[] where
   sTypesI = STyNil
--- Warning: this instance is somewhat overly general as it doesn't check that the names are ordered.
+-- Warning: this instance is somewhat overly general as it doesn't check for lack of duplicates
 instance ( kv ~ ( k SuperRecord.:= v ), KnownSymbol k, STypeI v, STypesI kvs ) => STypesI ( kv ': kvs ) where
   sTypesI = STyCons
 
 data SomeSType where
   SomeSType :: STypeI a => Proxy# a -> SomeSType
-
 instance Show SomeSType where
   show ( SomeSType ( _ :: Proxy# a ) ) = show ( sTypeI @a )
+instance Eq SomeSType where
+  ( SomeSType ( _ :: Proxy# a ) ) == ( SomeSType ( _ :: Proxy# b ) ) =
+    case eqTy @a @b of
+      Just _ -> True
+      _      -> False
 
 eqSTy :: SType a -> SType b -> Maybe ( a :~: b )
 eqSTy sTy_a@SFunTy sTy_b@SFunTy
@@ -263,7 +275,10 @@ someSTypes = go ( sTypesI @kvs )
     go STyNil = []
     go sTyCons@STyCons
       | ( _ :: STypes ( ( l SuperRecord.:= v ) ': lvs' ) ) <- sTyCons
-      = ( Text.pack $ symbolVal' ( proxy# :: Proxy# l ), SomeSType ( proxy# :: Proxy# v ) )
+      , let
+          l :: Text
+          l = Text.pack $ symbolVal' ( proxy# :: Proxy# l )
+      = ( l, SomeSType ( proxy# :: Proxy# v ) )
       : go ( sTypesI @lvs' )
 
 ------------------------------------------------

src/app/MetaBrush/MetaParameter/Interpolation.hs

@@ -1,6 +1,8 @@
 {-# LANGUAGE DataKinds              #-}
 {-# LANGUAGE FlexibleContexts       #-}
 {-# LANGUAGE FlexibleInstances      #-}
+{-# LANGUAGE GADTs                  #-}
+{-# LANGUAGE MagicHash              #-}
 {-# LANGUAGE MultiParamTypeClasses  #-}
 {-# LANGUAGE PolyKinds              #-}
 {-# LANGUAGE ScopedTypeVariables    #-}
@@ -12,7 +14,9 @@
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 
 module MetaBrush.MetaParameter.Interpolation
-  ( Interpolatable(..), MapDiff, HasDiff', HasTorsor )
+  ( Interpolatable(..)
+  , MapDiff, HasDiff', HasTorsor
+  )
   where
 
 -- base
@@ -20,15 +24,23 @@ import Data.Functor.Identity
   ( Identity(..) )
 import Data.Kind
   ( Type )
+import Data.List
+  ( intercalate )
 import Data.Monoid
   ( Sum )
+import GHC.Exts
+  ( Proxy#, proxy# )
 import GHC.TypeLits
-  ( Symbol )
+  ( Symbol, KnownSymbol, symbolVal' )
 
 -- acts
 import Data.Act
   ( Act(..), Torsor(..) )
 
+-- deepseq
+import Control.DeepSeq
+  ( NFData )
+
 -- groups
 import Data.Group
   ( Group(..) )
@@ -48,6 +60,8 @@ import Math.Module
   ( Module(..) )
 import Math.Vector2D
   ( Point2D, Vector2D )
+import MetaBrush.MetaParameter.AST
+  ( STypeI(..), STypesI )
 
 --------------------------------------------------------------------------------
 
@@ -78,8 +92,6 @@ type family MapDiff ( kvs :: [ Type ] ) = ( lvs :: [ Type ] ) | lvs -> kvs where
   MapDiff ( k SuperRecord.:= v ': kvs ) = ( k SuperRecord.:= Diff v ': MapDiff kvs )
 
