"size" function nodes down from 454 to 321

src/Eval.hs

@@ -3,11 +3,30 @@ module Eval where
 import Parser
 import Research
 
-import Data.List (partition, (\\))
+import           Data.List   (partition, (\\), elemIndex)
 import           Data.Map    (Map)
+import           Data.Set    (Set)
+
+import qualified Data.Foldable as F
 import qualified Data.Map as Map
 import qualified Data.Set as Set
 
+data DB
+  = BVar Int          -- bound (0 = nearest binder)
+  | BFree String      -- free/global
+  | BLam DB
+  | BApp DB DB
+  | BLeaf
+  | BStem DB
+  | BFork DB DB
+  | BStr String
+  | BInt Integer
+  | BList [DB]
+  | BEmpty
+  deriving (Eq, Show)
+
+type Uses = [Bool]
+
 evalSingle :: Env -> TricuAST -> Env
 evalSingle env term
   | SDef name [] body <- term
@@ -63,78 +82,74 @@ elimLambda :: TricuAST -> TricuAST
 elimLambda = go
   where
     go term
-      | etaReduction term   = elimLambda $ etaReduceResult term
+      | etaReduction term   = go (etaReduceResult term)
       | triagePattern term  = _TRI
       | composePattern term = _B
-      | lambdaList term     = elimLambda $ lambdaListResult term
+      | lambdaList term     = go (lambdaListResult term)
       | nestedLambda term   = nestedLambdaResult term
       | application term    = applicationResult term
       | otherwise           = term
 
-    etaReduction (SLambda [v] (SApp f (SVar x))) = v == x && not (isFree v f)
+    -- patterns (now DB-indexed where it matters)
+    etaReduction (SLambda [v] (SApp f (SVar x))) = v == x && not (usesBinder v f)
     etaReduction _ = False
-    etaReduceResult (SLambda [_] (SApp f _)) = f
 
-    triagePattern (SLambda [a] (SLambda [b] (SLambda [c] body))) = body == triageBody a b c
+    -- triage: \a b c -> TLeaf (TLeaf a b) c  (checked in DB with a↦2, b↦1, c↦0)
+    triagePattern (SLambda [a] (SLambda [b] (SLambda [c] body))) =
+      toDB [c,b,a] body == triageBodyDB
     triagePattern _ = False
 
-    composePattern (SLambda [f] (SLambda [g] (SLambda [x] body))) = body == composeBody f g x
+    -- compose: \f g x -> f (g x)  (checked in DB with f↦2, g↦1, x↦0)
+    composePattern (SLambda [f] (SLambda [g] (SLambda [x] body))) =
+      toDB [x,g,f] body == composeBodyDB
     composePattern _ = False
 
     lambdaList (SLambda [_] (SList _)) = True
     lambdaList _ = False
-    lambdaListResult (SLambda [v] (SList xs)) = SLambda [v] (foldr wrapTLeaf TLeaf xs)
-    wrapTLeaf m r = SApp (SApp TLeaf m) r
 
     nestedLambda (SLambda (_:_) _) = True
     nestedLambda _ = False
-    nestedLambdaResult (SLambda (v:vs) body)
-      | null vs   = toSKI v (elimLambda body)
-      | otherwise = elimLambda (SLambda [v] (SLambda vs body))
 
     application (SApp _ _) = True
     application _ = False
-    applicationResult (SApp f g) = SApp (elimLambda f) (elimLambda g)
 
-    toSKI x (SVar y)
+    -- rewrites
-      | x == y           = _I
+    etaReduceResult (SLambda [_] (SApp f _)) = f
-      | otherwise        = SApp _K (SVar y)
-    toSKI x t@(SApp n u)
-      | not (isFree x t) = SApp _K t
-      | otherwise        = SApp (SApp _S (toSKI x n)) (toSKI x u)
-    toSKI x (SList xs)
-      | not (isFree x (SList xs)) = SApp _K (SList xs)
-      | otherwise = SList (map (toSKI x) xs)
-    toSKI x t
-      | not (isFree x t) = SApp _K t
-      | otherwise        = errorWithoutStackTrace "Unhandled toSKI conversion"
 
