Definition dependency analysis

tricu now allows defining terms in any order and will resolve
dependencies to ensure that they're evaluated in the right order.
Undefined terms are detected and throw errors during dependency
ordering.
For now we can't define top-level mutually recursive terms.

demos/levelOrderTraversal.tri

@@ -1,11 +1,9 @@
 -- Level Order Traversal of a labelled binary tree
 -- Objective: Print each "level" of the tree on a separate line
 --
--- NOTICE: This demo relies on tricu base library functions
+-- We model labelled binary trees as nested lists where values act as labels. We
--- 
+-- require explicit notation of empty nodes. Empty nodes can be represented
--- We model labelled binary trees as sublists where values act as labels. We
+-- with an empty list, `[]`, which evaluates to a single node `t`.
--- require explicit not?ation of empty nodes. Empty nodes can be represented 
--- with an empty list, `[]`, which is equivalent to a single node `t`. 
 --
 -- Example tree inputs:
 -- [("1") [("2") [("4") t t] t] [("3") [("5") t t] [("6") t t]]]]
@@ -15,7 +13,6 @@
 --     2   3
 --    /   /  \
 --   4   5    6
---
 
 label = \node : head node
 

demos/size.tri

@@ -1,21 +1,21 @@
 compose = \f g x : f (g x)
 
-succ = y (\self : 
+succ = y (\self :
-  triage 
+  triage
-    1 
+    1
-    t 
+    t
-    (triage 
+    (triage
-      (t (t t)) 
+      (t (t t))
-      (\_ tail : t t (self tail)) 
+      (\_ tail : t t (self tail))
       t))
 
-size = (\x : 
+size = (\x :
-  (y (\self x : 
+  (y (\self x :
-    compose succ 
+    compose succ
-      (triage 
+      (triage
-        (\x : x) 
+        (\x : x)
-        self 
+        self
-        (\x y : compose (self x) (self y)) 
+        (\x y : compose (self x) (self y))
         x)) x 0))
 
 size size

lib/base.tri

@@ -18,9 +18,9 @@ y = ((\mut wait fun : wait mut (\x : fun (wait mut x)))
 triage = \leaf stem fork : t (t leaf stem) fork
 test   = triage "Leaf" (\_ : "Stem") (\_ _ : "Fork")
 
-matchBool = (\ot of : triage 
+matchBool = (\ot of : triage
-  of 
+  of
-  (\_ : ot) 
+  (\_ : ot)
   (\_ _ : ot)
 )
 
@@ -35,44 +35,44 @@ emptyList? = matchList true (\_ _ : false)
 head = matchList t (\head _ : head)
 tail = matchList t (\_ tail : tail)
 
-lconcat = y (\self : matchList 
+lconcat = y (\self : matchList
-  (\k : k) 
+  (\k : k)
   (\h r k : pair h (self r k)))
 
-lAnd = (triage 
+lAnd = (triage
-  (\_     : false) 
+  (\_     : false)
-  (\_ x   : x) 
+  (\_ x   : x)
   (\_ _ x : x))
 
-lOr = (triage 
+lOr = (triage
-  (\x     : x) 
+  (\x     : x)
-  (\_ _   : true) 
+  (\_ _   : true)
   (\_ _ _ : true))
 
-map_ = y (\self : 
+map_ = y (\self :
-  matchList 
+  matchList
-    (\_ : t) 
+    (\_ : t)
     (\head tail f : pair (f head) (self tail f)))
 map = \f l : map_ l f
 
-equal? = y (\self : triage 
+equal? = y (\self : triage
-  (triage 
+  (triage
-    true 
+    true
-    (\_   : false) 
+    (\_   : false)
-    (\_ _ : false)) 
+    (\_ _ : false))
-  (\ax : 
+  (\ax :
-    triage 
+    triage
-      false 
+      false
-      (self ax) 
+      (self ax)
-      (\_ _ : false)) 
+      (\_ _ : false))
-  (\ax ay : 
+  (\ax ay :
-    triage 
+    triage
-      false 
+      false
-      (\_ : false) 
+      (\_ : false)
       (\bx by : lAnd (self ax bx) (self ay by))))
 
