diff --git a/src/EvalBwd.purs b/src/EvalBwd.purs
index 1330ea262..a59c768ae 100644
--- a/src/EvalBwd.purs
+++ b/src/EvalBwd.purs
@@ -21,7 +21,6 @@ import Dict (fromFoldable, singleton, toUnfoldable) as D
 import Effect.Exception (Error)
 import Eval (eval)
 import Expr (Cont(..), Elim(..), Expr(..), RecDefs, VarDef(..), bv)
-import GaloisConnection (GaloisConnection)
 import Lattice (Raw, bot, botOf, expand, (∨))
 import Partial.Unsafe (unsafePartial)
 import Trace (AppTrace(..), Trace(..), VarDef(..)) as T
@@ -201,8 +200,20 @@ evalBwd' v (T.LetRec ρ t) =
    γ1' × ρ' × α' = closeDefsBwd γ2
 evalBwd' _ _ = error absurd
 
-traceGC :: forall a m. MonadError Error m => Ann a => Raw Env -> Raw Expr -> Trace -> m (GaloisConnection (EvalBwdResult a) (Val a))
-traceGC γ e t = pure $
-   { fwd: \{ γ: γ', e: e', α } -> snd $ fromRight $ runExcept $ eval γ' e' α
-   , bwd: \v -> evalBwd γ e v t
+-- TODO: somehow extend GaloisConnection, e.g. by aggregation or row polymorphism.
+type EvalGaloisConnection a b =
+   { γ :: Raw Env
+   , e :: Raw Expr
+   , t :: Trace
+   , v :: Raw Val
+   , fwd :: a -> b
+   , bwd :: b -> a
    }
+
+traceGC :: forall a m. MonadError Error m => Ann a => Raw Env -> Raw Expr -> m (EvalGaloisConnection (EvalBwdResult a) (Val a))
+traceGC γ e = do
+   t × v <- eval γ e bot
+   let
+      bwd v' = evalBwd γ e v' t
+      fwd { γ: γ', e: e', α } = snd $ fromRight $ runExcept $ eval γ' e' α
+   pure { γ, e, t, v, fwd, bwd }
diff --git a/src/EvalGraph.purs b/src/EvalGraph.purs
index 97ff05103..8d14b310e 100644
--- a/src/EvalGraph.purs
+++ b/src/EvalGraph.purs
@@ -2,7 +2,6 @@ module EvalGraph
    ( GraphConfig
    , apply
    , eval
-   , evalWithConfig
    , eval_module
    , graphGC
    , match
@@ -16,7 +15,7 @@ import Control.Monad.Error.Class (class MonadError)
 import Data.Array (range, singleton) as A
 import Data.Either (Either(..))
 import Data.Exists (runExists)
-import Data.List (List(..), (:), length, snoc, unzip, zip)
+import Data.List (List(..), length, snoc, unzip, zip, (:))
 import Data.Set (Set, empty, insert, intersection, singleton, union)
 import Data.Set as S
 import Data.Traversable (sequence, traverse)
@@ -25,8 +24,7 @@ import DataType (checkArity, arity, consistentWith, dataTypeFor, showCtr)
 import Dict (disjointUnion, fromFoldable, empty, get, keys, lookup, singleton) as D
 import Effect.Exception (Error)
 import Expr (Cont(..), Elim(..), Expr(..), VarDef(..), RecDefs, Module(..), fv, asExpr)
-import GaloisConnection (GaloisConnection)
-import Graph (class Graph, Vertex)
+import Graph (class Graph, Vertex, sinks)
 import Graph (vertices) as G
 import Graph.GraphWriter (class MonadGraphAlloc, alloc, new, runWithGraphAllocT)
 import Graph.Slice (bwdSlice, fwdSlice, vertices)
@@ -175,12 +173,14 @@ eval_module γ = go D.empty
       γ'' <- closeDefs (γ <+> γ') ρ αs
       go (γ' <+> γ'') (Module ds) αs
 
-evalWithConfig :: forall g m a. MonadError Error m => Graph g => GraphConfig g -> Expr a -> m ((g × Int) × Expr Vertex × Val Vertex)
-evalWithConfig { g, n, γα } e =
-   runWithGraphAllocT (g × n) $ do
-      eα <- alloc e
-      vα <- eval γα eα S.empty
-      pure (eα × vα)
+type EvalGaloisConnection g a b =
+   { gconfig :: GraphConfig g
+   , eα :: Expr Vertex
+   , g :: g
+   , vα :: Val Vertex
+   , fwd :: a -> b
+   , bwd :: b -> a
+   }
 