 
-
-
 instance  ( Monoid ( Super.Rec kvs ) 
           , SuperRecord.RecApply kvs kvs
               ( Tuple22C ( ConstC Group ) ( SuperRecord.Has kvs ) )

src/app/MetaBrush/Render/Document.hs

@@ -1,3 +1,4 @@
+{-# LANGUAGE AllowAmbiguousTypes   #-}
 {-# LANGUAGE BlockArguments        #-}
 {-# LANGUAGE DataKinds             #-}
 {-# LANGUAGE DeriveTraversable     #-}
@@ -31,6 +32,10 @@ import Data.Functor.Compose
   ( Compose(..) )
 import Data.Int
   ( Int32 )
+import Data.Maybe
+  ( mapMaybe )
+import Data.Type.Equality
+  ( (:~:)(Refl) )
 import GHC.Exts
   ( Proxy#, proxy# )
 import GHC.Generics
@@ -45,6 +50,10 @@ import Data.Act
   )
 
 -- containers
+import Data.Map.Strict
+  ( Map )
+import qualified Data.Map.Strict as Map
+  ( lookup )
 import Data.Sequence
   ( Seq(..) )
 import Data.Set
@@ -97,6 +106,8 @@ import Math.Vector2D
   ( Point2D(..), Vector2D(..) )
 import MetaBrush.Asset.Colours
   ( Colours, ColourRecord(..) )
+import MetaBrush.Brush
+  ( Brush(..), BrushReference(..) )
 import MetaBrush.Context
   ( Modifier(..)
   , HoldAction(..), PartialPath(..)
@@ -107,7 +118,7 @@ import MetaBrush.Document
   , Stroke(..), StrokeSpline
   , FocusState(..)
   , HoverContext(..), Hoverable(..)
-  , PointData(..), Brush(..), emptyBrush
+  , PointData(..)
   , _selection
   , coords
   )
@@ -118,11 +129,13 @@ import MetaBrush.Document.Serialise
 import MetaBrush.Document.Update
   ( DocChange(..) )
 import MetaBrush.MetaParameter.AST
-  ( AdaptableFunction(..), BrushFunction )
+  ( AdaptableFunction(..), BrushFunction, eqTys )
 import MetaBrush.MetaParameter.Interpolation
   ( MapDiff )
 import MetaBrush.UI.ToolBar
   ( Mode(..) )
+import MetaBrush.Unique
+  ( Unique )
 import MetaBrush.Util
   ( withRGBA )
 
@@ -159,7 +172,7 @@ renderDocument
 renderDocument
   cols fitParams mode debug ( viewportWidth, viewportHeight ) 
   modifiers mbMousePos mbHoldEvent mbPartialPath
-  doc@( Document { viewportCenter = Point2D cx cy, zoomFactor, documentContent = content } )
+  doc@( Document { viewportCenter = Point2D cx cy, zoomFactor, documentContent = content, documentBrushes } )
     = ( mbUpdatedDoc, drawingInstructions )
 
     where
@@ -170,7 +183,7 @@ renderDocument
         Cairo.translate ( 0.5 + 0.5 * fromIntegral viewportWidth ) ( 0.5 + 0.5 * fromIntegral viewportHeight )
         Cairo.scale zoomFactor zoomFactor
         Cairo.translate ( -cx ) ( -cy )
-        for_ strokesWithOutlineInfo
+        for_ strokesRenderData
           ( compositeRenders . getCompose . renderStroke cols mbHoverContext mode debug zoomFactor )
         renderSelectionRect
         Cairo.restore
@@ -223,11 +236,11 @@ renderDocument
               )
               ( PointData finalPoint Normal SuperRecord.rnil )
         = ( ( Stroke
-               { strokeSpline  = previewSpline
+               { strokeSpline   = previewSpline
-               , strokeVisible = True
+               , strokeVisible  = True
-               , strokeUnique  = undefined
+               , strokeUnique   = undefined
-               , strokeName    = undefined
+               , strokeName     = undefined
-               , strokeBrush   = emptyBrush
+               , strokeBrushRef = NoBrush
                }
             )
           : strokes content
@@ -236,40 +249,8 @@ renderDocument
         | otherwise
         = ( strokes content, True )
 