-filter_ = y (\self : matchList 
+filter_ = y (\self : matchList
-  (\_ : t) 
+  (\_ : t)
   (\head tail f : matchBool (t head) i (f head) (self tail f)))
 filter  = \f l : filter_ l f
 

src/Eval.hs

@@ -3,19 +3,19 @@ module Eval where
 import Parser
 import Research
 
+import Data.List (partition)
 import Data.Map  (Map)
-
 import qualified Data.Map as Map
 import qualified Data.Set as Set
 
 evalSingle :: Env -> TricuAST -> Env
 evalSingle env term
-  | SFunc name [] body <- term =
+  | SDef name [] body <- term =
       if
-        | Map.member name env -> 
+        | Map.member name env ->
-            errorWithoutStackTrace $ 
+            errorWithoutStackTrace $
               "Error: Identifier '" ++ name ++ "' is already defined."
-        | otherwise -> 
+        | otherwise ->
             let res = evalAST env body
             in Map.insert "__result" res (Map.insert name res env)
   | SApp func arg <- term =
@@ -23,18 +23,23 @@ evalSingle env term
       in Map.insert "__result" res env
   | SVar name <- term =
       case Map.lookup name env of
-        Just v  -> Map.insert "__result" v env
+        Just v  ->
-        Nothing -> errorWithoutStackTrace $ "Variable `" ++ name ++ "` not defined"
+          Map.insert "__result" v env
+        Nothing ->
+          errorWithoutStackTrace $ "Variable `" ++ name ++ "` not defined\n\
+          \This error should never occur here. Please report this as an issue."
   | otherwise =
       Map.insert "__result" (evalAST env term) env
 
 evalTricu :: Env -> [TricuAST] -> Env
-evalTricu env []     = env
+evalTricu env x = go env (reorderDefs env x)
-evalTricu env [x]    =
+  where
-  let updatedEnv = evalSingle env x
+    go env []     = env
-  in Map.insert "__result" (result updatedEnv) updatedEnv
+    go env [x]    =
-evalTricu env (x:xs) =
+      let updatedEnv = evalSingle env x
-  evalTricu (evalSingle env x) xs
+      in Map.insert "__result" (result updatedEnv) updatedEnv
+    go env (x:xs) =
+      evalTricu (evalSingle env x) xs
 