 graphGC
    :: forall g m
@@ -188,10 +188,15 @@ graphGC
    => Graph g
    => GraphConfig g
    -> Raw Expr
-   -> m (GaloisConnection (Set Vertex) (Set Vertex))
-graphGC { g: g0, n, γα } e = do
-   (g × _) × vα × eα <- evalWithConfig { g: g0, n, γα } e
-   pure $
-      { fwd: \αs -> G.vertices (fwdSlice αs g) `intersection` vertices vα
-      , bwd: \αs -> G.vertices (bwdSlice αs g) `intersection` vertices eα -- TODO: include γα
-      }
+   -> m (EvalGaloisConnection g (Set Vertex) (Set Vertex))
+graphGC gconfig@{ g, n, γα } e = do
+   (g' × _) × eα × vα <- do
+      runWithGraphAllocT (g × n) $ do
+         eα <- alloc e
+         vα <- eval γα eα S.empty
+         pure (eα × vα)
+   let
+      fwd αs = G.vertices (fwdSlice αs g') `intersection` vertices vα
+      -- TODO: want (vertices eα `union` foldMap vertices γα) rather than sinks g' here?
+      bwd αs = G.vertices (bwdSlice αs g') `intersection` sinks g'
+   pure { gconfig, eα, g: g', vα, fwd, bwd }
diff --git a/src/Graph/Slice.purs b/src/Graph/Slice.purs
index 5a34451a9..99200ff77 100644
--- a/src/Graph/Slice.purs
+++ b/src/Graph/Slice.purs
@@ -28,6 +28,11 @@ bwdSlice αs0 g0 = fst $ runWithGraph $ tailRecM go (empty × L.fromFoldable αs
       extend α βs
       pure $ Loop ((visited # insert α) × (L.fromFoldable βs <> αs))
 
+-- Doesn't do the final negation..
+fwdSliceDeMorgan :: forall g. Graph g => Set Vertex -> g -> g
+fwdSliceDeMorgan αs_0 g_0 =
+   bwdSlice (sinks g_0 `difference` αs_0) (op g_0)
+
 -- | De Morgan dual of backward slicing (◁_G)° ≡ Forward slicing on the opposite graph (▷_{G_op})
 bwdSliceDual :: forall g. Graph g => Set Vertex -> g -> g
 bwdSliceDual αs0 g0 = fwdSlice αs0 (op g0)
diff --git a/test/Util.purs b/test/Util.purs
index dee0486c2..6263c1d23 100644
--- a/test/Util.purs
+++ b/test/Util.purs
@@ -20,21 +20,20 @@ import Desugarable (desug, desugBwd)
 import Effect.Aff (Aff)
 import Effect.Class.Console (log)
 import Effect.Exception (Error)
-import Eval (eval)
-import EvalBwd (evalBwd)
-import EvalGraph (GraphConfig, evalWithConfig)
-import Graph (sinks, sources, vertices)
+import EvalBwd (traceGC)
+import EvalGraph (GraphConfig, graphGC)
+import Graph (sinks, vertices)
 import Graph.GraphImpl (GraphImpl)
-import Graph.Slice (bwdSlice, bwdSliceDual, fwdSlice, fwdSliceDual, fwdSliceAsDeMorgan) as G
+import Graph.Slice (bwdSliceDual, fwdSliceDual, fwdSliceDeMorgan) as G
 import Graph.Slice (selectαs, select𝔹s)
 import Heterogeneous.Mapping (hmap)
-import Lattice (bot, botOf, topOf, erase, Raw)
+import Lattice (botOf, topOf, erase, Raw)
 import Module (parse)
 import Parse (program)
 import Pretty (class Pretty, prettyP)
 import SExpr (Expr) as SE
 import Test.Spec.Assertions (fail)
-import Util (MayFailT, (×), successful)
+import Util (MayFailT, successful)
 import Val (Val(..), class Ann)
 
 type TestConfig =
@@ -66,96 +65,90 @@ testParse s = do
          lift $ fail "not equal"
 
 testTrace :: Raw SE.Expr -> GraphConfig GraphImpl -> TestConfig -> MayFailT Aff TraceRow
-testTrace s { γα: γ } { δv, bwd_expect, fwd_expect } = do
-   let s𝔹 × γ𝔹 = (botOf s) × (botOf <$> γ)
+testTrace s { γα } { δv, bwd_expect, fwd_expect } = do
    -- | Eval
-   e𝔹 <- desug s𝔹
+   e <- desug s
    tEval1 <- preciseTime
-   t × v𝔹 <- eval γ𝔹 e𝔹 bot
+   gc <- traceGC (erase <$> γα) e
    tEval2 <- preciseTime
 
    -- | Backward
    tBwd1 <- preciseTime
-   let
-      v𝔹' = δv v𝔹
-      { γ: γ𝔹', e: e𝔹' } = evalBwd (erase <$> γ𝔹) (erase e𝔹) v𝔹' t
+   let { γ: γ𝔹, e: e𝔹 } = gc.bwd (δv (botOf gc.v))
    tBwd2 <- preciseTime
-   let s𝔹' = desugBwd e𝔹' s
+   let s𝔹 = desugBwd e𝔹 s
 