-    -- Combinators and special forms
+    lambdaListResult (SLambda [v] (SList xs)) =
-    _S   = parseSingle "t (t (t t t)) t"
+      SLambda [v] (foldr wrapTLeaf TLeaf xs)
-    _K   = parseSingle "t t"
+      where
-    _I   = parseSingle "t (t (t t)) t"
+        wrapTLeaf m r = SApp (SApp TLeaf m) r
-    _B   = parseSingle "t (t (t t (t (t (t t t)) t))) (t t)"
-    _TRI = parseSingle "t (t (t t (t (t (t t t))))) t"
 
-    -- Pattern bodies
+    -- The key change: use DB bracket abstraction for the final parameter.
-    triageBody a b c = SApp (SApp TLeaf (SApp (SApp TLeaf (SVar a)) (SVar b))) (SVar c)
+    nestedLambdaResult (SLambda (v:vs) body)
-    composeBody f g x = SApp (SVar f) (SApp (SVar g) (SVar x))
+      | null vs   =
+          let body' = go body
+              db    = toDB [v] body'
+          in toSKIKiselyov db 
+      | otherwise = go (SLambda [v] (SLambda vs body))
+
+    applicationResult (SApp f g) = SApp (go f) (go g)
+
+-- combinators and special forms (unchanged)
+_S   = parseSingle "t (t (t t t)) t"
+_K   = parseSingle "t t"
+_I   = parseSingle "t (t (t t)) t"
+_R   = parseSingle "(t (t (t t (t (t (t (t (t (t (t t (t (t (t t t)) t))) (t (t (t t (t t))) (t (t (t t t)) t)))) (t t (t t))))))) (t t))"
+_C   = parseSingle "(t (t (t (t (t t (t (t (t t t)) t))) (t (t (t t (t t))) (t (t (t t t)) t)))) (t t (t t)))"
+_B   = parseSingle "t (t (t t (t (t (t t t)) t))) (t t)"
+_T   = SApp _C _I
+_TRI = parseSingle "t (t (t t (t (t (t t t))))) t"
+
+-- pattern bodies (kept for reference; checks are now DB-based)
+triageBody a b c   = SApp (SApp TLeaf (SApp (SApp TLeaf (SVar a)) (SVar b))) (SVar c)
+composeBody f g x  = SApp (SVar f) (SApp (SVar g) (SVar x))
 
 isFree :: String -> TricuAST -> Bool
-isFree x = Set.member x . freeVars
+isFree x t = Set.member x (freeVars t)
 
-freeVars :: TricuAST -> Set.Set String
+freeVars :: TricuAST -> Set String
-freeVars (SVar    v    ) = Set.singleton v
+freeVars = freeDBNames . toDB []
-freeVars (SList   s    ) = foldMap freeVars s
-freeVars (SLambda v b  ) = foldr Set.delete (freeVars b) v
-freeVars (SApp    f a  ) = freeVars f <> freeVars a
-freeVars (TFork   l r  ) = freeVars l <> freeVars r
-freeVars (SDef   _ _ b)  = freeVars b
-freeVars (TStem   t    ) = freeVars t
-freeVars (SInt    _    ) = Set.empty
-freeVars (SStr    _    ) = Set.empty
-freeVars  TLeaf          = Set.empty
-freeVars  _              = Set.empty
 