 evalAST :: Env -> TricuAST -> T
 evalAST env term
@@ -61,13 +66,13 @@ elimLambda = go
     go (SLambda [v] (SApp f (SVar x)))
       | v == x && not (isFree v f) = elimLambda f
     -- Triage optimization
-    go (SLambda [a] (SLambda [b] (SLambda [c] body))) 
+    go (SLambda [a] (SLambda [b] (SLambda [c] body)))
       | body == triageBody         = _TRIAGE
       where
         triageBody =
           (SApp (SApp TLeaf (SApp (SApp TLeaf (SVar a)) (SVar b))) (SVar c))
     -- Composition optimization
-    go (SLambda [f] (SLambda [g] (SLambda [x] body))) 
+    go (SLambda [f] (SLambda [g] (SLambda [x] body)))
       | body == composeBody        = _COMPOSE
       where
         composeBody = SApp (SVar f) (SApp (SVar g) (SVar x))
@@ -93,20 +98,84 @@ elimLambda = go
     _I       = parseSingle "t (t (t t)) t"
     _TRIAGE  = parseSingle "t (t (t t (t (t (t t t))))) t"
     _COMPOSE = parseSingle "t (t (t t (t (t (t t t)) t))) (t t)"
-    
+
-    isFree x = Set.member x . freeVars
+isFree :: String -> TricuAST -> Bool
-    freeVars (SVar    v    ) = Set.singleton v
+isFree x = Set.member x . freeVars
-    freeVars (SInt    _    ) = Set.empty
+
-    freeVars (SStr    _    ) = Set.empty
+freeVars :: TricuAST -> Set.Set String
-    freeVars (SList   s    ) = foldMap freeVars s
+freeVars (SVar    v    ) = Set.singleton v
-    freeVars (SApp    f a  ) = freeVars f <> freeVars a
+freeVars (SInt    _    ) = Set.empty
-    freeVars (TLeaf        ) = Set.empty
+freeVars (SStr    _    ) = Set.empty
-    freeVars (SFunc   _ _ b) = freeVars b
+freeVars (SList   s    ) = foldMap freeVars s
-    freeVars (TStem   t    ) = freeVars t
+freeVars (SApp    f a  ) = freeVars f <> freeVars a
-    freeVars (TFork   l r  ) = freeVars l <> freeVars r
+freeVars (TLeaf        ) = Set.empty
-    freeVars (SLambda v b  ) = foldr Set.delete (freeVars b) v
+freeVars (SDef   _ _ b) = freeVars b
+freeVars (TStem   t    ) = freeVars t
+freeVars (TFork   l r  ) = freeVars l <> freeVars r
+freeVars (SLambda v b  ) = foldr Set.delete (freeVars b) v
+
+reorderDefs :: Env -> [TricuAST] -> [TricuAST]
+reorderDefs env defs
+  | not (null missingDeps) =
+      errorWithoutStackTrace $
+        "Missing dependencies detected: " ++ show missingDeps
+  | otherwise = orderedDefs ++ others
+  where
+    (defsOnly, others) = partition isDef defs
+    graph              = buildDepGraph defsOnly
+    sortedDefs         = sortDeps graph
+    defMap             = Map.fromList [(name, def) | def@(SDef name _ _) <- defsOnly]
+    orderedDefs        = map (\name -> defMap Map.! name) sortedDefs
+    topDefNames        = Set.fromList (Map.keys defMap)
+    envNames           = Set.fromList (Map.keys env)
+    freeVarsDefs       = foldMap (\(SDef _ _ body) -> freeVars body) defsOnly
+    freeVarsOthers     = foldMap freeVars others
+    allFreeVars        = freeVarsDefs <> freeVarsOthers
+    validNames         = topDefNames `Set.union` envNames
+    missingDeps        = Set.toList (allFreeVars `Set.difference` validNames)
+
+    isDef (SDef _ _ _) = True
+    isDef _            = False
+
+buildDepGraph :: [TricuAST] -> Map.Map String (Set.Set String)
+buildDepGraph topDefs
+  | not (null duplicateNames) =
+      errorWithoutStackTrace $
+        "Duplicate definitions detected: " ++ show duplicateNames
+  | otherwise =
+      Map.fromList
+        [ (name, depends topDefs (SDef name [] body))
+        | SDef name _ body <- topDefs]
+  where
+    names = [name | SDef name _ _ <- topDefs]
+    duplicateNames =
+      [ name | (name, count) <- Map.toList (countOccurrences names) , count > 1]
+    countOccurrences = foldr (\x -> Map.insertWith (+) x 1) Map.empty
+
+sortDeps :: Map.Map String (Set.Set String) -> [String]
+sortDeps graph = go [] (Map.keys graph)
+  where
+    go sorted [] = sorted
+    go sorted remaining
+      | null ready =
+          errorWithoutStackTrace
+            "ERROR: Top-level cyclic dependency detected and prohibited\n\
+           \RESOLVE: Use nested lambdas"
+      | otherwise = go (sorted ++ ready) notReady
+      where
+        ready    = [ name | name <- remaining
+                    , all (`elem` sorted) (Set.toList (graph Map.! name))]
+        notReady =
+          [ name | name <- remaining , name `notElem` ready]
+
+depends :: [TricuAST] -> TricuAST -> Set.Set String
+depends topDefs (SDef _ _ body) =
+  Set.intersection
+    (Set.fromList [n | SDef n _ _ <- topDefs])
+    (freeVars body)
+depends _ _ = Set.empty
 
 result :: Env -> T
 result r = case Map.lookup "__result" r of
   Just a -> a
-  Nothing -> errorWithoutStackTrace "No __result field found in provided environment"
+  Nothing -> errorWithoutStackTrace "No __result field found in provided env"