-      strokesWithOutlineInfo :: [ ( Stroke, Maybe ( Either ( SplinePts Closed ) ( SplinePts Closed, SplinePts Closed ), Seq FitPoint ) ) ]
+      strokesRenderData :: [ StrokeRenderData ]
-      strokesWithOutlineInfo =
+      strokesRenderData = mapMaybe ( strokeRenderData fitParams documentBrushes ) modifiedStrokes
-        fmap
-          ( \ stroke@(
-                Stroke
-                  { strokeSpline = spline :: StrokeSpline clo ( Super.Rec pointFields )
-                  , strokeBrush  =
-                      strokeBrush@(
-                        BrushData { brushFunction = ( AdaptableFunction brushFn ) :: BrushFunction brushFields }
-                      )
-                  , ..
-                  } ) ->
-            if strokeVisible
-            then
-              case ( proxy# :: Proxy# ( brushFields `SuperRecord.Intersect` pointFields ) ) of
-                ( _ :: Proxy# usedFields ) ->
-                  let
-                    -- Get the adaptable brush shape (function),
-                    -- specialising it to the type we are using.
-                    toUsedParams :: Super.Rec pointFields -> Super.Rec usedFields
-                    brushShapeFn :: Super.Rec usedFields -> SplinePts Closed
-                    ( toUsedParams, brushShapeFn ) = brushFn @pointFields @usedFields
-
-                    -- Compute the outline using the brush function.
-                    newSpline :: Spline clo CachedStroke ( PointData ( Super.Rec pointFields ) )
-                    outline :: Either ( SplinePts Closed ) ( SplinePts Closed, SplinePts Closed )
-                    fitPts :: Seq FitPoint
-                    ( newSpline, outline, fitPts ) =
-                      computeStrokeOutline @( Super.Rec ( MapDiff usedFields ) ) @clo @( Super.Rec usedFields )
-                        fitParams ( toUsedParams . brushParams ) brushShapeFn spline
-                  in ( Stroke { strokeSpline = newSpline, .. } , Just ( outline, fitPts ) )
-            else ( stroke , Nothing )
-          )
-          modifiedStrokes
 
       mbUpdatedDoc :: Maybe Document
       mbUpdatedDoc
@@ -284,33 +265,83 @@ renderDocument
         | otherwise
         = Nothing -- TODO: update the original document in this case too (by undoing the modifications)
 
+-- | Utility type to gather information needed to render a stroke.
+--   - No outline: just the underlying spline.
+--   - Outline: keep track of the function which returns brush shape.
+data StrokeRenderData where
+  StrokeRenderData
+    :: forall pointParams clo
+    . ( KnownSplineType clo, Show pointParams )
+    =>  { strokeDataSpline :: !( StrokeSpline clo pointParams ) }
+    -> StrokeRenderData
+  StrokeWithOutlineRenderData
+    :: forall pointParams clo
+    .  ( KnownSplineType clo, Show pointParams )
+    =>  { strokeDataSpline    :: !( StrokeSpline clo pointParams )
+        , strokeOutlineData   :: !( Either
+                                    ( SplinePts Closed )
+                                    ( SplinePts Closed, SplinePts Closed )
+                                  , Seq FitPoint
+                                  )
+        , strokeBrushFunction :: pointParams -> SplinePts Closed
+        }
+    -> StrokeRenderData
+
+-- | Compute the data necessary to render a stroke.
+--
+-- - If the stroke has an associated brush, this consists of:
+--    - the path that the brush follows,
+--    - the computed outline (using fitting algorithm),
+--    - the brush shape function.
+-- - Otherwise, this consists of the underlying spline path only.
+strokeRenderData :: FitParameters -> Map Unique Brush -> Stroke -> Maybe StrokeRenderData
+strokeRenderData fitParams brushes ( Stroke { strokeSpline = spline :: StrokeSpline clo ( Super.Rec pointFields ), .. } ) =
+  if strokeVisible
+  then case strokeBrushRef of
+    BrushReference ( _ :: Proxy# brushFields ) brushUnique
+      -- TODO: could emit a warning if the following lookup fails.
+      | Just ( BrushData { brushFunction = AdaptableFunction brushFn :: BrushFunction brushFields' } ) <- Map.lookup brushUnique brushes
+      -- TODO: the following check could be skipped if we are feeling confident.
+      , Just Refl <- eqTys @brushFields @brushFields' -- Refl <- ( unsafeCoerce Refl :: brushFields :~: brushFields' )
+      , ( _ :: Proxy# usedFields ) <- ( proxy# :: Proxy# ( brushFields `SuperRecord.Intersect` pointFields ) )
+      , let
+          -- Get the adaptable brush shape (function),
+          -- specialising it to the type we are using.
+          toUsedParams :: Super.Rec pointFields -> Super.Rec usedFields
+          brushShapeFn :: Super.Rec usedFields -> SplinePts Closed
+          ( toUsedParams, brushShapeFn ) = brushFn @pointFields @usedFields
+          -- Compute the outline using the brush function.
+          newSpline :: Spline clo CachedStroke ( PointData ( Super.Rec pointFields ) )
+          outline :: Either ( SplinePts Closed ) ( SplinePts Closed, SplinePts Closed )
+          fitPts :: Seq FitPoint
+          ( newSpline, outline, fitPts ) =
+            computeStrokeOutline @( Super.Rec ( MapDiff usedFields ) ) @clo @( Super.Rec usedFields )
+              fitParams ( toUsedParams . brushParams ) brushShapeFn spline
+      -> Just $
+            StrokeWithOutlineRenderData
+              { strokeDataSpline    = newSpline
+              , strokeOutlineData   = ( outline, fitPts )
+              , strokeBrushFunction = brushShapeFn . toUsedParams
+              }
+    _ -> Just $
+            StrokeRenderData
+              { strokeDataSpline = spline }
+  else Nothing
 
