From 30b9505d5f224bc8cbd403aa5e1bcc1b3c28e05f Mon Sep 17 00:00:00 2001
From: James Eversole <james@eversole.co>
Date: Thu, 6 Feb 2025 08:32:17 -0600
Subject: [PATCH] Clearer definition for apply

---
 lib/patterns.tri | 23 ++++++++++++-----------
 src/Research.hs  | 32 ++++++++++++++++++++------------
 test/Spec.hs     |  8 ++++----
 3 files changed, 36 insertions(+), 27 deletions(-)

diff --git a/lib/patterns.tri b/lib/patterns.tri
index 68dc822..48b2d12 100644
--- a/lib/patterns.tri
+++ b/lib/patterns.tri
@@ -22,14 +22,15 @@ match = (\value patterns :
 
 otherwise = const (t t)
 
--- matchExample = (\x : match x [[(equal? 1)  (\_ : "one")]
---                               [(equal? 2)  (\_ : "two")]
---                               [(equal? 3)  (\_ : "three")]
---                               [(equal? 4)  (\_ : "four")]
---                               [(equal? 5)  (\_ : "five")]
---                               [(equal? 6)  (\_ : "six")]
---                               [(equal? 7)  (\_ : "seven")]
---                               [(equal? 8)  (\_ : "eight")]
---                               [(equal? 9)  (\_ : "nine")]
---                               [(equal? 10) (\_ : "ten")]
---                               [ otherwise  (\_ : "I ran out of fingers!")]])
+matchExample = (\x : match x
+  [[(equal? 1)  (\_ : "one")]
+  [(equal? 2)  (\_ : "two")]
+  [(equal? 3)  (\_ : "three")]
+  [(equal? 4)  (\_ : "four")]
+  [(equal? 5)  (\_ : "five")]
+  [(equal? 6)  (\_ : "six")]
+  [(equal? 7)  (\_ : "seven")]
+  [(equal? 8)  (\_ : "eight")]
+  [(equal? 9)  (\_ : "nine")]
+  [(equal? 10) (\_ : "ten")]
+  [ otherwise  (\_ : "I ran out of fingers!")]])
diff --git a/src/Research.hs b/src/Research.hs
index ddec44a..8f74e97 100644
--- a/src/Research.hs
+++ b/src/Research.hs
@@ -55,15 +55,24 @@ data EvaluatedForm = TreeCalculus | FSL | AST | Ternary | Ascii | Decode
 -- Environment containing previously evaluated TC terms
 type Env = Map.Map String T
 
--- Tree Calculus Reduction
+-- Tree Calculus Reduction Rules
+{- 
+  The t operator is left associative.
+  1.  t  t      a b       -> a
+  2.  t (t a)   b c       -> a c (b c)
+  3a. t (t a b) c t       -> a
+  3b. t (t a b) c (t u)   -> b u
+  3c. t (t a b) c (t u v) -> c u v
+-}
 apply :: T -> T -> T
-apply Leaf b                            = Stem b
-apply (Stem a) b                        = Fork a b
-apply (Fork Leaf a) _                   = a
-apply (Fork (Stem a1) a2) b             = apply (apply a1 b) (apply a2 b)
-apply (Fork (Fork a1 a2) a3) Leaf       = a1
-apply (Fork (Fork a1 a2) a3) (Stem u)   = apply a2 u
-apply (Fork (Fork a1 a2) a3) (Fork u v) = apply (apply a3 u) v
+apply (Fork Leaf a)         _         = a
+apply (Fork (Stem a) b) c             = apply (apply a c) (apply b c)
+apply (Fork (Fork a  b) c)  Leaf      = a
+apply (Fork (Fork a  b) c) (Stem u)   = apply b u
+apply (Fork (Fork a  b) c) (Fork u v) = apply (apply c u) v
+-- Left associative `t`
+apply  Leaf b                         = Stem b
+apply (Stem a) b                      = Fork a b
 
 -- Booleans
 _false :: T
@@ -77,7 +86,7 @@ _not = Fork (Fork _true (Fork Leaf _false)) Leaf
 
 -- Marshalling
 ofString :: String -> T
-ofString str = ofList (map ofNumber (map fromEnum str))
+ofString str = ofList $ map (ofNumber . fromEnum) str
 
 ofNumber :: Int -> T
 ofNumber 0 = Leaf
@@ -87,8 +96,7 @@ ofNumber n =
     (ofNumber (n `div` 2))
 
 ofList :: [T] -> T
-ofList [] = Leaf
-ofList (x:xs) = Fork x (ofList xs)
+ofList = foldr Fork Leaf
 
 toNumber :: T -> Either String Int
 toNumber Leaf = Right 0
@@ -126,7 +134,7 @@ toSimpleT s = T.unpack
   $ replace "Fork" "t"
   $ replace "Stem" "t"
   $ replace "Leaf" "t"
-  $ (T.pack s)
+  $ T.pack s
 
 toTernaryString :: T -> String
 toTernaryString Leaf = "0"
diff --git a/test/Spec.hs b/test/Spec.hs
index 3a8dcfc..5a468b4 100644
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -329,20 +329,20 @@ lambdas = testGroup "Lambda Evaluation Tests"
         let input = "f = (\\x : (\\y : x y))\ng = (\\z : z)\nf g t"
         runTricu input @?= "Leaf"
 
-  , testCase "Lambda with a string literal" $ do
+  , testCase "Lambda applied to string literal" $ do
         let input = "f = (\\x : x)\nf \"hello\""
         runTricu input @?= "Fork (Fork Leaf (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork Leaf (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) (Fork (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork (Stem Leaf) Leaf))))))) Leaf))))"
 
 
-   , testCase "Lambda with an integer literal" $ do
+   , testCase "Lambda applied to integer literal" $ do
         let input = "f = (\\x : x)\nf 42"
         runTricu input @?= "Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) (Fork Leaf (Fork (Stem Leaf) Leaf)))))"
 
-   , testCase "Lambda with a list literal" $ do
+   , testCase "Lambda applied to list literal" $ do
         let input = "f = (\\x : x)\nf [t (t t)]"
         runTricu input @?= "Fork Leaf (Fork (Stem Leaf) Leaf)"
 
-  , testCase "Lambda with list literal" $ do
+  , testCase "Lambda containing list literal" $ do
       let input = "(\\a : [(a)]) 1"
       runTricu input @?= "Fork (Fork (Stem Leaf) Leaf) Leaf"
   ]