src/Parser.hs

@@ -112,7 +112,7 @@ parseFunctionM = do
   _    <- satisfyM (== LAssign)
   scnParserM
   body <- parseExpressionM
-  pure (SFunc name (map getIdentifier args) body)
+  pure (SDef name (map getIdentifier args) body)
 
 parseLambdaM :: ParserM TricuAST
 parseLambdaM = do

src/Research.hs

@@ -19,7 +19,7 @@ data TricuAST
   | SInt Int
   | SStr String
   | SList [TricuAST]
-  | SFunc String [String] TricuAST
+  | SDef String [String] TricuAST
   | SApp TricuAST TricuAST
   | TLeaf
   | TStem TricuAST

test/Spec.hs

@@ -85,7 +85,7 @@ parser = testGroup "Parser Tests"
 
   , testCase "Parse function definitions" $ do
       let input = "x = (\\a b c : a)"
-          expect = SFunc "x" [] (SLambda ["a"] (SLambda ["b"] (SLambda ["c"] (SVar "a"))))
+          expect = SDef "x" [] (SLambda ["a"] (SLambda ["b"] (SLambda ["c"] (SVar "a"))))
       parseSingle input @?= expect
 
   , testCase "Parse nested Tree Calculus terms" $ do
@@ -105,7 +105,7 @@ parser = testGroup "Parser Tests"
 
   , testCase "Parse function with applications" $ do
       let input  = "f = (\\x : t x)"
-          expect = SFunc "f" [] (SLambda ["x"] (SApp TLeaf (SVar "x")))
+          expect = SDef "f" [] (SLambda ["x"] (SApp TLeaf (SVar "x")))
       parseSingle input @?= expect
 
   , testCase "Parse nested lists" $ do
@@ -147,7 +147,7 @@ parser = testGroup "Parser Tests"
 
   , testCase "Parse nested parentheses in function body" $ do
       let input  = "f = (\\x : t (t (t t)))"
-          expect = SFunc "f" [] (SLambda ["x"] (SApp TLeaf (SApp TLeaf (SApp TLeaf TLeaf))))
+          expect = SDef "f" [] (SLambda ["x"] (SApp TLeaf (SApp TLeaf (SApp TLeaf TLeaf))))
       parseSingle input @?= expect
 
   , testCase "Parse lambda abstractions" $ do
@@ -157,12 +157,12 @@ parser = testGroup "Parser Tests"
 
   , testCase "Parse multiple arguments to lambda abstractions" $ do
       let input  = "x = (\\a b : a)"
-          expect = SFunc "x" [] (SLambda ["a"] (SLambda ["b"] (SVar "a")))
+          expect = SDef "x" [] (SLambda ["a"] (SLambda ["b"] (SVar "a")))
       parseSingle input @?= expect
 
   , testCase "Grouping T terms with parentheses in function application" $ do
       let input  = "x = (\\a : a)\nx (t)"
-          expect = [SFunc "x" [] (SLambda ["a"] (SVar "a")),SApp (SVar "x") TLeaf]
+          expect = [SDef "x" [] (SLambda ["a"] (SVar "a")),SApp (SVar "x") TLeaf]
       parseTricu input @?= expect
 
   , testCase "Comments 1" $ do

test/size.tri

@@ -0,0 +1,21 @@
+compose = \f g x : f (g x)
+
+succ = y (\self :
+  triage
+    1
+    t
+    (triage
+      (t (t t))
+      (\_ tail : t t (self tail))
+      t))
+
+size = (\x :
+  (y (\self x :
+    compose succ
+      (triage
+        (\x : x)
+        self
+        (\x y : compose (self x) (self y))
+        x)) x 0))
+
+size size

test/undefined.tri

@@ -0,0 +1 @@
+namedTerm = undefinedForTesting

tricu.cabal

@@ -1,7 +1,7 @@
 cabal-version: 1.12
 
 name:           tricu
-version:        0.9.0
+version:        0.10.0
 description:    A micro-language for exploring Tree Calculus
 author:         James Eversole
 maintainer:     james@eversole.co