 renderStroke
   :: Colours -> Maybe HoverContext -> Mode -> Bool -> Double 
-  -> ( Stroke, Maybe ( Either ( SplinePts Closed ) ( SplinePts Closed, SplinePts Closed ), Seq FitPoint ) )
+  -> StrokeRenderData
   -> Compose Renders Cairo.Render ()
-renderStroke cols@( Colours { brush } ) mbHoverContext mode debug zoom
+renderStroke cols@( Colours { brush } ) mbHoverContext mode debug zoom = \case
-  ( Stroke
+  StrokeRenderData { strokeDataSpline } ->
-    { strokeSpline = strokeSpline :: StrokeSpline clo ( Super.Rec pointFields )
+    renderStrokeSpline cols mode mbHoverContext zoom ( const ( pure () ) ) strokeDataSpline
-    , strokeVisible
+  StrokeWithOutlineRenderData strokeDataSpline strokeOutlineData strokeBrushFunction ->
-    , strokeBrush = BrushData { brushFunction = ( AdaptableFunction brushFn ) :: BrushFunction brushFields }
+    renderStrokeSpline cols mode mbHoverContext zoom
-    }
+      ( when ( mode == BrushMode )
-  , mbOutlineData )
+      . renderBrushShape ( cols { path = brush } ) mbHoverContext ( 1.5 * zoom ) strokeBrushFunction
-    | strokeVisible
+      )
-    , ( _ :: Proxy# usedFields ) <- proxy# :: Proxy# ( brushFields `SuperRecord.Intersect` pointFields )
+      strokeDataSpline
-    , let
+    *> Compose blank { renderStrokes = drawOutline cols debug zoom strokeOutlineData }
-        -- Get the adaptable brush shape (function),
-        -- specialising it to the type we are using.
-        toUsedParams :: Super.Rec pointFields -> Super.Rec usedFields
-        brushShapeFn :: Super.Rec usedFields -> SplinePts Closed
-        ( toUsedParams, brushShapeFn ) = brushFn @pointFields @usedFields
-    = renderStrokeSpline cols mode mbHoverContext zoom
-        ( when ( mode == BrushMode ) . renderBrushShape ( cols { path = brush } ) mbHoverContext ( 1.5 * zoom ) ( brushShapeFn . toUsedParams ) )
-        strokeSpline
-    *> for_ mbOutlineData \outlineData ->
-        Compose blank { renderStrokes = drawOutline cols debug zoom outlineData }
-    | otherwise
-    = pure ()
 
 -- | Render a sequence of stroke points.
 --