5 files changed, 84 insertions, 11 deletions
diff --git a/bruijn.cabal b/bruijn.cabal
index 676ad66..18de000 100644
--- a/bruijn.cabal
+++ b/bruijn.cabal
@@ -21,7 +21,6 @@ data-files:
     std/Box.bruijn
     std/Char.bruijn
     std/Combinator.bruijn
-    std/Float.bruijn
     std/List.bruijn
     std/Logic.bruijn
     std/Math.bruijn
diff --git a/editors/vim/syntax/bruijn.vim b/editors/vim/syntax/bruijn.vim
index 2556ceb..fbe7a47 100644
--- a/editors/vim/syntax/bruijn.vim
+++ b/editors/vim/syntax/bruijn.vim
@@ -10,6 +10,8 @@ syn match bruijnAbstraction /[[\]]/
 syn match bruijnIndex /\([^0-9A-Za-z]\)\@<=\d\([^0-9]\)\@=/
 syn match bruijnChar /'\@<=.'\@=/
 syn match bruijnNumber /([+-]\d\+[dubt]\?)/
+syn match bruijnFloat /([+-]\d\+\.\d\+[fr]\?)/
+syn match bruijnComplex /([+-]\d\+\.\d\+i[+-]\d\+\.\d\+)/
 syn match bruijnDefinition /^\t*\S\+/
 syn match bruijnType /\( ⧗ \)\@<=.*$/
 syn match bruijnTypeDelim / ⧗ /
@@ -22,6 +24,8 @@ syn region bruijnString start=+"+ end=+"+ oneline
 
 hi def link bruijnIndex Special
 hi def link bruijnNumber Number
+hi def link bruijnFloat Number
+hi def link bruijnComplex Number
 hi def link bruijnString String
 hi def link bruijnChar String
 hi def link bruijnDefinition Define
@@ -60,6 +64,7 @@ abbreviate <buffer> kket ⟫
 abbreviate <buffer> <=? ≤
 abbreviate <buffer> >=? ≥
 abbreviate <buffer> /= ≠
+abbreviate <buffer> ~= ≈
 abbreviate <buffer> ! ¬
 abbreviate <buffer> _0 ₀
 abbreviate <buffer> _1 ₁
diff --git a/src/Helper.hs b/src/Helper.hs
index 8ea5600..921604c 100644
--- a/src/Helper.hs
+++ b/src/Helper.hs
@@ -344,7 +344,9 @@ maybeHumanifyExpression e =
     <|> binaryToChar e
     <|> binaryToString e
     <|> ternaryToString e
-    <|> rationalToFloat e
+    <|> rationalToString e
+    <|> realToString e
+    <|> complexToString e
     <|> humanifyString e
     <|> humanifyList e
     <|> humanifyPair e
@@ -398,8 +400,9 @@ floatToRational f = Abstraction
 floatToReal :: Rational -> Expression
 floatToReal = Abstraction . floatToRational
 
-floatToComplex :: Rational -> Expression
-floatToComplex f = Bruijn 0
+floatToComplex :: Rational -> Rational -> Expression
+floatToComplex r i = Abstraction
+  $ Application (Application (Bruijn 0) (floatToReal r)) (floatToReal i)
 
 -- Dec to Bal3 in Bruijn encoding: reversed application with 0=>0; 1=>1; T=>2; end=>3
 -- e.g. 0=0=[[[[3]]]]; 2=1T=[[[[2 (1 3)]]]] -5=T11=[[[[1 (1 (2 3))]]]]
@@ -504,11 +507,10 @@ ternaryToDecimal e = do
     resolve' n
   resolve _ = Nothing
 