 reorderDefs :: Env -> [TricuAST] -> [TricuAST]
 reorderDefs env defs
@@ -215,3 +230,284 @@ mainResult :: Env -> T
 mainResult r = case Map.lookup "main" r of
   Just  a -> a
   Nothing -> errorWithoutStackTrace "No valid definition for `main` found."
+
+-- Convert named TricuAST to De Bruijn form
+toDB :: [String] -> TricuAST -> DB
+toDB env = \case
+  SVar v       -> maybe (BFree v) BVar (elemIndex v env)
+  SLambda vs b ->
+    let env' = reverse vs ++ env
+        body = toDB env' b
+    in foldr (\_ acc -> BLam acc) body vs
+  SApp f a     -> BApp (toDB env f) (toDB env a)
+  TLeaf        -> BLeaf
+  TStem t      -> BStem (toDB env t)
+  TFork l r    -> BFork (toDB env l) (toDB env r)
+  SStr s       -> BStr s
+  SInt n       -> BInt n
+  SList xs     -> BList (map (toDB env) xs)
+  SEmpty       -> BEmpty
+  SDef{}       -> error "toDB: unexpected SDef at this stage"
+  SImport _ _  -> BEmpty
+
+-- Does a term depend on the current binder (level 0)?
+dependsOnLevel :: Int -> DB -> Bool
+dependsOnLevel lvl = \case
+  BVar k      -> k == lvl
+  BLam t      -> dependsOnLevel (lvl + 1) t
+  BApp f a    -> dependsOnLevel lvl f || dependsOnLevel lvl a
+  BStem t     -> dependsOnLevel lvl t
+  BFork l r   -> dependsOnLevel lvl l || dependsOnLevel lvl r
+  BList xs    -> any (dependsOnLevel lvl) xs
+  _           -> False
+
+-- Collect free *global* names (i.e., unbound)
+freeDBNames :: DB -> Set String
+freeDBNames = \case
+  BFree s   -> Set.singleton s
+  BVar _    -> mempty
+  BLam t    -> freeDBNames t
+  BApp f a  -> freeDBNames f <> freeDBNames a
+  BLeaf     -> mempty
+  BStem t   -> freeDBNames t
+  BFork l r -> freeDBNames l <> freeDBNames r
+  BStr _    -> mempty
+  BInt _    -> mempty
+  BList xs  -> foldMap freeDBNames xs
+  BEmpty    -> mempty
+
+-- Helper: “is the binder named v used in body?”
+usesBinder :: String -> TricuAST -> Bool
+usesBinder v body = dependsOnLevel 0 (toDB [v] body)
+
+-- Expected DB bodies for the named special patterns (under env [a,b,c] -> indices 2,1,0)
+triageBodyDB :: DB
+triageBodyDB =
+  BApp (BApp BLeaf (BApp (BApp BLeaf (BVar 2)) (BVar 1))) (BVar 0)
+
+composeBodyDB :: DB
+composeBodyDB =
+  BApp (BVar 2) (BApp (BVar 1) (BVar 0))
+
+-- Convert DB -> TricuAST for subterms that contain NO binders (no BLam, no BVar)
+fromDBClosed :: DB -> TricuAST
+fromDBClosed = \case
+  BFree s   -> SVar s
+  BApp f a  -> SApp (fromDBClosed f) (fromDBClosed a)
+  BLeaf     -> TLeaf
+  BStem t   -> TStem (fromDBClosed t)
+  BFork l r -> TFork (fromDBClosed l) (fromDBClosed r)
+  BStr s    -> SStr s
+  BInt n    -> SInt n
+  BList xs  -> SList (map fromDBClosed xs)
+  BEmpty    -> SEmpty
+  -- Anything bound would be a logic error if we call this correctly.
+  BLam _    -> error "fromDBClosed: unexpected BLam"
+  BVar _    -> error "fromDBClosed: unexpected bound variable"
+
+-- DB-native bracket abstraction over the innermost binder (level 0).
+-- This mirrors your old toSKI, but is purely index-driven.
+toSKIDB :: DB -> TricuAST
+toSKIDB t
+  | not (dependsOnLevel 0 t) = SApp _K (fromDBClosed t)
+toSKIDB (BVar 0)             = _I
+toSKIDB (BApp n u)           = SApp (SApp _S (toSKIDB n)) (toSKIDB u)
+toSKIDB (BList xs) =
+  let anyUses = any (dependsOnLevel 0) xs
+  in if not anyUses
+        then SApp _K (SList (map fromDBClosed xs))
+        else SList (map toSKIDB xs)
+toSKIDB other =
+  errorWithoutStackTrace $ "Unhandled toSKI(DB) conversion: " ++ show other
+
+app2 :: TricuAST -> TricuAST -> TricuAST
+app2 f x = SApp f x
+
+app3 :: TricuAST -> TricuAST -> TricuAST -> TricuAST
