Add Mirror and Snoc type classes to Symbol

bower.json

@@ -18,5 +18,9 @@
   "dependencies": {
     "purescript-prelude": "^5.0.0",
     "purescript-type-equality": "^4.0.0"
+  },
+  "devDependencies": {
+    "purescript-assert": "^5.0.0",
+    "purescript-console": "^5.0.0"
   }
 }

src/Type/Data/Symbol.purs

@@ -1,12 +1,18 @@
 module Type.Data.Symbol
-  ( module Prim.Symbol
-  , module Data.Symbol
-  , append
-  , compare
-  , uncons
+  ( append
   , class Equals
+  , class Reverse
+  , class ReverseP
+  , class Snoc
+  , compare
   , equals
-  ) where
+  , reverse
+  , module Data.Symbol
+  , module Prim.Symbol
+  , snoc
+  , uncons
+  )
+  where
 
 import Prim.Symbol (class Append, class Compare, class Cons)
 import Data.Symbol (SProxy(..), class IsSymbol, reflectSymbol, reifySymbol)
@@ -33,3 +39,47 @@ instance equalsSymbol
 
 equals :: forall proxy l r o. Equals l r o => proxy l -> proxy r -> Proxy o
 equals _ _ = Proxy
+
+
+-- Reverse
+
+class ReverseP (a :: Symbol) (reversed :: Symbol) | a -> reversed, reversed -> a
+
+instance reverseEmpty :: ReverseP "" ""
+else
+instance reverseCons :: 
+  ( Cons head tail sym
+  , ReverseP tailReverse tail
+  , ReverseP tail tailReverse
+  , Append tailReverse head reversed
+  ) => ReverseP sym reversed
+
+class Reverse (a :: Symbol) (reversed :: Symbol) | a -> reversed, reversed -> a
+
+instance reverseReverseP :: (ReverseP a b, ReverseP b a) => Reverse a b
+
+--| ```purescript
+--| > :t reverse (Proxy :: Proxy "symbol")
+--| Proxy @Symbol "lobmys"
+--| ```
+-- | 
+reverse :: ∀ proxy a b. Reverse a b => proxy a -> Proxy b
+reverse _ = Proxy
+
+-- Snoc
+
+--| ```purescript
+--| Snoc "symbo" "l" ?x ~~> ?x = "symbol"
+--| Snoc ?a ?b "symbol" ~~> ?a = "symbo", ?b = "l"
+--| ```
+-- | `end` must be a single character
+class Snoc (list :: Symbol) (end :: Symbol) (symbol :: Symbol) | end list -> symbol, symbol -> end list
+
+instance snocReverse :: (Reverse sym reversed, Cons end listReverse reversed, Reverse listReverse list) => Snoc list end sym
+
+--| ```purescript
+--| > :t snoc (Proxy :: Proxy "symbo") (Proxy :: Proxy "l")
+--| Proxy @Symbol "symbol"
+--| ```
+snoc :: ∀a b c. Snoc a b c => Proxy a -> Proxy b -> Proxy c
+snoc _ _ = Proxy

test/Main.purs

@@ -0,0 +1,64 @@
+module Test.Main where
+
+import Prelude
+
+import Debug (spy)
+import Effect (Effect)
+import Effect.Class.Console (log)
+import Prim.Symbol (class Cons)
+import Test.Assert (assertTrue)
+import Type.Data.Symbol (class IsSymbol, class Reverse, class ReverseP, class Snoc, reflectSymbol, reverse, snoc)
+import Type.Proxy (Proxy(..))
+
+-- reverse
+testReverse :: Proxy "lobmys"
+testReverse = reverse (Proxy :: Proxy "symbol")
+
+testReverseForward :: Proxy _
+testReverseForward = reverse (Proxy:: Proxy "symbol")
+
+testReverseBackward :: Proxy "lobmyys"
+testReverseBackward = reverse (Proxy :: Proxy _)
+
+testReverseSingle :: Proxy "s"
+testReverseSingle = reverse $ Proxy :: Proxy "s"
+
+testReverseEmpty :: Proxy ""
+testReverseEmpty = reverse $ Proxy :: Proxy ""
+
+-- Reversing a reversed Symbol should be the same as the Symbol itself
+propReverseIdem :: forall a b . IsSymbol a => IsSymbol b => Reverse a b => Reverse b a => Proxy a -> Boolean
+propReverseIdem p = reflectSymbol p == reflectSymbol sameThing
+  where
+  sameThing = reverse (reverse p :: Proxy b)
+
+testUnicode :: Proxy "🍎enip"
+testUnicode = reverse (Proxy :: Proxy "pine🍎")
+
+-- snoc
+testSnoc :: Proxy "symbol"
+testSnoc = snoc (Proxy :: Proxy "symbo") (Proxy :: Proxy "l")
+
+testSnocForward :: Proxy _
+testSnocForward = snoc (Proxy :: Proxy "symbo") (Proxy :: Proxy "l")
+
+testSnocBackwardLeft :: Proxy "symbol"
+testSnocBackwardLeft = snoc (Proxy :: Proxy _) (Proxy :: Proxy "l")
+
+testSnocBackwardRight :: Proxy "symbol"
+testSnocBackwardRight = snoc (Proxy :: Proxy "symbo") (Proxy :: Proxy _)
+
+testSnocBackwardBoth :: Proxy "symbol"
+testSnocBackwardBoth = snoc (Proxy :: Proxy _) (Proxy :: Proxy _)
+
+testSnocEmpty :: Proxy "s"
+testSnocEmpty = snoc (Proxy :: Proxy "") (Proxy :: Proxy "s")
+
+main :: Effect Unit
+main = do
+  assertTrue $ propReverseIdem (Proxy :: Proxy "Test Symbol")
+  assertTrue $ propReverseIdem (Proxy :: Proxy "Unico∀e")
+  assertTrue $ propReverseIdem (Proxy :: Proxy "<-<>")
+  assertTrue $ propReverseIdem (Proxy :: Proxy "")
+  assertTrue $ propReverseIdem (Proxy :: Proxy "1")
+  assertTrue $ propReverseIdem (Proxy :: Proxy "pine🍎")