[doc] Thin.hs

Src/Thin.hs

@@ -1,36 +1,47 @@
+{- Description: Thinnings. Used as co-de Bruijn indices for syntax with binding.
+
+ Note that this is largely standalone, depending only on Bwd (snoc lists).
+
+ While Thinnings are conceptually about what things are used by what, they can
+ adequately be represented by sequences of bits.
+-}
 module Thin where
 
-import Data.Bits
-import Control.Monad
+import Data.Bits (Bits(bit), xor, shiftL, shiftR, complement, zeroBits, (.&.),
+  testBit, (.|.), popCount)
+import Control.Monad (guard)
 
-import GHC.Stack
+import GHC.Stack (HasCallStack) -- for nicer debuggin
 
-import Bwd
+import Bwd (Bwd(B0,(:<))) -- note how we only use the type itself
 
+-- | de Bruijn index
 newtype DB = DB { dbIndex :: Int }
   deriving (Show, Eq, Ord)
 
+-- | Predecessor on DB indices - can fail.
 prd :: HasCallStack => DB -> DB
 prd (DB i) | i <= 0 = error ("Took the prdecessor of DB index " ++ show i)
 prd (DB i) = DB (i - 1)
 
+-- | Successor on DB indices
 scc :: DB -> DB
 scc (DB i) = DB (i + 1)
 
+-- | Thinning representation.
 data Th = Th
-  { thinning :: Integer
-  , bigEnd   :: Int  -- must be non-negative
+  { thinning :: Integer -- the actual bit representation of the thinning
+  , bigEnd   :: Int     -- (the representation of) its size, must be non-negative
   }
 
+-- | 'Thinnable' with a shorter name.
 class Thable t where
   (*^) :: HasCallStack => t -> Th -> t
 
+-- | 'Selectable' with a shorter name
 class Selable t where
   (^?) :: Th -> t -> t
 
-instance Thable (CdB a) where
-  CdB a th *^ ph = CdB a (th *^ ph)
-
 {-
 thinning composition is diagrammatic
 good luck enforcing composability!
@@ -43,57 +54,69 @@ o----->o----->o
 o----->o----->o
 -}
 
-instance Thable Th where
-  _  *^ Th _  0 = none 0
-  th *^ ph = case thun ph of
-    (ph, False) -> (th *^ ph) -? False
-    (ph, True)  -> case thun th of
-      (th, b) -> (th *^ ph) -? b
-
-instance Selable Th where
-  (^?) = (*^)
-
-instance Thable DB where
-  DB i *^ th | i >= bigEnd th = error $ "Failed thinning " ++ show i ++ " by " ++ show th
-  i *^ th = case thun th of
-    (th, False) -> scc (i *^ th)
-    (th, True) -> case i of
-      DB 0 -> DB 0
-      i -> scc (prd i *^ th)
-
--- 2^(i-1), which is a remarkably well behaved thing
+-- | 'full' thinning, i.e. 2^(i-1), which is a remarkably well behaved thing
 full :: Bits a => Int -> a
 full i = xor (shiftL ones i) ones where ones = complement zeroBits
 
+-- | frequent pattern: getting the 'bits' for the lower part of a thinning
+theBits :: Th -> Integer
+theBits (Th th i) = th .&. full i
+
+-- | Two thinnings are equal when they are of the same size, and have the 
+-- pattern of bits at that size.
 instance Eq Th where
-  Th th i == Th ph j = (i == j) && ((th .&. full i) == (ph .&. full j))
+  x == y = bigEnd x == bigEnd y && theBits x == theBits y
+  -- Th th i == Th ph j = (i == j) && ((th .&. full i) == (ph .&. full j))
 
+-- | Order two thinings by first comparing their size, then their bit patterns
 instance Ord Th where
-  compare (Th th i) (Th ph j) = compare (i, th .&. full i) (j, ph .&. full j)
+  -- compare (Th th i) (Th ph j) = compare (i, th .&. full i) (j, ph .&. full j)
+  compare x y = compare (bigEnd x, theBits x) (bigEng y, theBits y)
 
+-- | Number of set bits in the part we care about
 weeEnd :: Th -> Int
-weeEnd (Th th i) = popCount (th .&. full i)
+weeEnd = popCount . theBits
 
+-- | Particular thinnings (at a given size): all used, none used.
 ones, none :: Int -> Th
 ones i = Th (full i) i
 none i = Th 0 i
 
-is0s, is1s :: Th -> Bool
-is0s th = th == none (bigEnd th)
+-- | Is this the thinning where everything is used?
+is1s :: Th -> Bool
 is1s th = th == ones (bigEnd th)
 
--- snoc for bits
+-- | (-?) is snoc for thinnings-as-bits
 (-?) :: Th -> Bool -> Th
 Th th i -? b = Th (go b) (i+1) where
   th' = shiftL th 1
   go True  = th' .|. bit 0
   go False = th'
 
--- inverts snoc
+-- | thun inverts snoc, i.e. pulls off the lower-order bit
 thun :: HasCallStack => Th -> (Th, Bool)
 thun (Th th i) | i <= 0 = error $ "thun with i = " ++ show i
 thun (Th th i) = (Th (shiftR th 1) (i-1), testBit th 0)
 
+-- Thinnigs are thinnable...
+instance Thable Th where
+  _  *^ Th _  0 = none 0
+  th *^ ph = case thun ph of
+    (ph, False) -> (th *^ ph) -? False
+    (ph, True)  -> case thun th of
+      (th, b) -> (th *^ ph) -? b
+
+instance Selable Th where
+  (^?) = (*^)
+
+instance Thable DB where
+  DB i *^ th | i >= bigEnd th = error $ "Failed thinning " ++ show i ++ " by " ++ show th
+  i *^ th = case thun th of
+    (th, False) -> scc (i *^ th)
+    (th, True) -> case i of
+      DB 0 -> DB 0
+      i -> scc (prd i *^ th)
+
 instance Show Th where
   show th@(Th _ i) = "[" ++ go i th "]" where
     go 0 th = id
@@ -150,6 +173,9 @@ chopTh w th = case thun th of
 data CdB a = CdB a Th
   deriving (Show, Eq, Ord)
 
+instance Thable (CdB a) where
+  CdB a th *^ ph = CdB a (th *^ ph)
+
 weak :: CdB a -> CdB a
 weak (CdB t th) = CdB t (th -? False)