+app3 f x y = SApp (SApp f x) y
+
+-- Core converter that *does not* perform the λ-step; it just returns (Γ, d).
+-- Supported shapes: variables, applications, closed literals (Leaf/Int/Str/Empty),
+-- closed lists. For anything where the binder occurs under structural nodes
+-- (Stem/Fork/List-with-use), we deliberately bail so the caller can fall back.
+kisConv :: DB -> Either String (Uses, TricuAST)
+kisConv = \case
+  BVar 0     -> Right ([True], _I)
+  BVar n | n > 0 -> do
+    (g,d) <- kisConv (BVar (n - 1))
+    Right (False:g, d)
+  BApp e1 e2 -> do
+    (g1,d1) <- kisConv e1
+    (g2,d2) <- kisConv e2
+    let g = zipWithDefault False (||) g1 g2   -- <— propagate Γ outside (#)
+        d = kisHash (g1,d1) (g2,d2)           -- <— (#) yields only the term
+    Right (g, d)
+  -- Treat closed constants as free 'combinator leaves' (no binder use).
+  BLeaf      -> Right ([], TLeaf)
+  BStr s     -> Right ([], SStr s)
+  BInt n     -> Right ([], SInt n)
+  BEmpty     -> Right ([], SEmpty)
+  -- Closed list: allowed. If binder is used anywhere, we punt to fallback.
+  BList xs
+    | any (dependsOnLevel 0) xs -> Left "List with binder use: fallback"
+    | otherwise                 -> Right ([], SList (map fromDBClosed xs))
+  -- For structural nodes, only allow if *closed* wrt the binder.
+  BStem t
+    | dependsOnLevel 0 t -> Left "Stem with binder use: fallback"
+    | otherwise          -> Right ([], TStem (fromDBClosed t))
+  BFork l r
+    | dependsOnLevel 0 l || dependsOnLevel 0 r -> Left "Fork with binder use: fallback"
+    | otherwise                                -> Right ([], TFork (fromDBClosed l) (fromDBClosed r))
+  -- We shouldn’t see BLam under elim; treat as unsupported so we fallback.
+  BLam _      -> Left "Nested lambda under body: fallback"
+  BFree s     -> Right ([], SVar s)
+
+-- Application combiner with K-optimization (lazy weakening).
+-- Mirrors Lynn’s 'optK' rules: choose among S, B, C, R based on leading flags.
+-- η-aware (#) with K-optimization (adapted from TS kiselyov_eta)
+kisHash :: (Uses, TricuAST) -> (Uses, TricuAST) -> TricuAST
+kisHash (g1, d1) (g2, d2) =
+  case g1 of
+    [] -> case g2 of
+      []            -> SApp d1 d2
+      True:gs2      -> if isId2 (g2, d2)
+                         then d1
+                         else kisHash ([], SApp _B d1) (gs2, d2)
+      False:gs2     -> kisHash ([], d1) (gs2, d2)
+
+    True:gs1 -> case g2 of
+      []            -> if isId2 (g1, d1)
+                         then SApp _T d2
+                         else kisHash ([], SApp _R d2) (gs1, d1)
+      _ ->
+        if isId2 (g1, d1) && case g2 of { False:_ -> True; _ -> False }
+          then kisHash ([], _T) (tail g2, d2)
+        else
+          -- NEW: coalesce the longest run of identical head pairs and apply bulk op once
+          let ((h1, h2), count) = headPairRun g1 g2
+              g1' = drop count g1
+              g2' = drop count g2
+          in case (h1, h2) of
+               (False, False) ->
+                 kisHash (g1', d1) (g2', d2)
+               (False, True)  ->
+                 let d1' = kisHash ([], bulkB count) (g1', d1)
+                 in  kisHash (g1', d1') (g2', d2)
+               (True, False)  ->
+                 let d1' = kisHash ([], bulkC count) (g1', d1)
+                 in  kisHash (g1', d1') (g2', d2)
+               (True, True)   ->
+                 let d1' = kisHash ([], bulkS count) (g1', d1)
+                 in  kisHash (g1', d1') (g2', d2)
+
+    False:gs1 -> case g2 of