    -- | Forward (round-tripping)
-   e𝔹'' <- desug s𝔹'
+   e𝔹' <- desug s𝔹
    tFwd1 <- preciseTime
-   _ × v𝔹'' <- eval γ𝔹' e𝔹'' top
+   let v𝔹 = gc.fwd { γ: γ𝔹, e: e𝔹', α: top }
    tFwd2 <- preciseTime
 
    lift do
-      unless (isGraphical v𝔹') $
-         log (prettyP v𝔹'')
+      unless (isGraphical gc.v) $
+         log (prettyP v𝔹)
       -- | Check backward selections
       unless (null bwd_expect) $
-         checkPretty "Trace-based source selection" bwd_expect s𝔹'
+         checkPretty "Trace-based source selection" bwd_expect s𝔹
       -- | Check round-trip selections
-      unless (isGraphical v𝔹') $
-         checkPretty "Trace-based value" fwd_expect v𝔹''
+      unless (isGraphical gc.v) $
+         checkPretty "Trace-based value" fwd_expect v𝔹
 
    pure { tEval: tdiff tEval1 tEval2, tBwd: tdiff tBwd1 tBwd2, tFwd: tdiff tFwd1 tFwd2 }
 
 testGraph :: Raw SE.Expr -> GraphConfig GraphImpl -> TestConfig -> MayFailT Aff GraphRow
-testGraph s gconf { δv, bwd_expect, fwd_expect } = do
+testGraph s gconfig { δv, bwd_expect, fwd_expect } = do
    -- | Eval
    e <- desug s
    tEval1 <- preciseTime
-   (g × _) × eα × vα <- evalWithConfig gconf e
+   gc <- graphGC gconfig e
    tEval2 <- preciseTime
 
    -- | Backward
    tBwd1 <- preciseTime
    let
-      αs_out = selectαs (δv (botOf vα)) vα
-      gbwd = G.bwdSlice αs_out g
-      αs_in = sinks gbwd
-      e𝔹 = select𝔹s eα αs_in
+      αs_out = selectαs (δv (botOf gc.vα)) gc.vα
+      αs_in = gc.bwd αs_out
+      e𝔹 = select𝔹s gc.eα αs_in
    tBwd2 <- preciseTime
-   let
-      s𝔹 = desugBwd e𝔹 (erase s)
+   let s𝔹 = desugBwd e𝔹 s
 
    -- | De Morgan dual of backward
    tBwdDual1 <- preciseTime
    let
-      αs_out_dual = selectαs (δv (botOf vα)) vα
-      gbwd_dual = G.bwdSliceDual αs_out_dual g
+      αs_out_dual = selectαs (δv (botOf gc.vα)) gc.vα
+      gbwd_dual = G.bwdSliceDual αs_out_dual gc.g
       αs_in_dual = sinks gbwd_dual
-      e𝔹_dual = select𝔹s eα αs_in_dual
+      e𝔹_dual = select𝔹s gc.eα αs_in_dual
    tBwdDual2 <- preciseTime
 
    -- | Backward (all outputs selected)
    tBwdAll1 <- preciseTime
    let
-      αs_out_all = selectαs (topOf vα) vα
-      gbwd_all = G.bwdSlice αs_out_all g
-      αs_in_all = sinks gbwd_all
-      e𝔹_all = select𝔹s eα αs_in_all
+      αs_out_all = selectαs (topOf gc.vα) gc.vα
+      αs_in_all = gc.bwd αs_out_all
+      e𝔹_all = select𝔹s gc.eα αs_in_all
    tBwdAll2 <- preciseTime
 
    -- | Forward (round-tripping)
    tFwd1 <- preciseTime
    let
-      gfwd = G.fwdSlice αs_in g
-      v𝔹 = select𝔹s vα (vertices gfwd)
+      αs_out' = gc.fwd αs_in
+      v𝔹 = select𝔹s gc.vα αs_out'
    tFwd2 <- preciseTime
 
    -- | De Morgan dual of forward
    tFwdDual1 <- preciseTime
    let
-      gfwd_dual = G.fwdSliceDual αs_in g
-      v𝔹_dual = select𝔹s vα (vertices gfwd_dual)
+      gfwd_dual = G.fwdSliceDual αs_in gc.g
+      v𝔹_dual = select𝔹s gc.vα (vertices gfwd_dual)
    tFwdDual2 <- preciseTime
 
    -- | Forward (round-tripping) using De Morgan dual
    tFwdAsDeMorgan1 <- preciseTime
    let
-      gfwd_demorgan = G.fwdSliceAsDeMorgan αs_in g
-      v𝔹_demorgan = select𝔹s vα (vertices gfwd_demorgan) <#> not
+      gfwd_demorgan = G.fwdSliceDeMorgan αs_in gc.g
+      v𝔹_demorgan = select𝔹s gc.vα (vertices gfwd_demorgan) <#> not
    tFwdAsDeMorgan2 <- preciseTime
 
    lift do
@@ -166,8 +159,8 @@ testGraph s gconf { δv, bwd_expect, fwd_expect } = do
       unless (isGraphical v𝔹) do
          checkPretty "Graph-based value" fwd_expect v𝔹
          checkPretty "Graph-based value (De Morgan)" fwd_expect v𝔹_demorgan
-      sources gbwd `shouldSatisfy "fwd ⚬ bwd round-tripping property"`
-         (flip subset (sources gfwd))
+      αs_out `shouldSatisfy "fwd ⚬ bwd round-tripping property"`
+         (flip subset αs_out')
       -- | To avoid unused variables when benchmarking
       unless false do
          log (prettyP e𝔹_dual)