-rationalToFloat :: Expression -> Maybe String
-rationalToFloat (Abstraction (Application (Application (Bruijn 0) a) b)) = do
+rationalToString :: Expression -> Maybe String
+rationalToString (Abstraction (Application (Application (Bruijn 0) a) b)) = do
   n <- ternaryToDecimal a
   d <- ternaryToDecimal b
-  -- let (h, r) = properFraction (n % (d + 1))
   Just
     $  show n
     <> "/"
@@ -519,4 +521,39 @@ rationalToFloat (Abstraction (Application (Application (Bruijn 0) a) b)) = do
                       ""
        )
     <> ")"
-rationalToFloat _ = Nothing
+rationalToString _ = Nothing
+
+realToString :: Expression -> Maybe String
+realToString (Abstraction e) = rationalToString e
+realToString _               = Nothing
+
+complexToString :: Expression -> Maybe String
+complexToString (Abstraction (Application (Application (Bruijn 0) (Abstraction (Abstraction (Application (Application (Bruijn 0) lr) rr)))) (Abstraction (Abstraction (Application (Application (Bruijn 0) li) ri)))))
+  = do
+    nlr <- ternaryToDecimal lr
+    drr <- ternaryToDecimal rr
+    nli <- ternaryToDecimal li
+    dri <- ternaryToDecimal ri
+    Just
+      $  show nlr
+      <> "/"
+      <> show (drr + 1)
+      <> " + "
+      <> show nli
+      <> "/"
+      <> show (dri + 1)
+      <> "i"
+      <> " (approx. "
+      <> (showFFloatAlt
+           (Just 8)
+           ((fromIntegral nlr) / (fromIntegral $ drr + 1) :: Double)
+           ""
+         )
+      <> "+"
+      <> (showFFloatAlt
+           (Just 8)
+           ((fromIntegral nli) / (fromIntegral $ dri + 1) :: Double)
+           ""
+         )
+      <> "i)"
+complexToString _ = Nothing
diff --git a/src/Parser.hs b/src/Parser.hs
index a63b4a2..a24db6f 100644
--- a/src/Parser.hs
+++ b/src/Parser.hs
@@ -149,13 +149,12 @@ parseFloat :: Parser Expression
 parseFloat = do
   _    <- string "(" <?> "float start"
   num  <- signedFloat <?> "signed float"
-  base <- try (oneOf "frc") <|> return 'f'
+  base <- try (oneOf "fr") <|> return 'f'
   _    <- string ")" <?> "float end"
   pure $ f base num
  where
   f 'f' = floatToRational
   f 'r' = floatToReal
-  f 'c' = floatToComplex -- TODO: imaginary
   f _   = invalidProgramState
   sign :: Parser (Rational -> Rational)
   sign = (char '-' >> return negate) <|> (char '+' >> return id)
@@ -168,6 +167,26 @@ parseFloat = do
   signedFloat :: Parser Rational
   signedFloat = ap sign float
 
+parseComplex :: Parser Expression
+parseComplex = do
+  _         <- string "(" <?> "complex start"
+  real      <- signedFloat <?> "signed complex"
+  _         <- char 'i'
+  imaginary <- signedFloat <?> "signed complex"
+  _         <- string ")" <?> "complex end"
+  pure $ floatToComplex real imaginary
+ where
+  sign :: Parser (Rational -> Rational)
+  sign = (char '-' >> return negate) <|> (char '+' >> return id)
+  float :: Parser Rational
+  float = do
+    a <- read <$> some digitChar <?> "digits"
+    _ <- char '.' <?> "float delimiter"
+    b <- read <$> some digitChar <?> "digits"
+    return $ convertToRational a b
+  signedFloat :: Parser Rational
+  signedFloat = ap sign float
+
 specialEscape :: Parser Char
 specialEscape =
   choice (zipWith (\c r -> r <$ char c) "bnfrt\\\"/" "\b\n\f\r\t\\\"/")
@@ -233,6 +252,7 @@ parseSingleton :: Parser Expression
 parseSingleton =
   let parseSingletonExpression =
         parseBruijn
+          <|> try parseComplex
           <|> try parseNumeral
           <|> try parseFloat
           <|> parseString
diff --git a/std/Math/Complex.bruijn b/std/Math/Complex.bruijn
index f40f876..ec83462 100644
--- a/std/Math/Complex.bruijn
+++ b/std/Math/Complex.bruijn
@@ -10,23 +10,35 @@
 # adds two complex numbers
 add &[[&[[(R.add 3 1) : (R.add 2 0)]]]] ⧗ Complex → Complex → Complex
 
+…+… add
+
 # subtracts two complex numbers
 sub &[[&[[(R.sub 3 1) : (R.sub 2 0)]]]] ⧗ Complex → Complex → Complex
 
+…+… sub
+
 # multiplies two complex numbers
 mul &[[&[[p : q]]]] ⧗ Complex → Complex → Complex
 	p R.sub (R.mul 3 1) (R.mul 2 0)
 	q R.add (R.mul 3 0) (R.mul 2 1)
 
+…⋅… mul
+
 # divides two complex numbers
 div &[[&[[p : q]]]] ⧗ Complex → Complex → Complex
 	p R.div (R.add (R.mul 3 1) (R.mul 2 0)) (R.add (R.mul 1 1) (R.mul 0 0))
 	q R.div (R.sub (R.mul 2 1) (R.mul 1 0)) (R.add (R.mul 1 1) (R.mul 0 0))
 
+…/… div
+
 # negates a complex number
 negate &[[(R.negate 1) : (R.negate 0)]] ⧗ Complex → Complex
 
+-‣ negate
+
 # inverts a complex number
-invert &[[p : q]]
+invert &[[p : q]] ⧗ Complex → Complex
 	p R.div 1 (R.add (R.mul 1 1) (R.mul 0 0))
 	q R.div 0 (R.add (R.mul 1 1) (R.mul 0 0))
+
+~‣ invert