+      []            -> kisHash (gs1, d1) ([], d2)
+      _             ->
+        if isId2 (g1, d1) && case g2 of { False:_ -> True; _ -> False }
+          then kisHash ([], _T) (tail g2, d2)
+        else case g2 of
+          True:gs2   ->
+            let d1' = kisHash ([], _B) (gs1, d1)
+            in  kisHash (gs1, d1') (gs2, d2)
+          False:gs2  ->
+            kisHash (gs1, d1) (gs2, d2)
+  where
+    tail (_:xs) = xs
+    tail []     = []
+
+
+toSKIKiselyov :: DB -> TricuAST
+toSKIKiselyov body =
+  case kisConv body of
+    Right ([], d)          -> SApp _K d
+    Right (True:_ , d)     -> d
+    Right (False:g, d)     -> kisHash ([], _K) (g, d)  -- no snd
+    Left _                 -> starSKIBCOpEtaDB body   -- was: toSKIDB body
+
+zipWithDefault :: a -> (a -> a -> a) -> [a] -> [a] -> [a]
+zipWithDefault d f []     ys     = map (f d) ys
+zipWithDefault d f xs     []     = map (\x -> f x d) xs
+zipWithDefault d f (x:xs) (y:ys) = f x y : zipWithDefault d f xs ys
+
+isNode :: TricuAST -> Bool
+isNode t = case t of
+  TLeaf -> True
+  _     -> False
+
+isApp2 :: TricuAST -> Maybe (TricuAST, TricuAST)
+isApp2 (SApp a b) = Just (a, b)
+isApp2 _          = Nothing
+
+isKop :: TricuAST -> Bool
+isKop t = case isApp2 t of
+  Just (a,b) -> isNode a && isNode b
+  _          -> False
+
+-- detects the two canonical I-shapes in the tree calculus:
+--   △ (△ (△ △)) x    OR    △ (△ △ △) △
+isId :: TricuAST -> Bool
+isId t = case isApp2 t of
+  Just (ab, c) -> case isApp2 ab of
+    Just (a, b) | isNode a ->
+      case isApp2 b of
+        Just (b1, b2) ->
+          (isNode b1 && isKop b2) ||
+          (isKop b1 && isNode b2 && isNode c)
+        _ -> False
+    _ -> False
+  _ -> False
+
+-- head-True only, tail empty, and term is identity
+isId2 :: (Uses, TricuAST) -> Bool
+isId2 (True:[], t) = isId t
+isId2 _            = False
+
+-- Bulk helpers built from SKI (no new primitives)
+bPrime :: TricuAST
+bPrime = SApp _B _B                            -- B' = B B
+
+cPrime :: TricuAST
+cPrime = SApp (SApp _B (SApp _B _C)) _B        -- C' = B (B C) B
+
+sPrime :: TricuAST
+sPrime = SApp (SApp _B (SApp _B _S)) _B        -- S' = B (B S) B
+
+bulkB :: Int -> TricuAST
+bulkB n | n <= 1    = _B
+        | otherwise = SApp bPrime (bulkB (n - 1))
+
+bulkC :: Int -> TricuAST
+bulkC n | n <= 1    = _C
+        | otherwise = SApp cPrime (bulkC (n - 1))
+
+bulkS :: Int -> TricuAST
+bulkS n | n <= 1    = _S
+        | otherwise = SApp sPrime (bulkS (n - 1))
+
+-- Count how many leading pairs (a,b) repeat at the head of zip g1 g2
+headPairRun :: [Bool] -> [Bool] -> ((Bool, Bool), Int)
+headPairRun g1 g2 =
+  case zip g1 g2 of
+    []       -> ((False, False), 0)
+    (h:rest) -> (h, 1 + length (takeWhile (== h) rest))
+
+-- DB-native star_skibc_op_eta (adapted from strategies.mts), binder = level 0
+starSKIBCOpEtaDB :: DB -> TricuAST
+starSKIBCOpEtaDB t
+  | not (dependsOnLevel 0 t) = SApp _K (fromDBClosed t)
+starSKIBCOpEtaDB (BVar 0)     = _I
+starSKIBCOpEtaDB (BApp e1 e2)
+  -- if binder not in right: use C
+  | not (dependsOnLevel 0 e2)
+  = SApp (SApp _C (starSKIBCOpEtaDB e1)) (fromDBClosed e2)
+  -- if binder not in left:
+  | not (dependsOnLevel 0 e1)
+  = case e2 of
+      -- η case: \x. f x  ==>  f
+      BVar 0 -> fromDBClosed e1
+      _      -> SApp (SApp _B (fromDBClosed e1)) (starSKIBCOpEtaDB e2)
+  -- otherwise: S
+  | otherwise
+  = SApp (SApp _S (starSKIBCOpEtaDB e1)) (starSKIBCOpEtaDB e2)
+-- Structural nodes with binder underneath: fall back to plain SKI (rare)
+starSKIBCOpEtaDB other        = toSKIDB other

test/Spec.hs

@@ -35,6 +35,8 @@ tests = testGroup "Tricu Tests"
   , modules
   , demos
   , decoding
+	, elimLambdaSingle
+	, stressElimLambda
   ]
 
 lexer :: TestTree
@@ -533,7 +535,7 @@ demos = testGroup "Test provided demo functionality"
       decodeResult res @?= "\"(t (t (t t) (t t t)) (t t (t t t)))\""
   , testCase "Determining the size of functions" $ do
       res     <- liftIO $ evaluateFileResult "./demos/size.tri"
-      decodeResult res @?= "454"
+      decodeResult res @?= "321"
   , testCase "Level Order Traversal demo" $ do
       res     <- liftIO $ evaluateFileResult "./demos/levelOrderTraversal.tri"
       decodeResult res @?= "\"\n1 \n2 3 \n4 5 6 7 \n8 11 10 9 12 \""
@@ -570,3 +572,72 @@ decoding = testGroup "Decoding Tests"
       let input = ofList [ofList [ofString "nested"], ofString "string"]
       decodeResult input @?= "[[\"nested\"], \"string\"]"
   ]
+
+elimLambdaSingle :: TestTree
+elimLambdaSingle = testCase "elimLambda preserves eval, fires eta, and SDef binds" $ do
+  -- 1) eta reduction, purely structural and parsed from source
+  let [etaIn] = parseTricu "x : f x"
+      [fRef ] = parseTricu "f"
+  elimLambda etaIn @?= fRef
+
+  -- 2) SDef binds its own name and parameters
+  let [defFXY] = parseTricu "f x y : f x"
+      fv       = freeVars defFXY
+  assertBool "f should be bound in SDef" ("f" `Set.notMember` fv)
+  assertBool "x should be bound in SDef" ("x" `Set.notMember` fv)
+  assertBool "y should be bound in SDef" ("y" `Set.notMember` fv)
+
+  -- 3) semantics preserved on a small program that exercises compose and triage
+  let src =
+        unlines
+          [ "false = t"
+          , "_     = t"
+          , "true  = t t"
+          , "id    = a : a"
+          , "const = a b : a"
+          , "compose = f g x : f (g x)"
+          , "triage = leaf stem fork : t (t leaf stem) fork"
+          , "test   = triage \"Leaf\" (_ : \"Stem\") (_ _ : \"Fork\")"
+          , "main   = compose id id test"
+          ]
+      prog        = parseTricu src
+      progElim    = map elimLambda prog
+      evalBefore  = result (evalTricu Map.empty prog)
+      evalAfter   = result (evalTricu Map.empty progElim)
+  evalAfter @?= evalBefore
+
+stressElimLambda :: TestTree
+stressElimLambda = testCase "stress elimLambda on wide list under deep curried lambda" $ do
+  let numVars = 200
+      numBody = 800
+      vars    = [ "x" ++ show i | i <- [1..numVars] ]
+      body    = "(" ++ unwords (replicate numBody "t") ++ ")"
+      etaOne  = "h : f h"
+      etaTwo  = "k : id k"
+      defId   = "id = a : a"
+      lambda  = unwords vars ++ " : " ++ body
+      src     = unlines
+                  [ defId
+                  , etaOne
+                  , "compose = f g x : f (g x)"
+                  , "f = t t"
+                  , etaTwo
+                  , lambda
+                  , "main = compose id id (" ++ head vars ++ " : f " ++ head vars ++ ")"
+                  ]
+      prog    = parseTricu src
+
+  let out = map elimLambda prog
+  let noLambda term = case term of
+        SLambda _ _ -> False
+        SApp f g    -> noLambda f && noLambda g
+        SList xs    -> all noLambda xs
+        TFork l r   -> noLambda l && noLambda r
+        TStem u     -> noLambda u
+        _           -> True
+
+  assertBool "all lambdas eliminated" (all noLambda out)
+
+  let before = result (evalTricu Map.empty prog)
+      after  = result (evalTricu Map.empty out)
+  after @?= before