From f08a9fb208a32ee8f450649095c4f8a0f05931da Mon Sep 17 00:00:00 2001
From: Eduardo Julian
Date: Mon, 4 Sep 2017 19:41:59 -0400
Subject: - Re-named "real" numbers to "frac"(tions).

---
 stdlib/source/lux.lux                         |  92 +++++-----
 stdlib/source/lux/control/concatenative.lux   |  24 +--
 stdlib/source/lux/data/color.lux              | 232 +++++++++++++-------------
 stdlib/source/lux/data/format/css.lux         |   2 +-
 stdlib/source/lux/data/format/json.lux        |   8 +-
 stdlib/source/lux/data/format/json/codec.lux  |  38 ++---
 stdlib/source/lux/data/format/json/reader.lux |   6 +-
 stdlib/source/lux/data/number.lux             | 156 ++++++++---------
 stdlib/source/lux/data/number/complex.lux     | 200 +++++++++++-----------
 stdlib/source/lux/data/text/format.lux        |   2 +-
 stdlib/source/lux/host.js.lux                 |   6 +-
 stdlib/source/lux/host.jvm.lux                |   4 +-
 stdlib/source/lux/macro.lux                   |   2 +-
 stdlib/source/lux/macro/code.lux              |   8 +-
 stdlib/source/lux/macro/poly.lux              |   4 +-
 stdlib/source/lux/macro/poly/eq.lux           |   2 +-
 stdlib/source/lux/macro/syntax.lux            |   2 +-
 stdlib/source/lux/math.lux                    |  16 +-
 stdlib/source/lux/math/logic/fuzzy.lux        |  18 +-
 stdlib/source/lux/math/random.lux             |  12 +-
 20 files changed, 417 insertions(+), 417 deletions(-)

(limited to 'stdlib/source')

diff --git a/stdlib/source/lux.lux b/stdlib/source/lux.lux
index 7a49fb2ec..d29e4fca5 100644
--- a/stdlib/source/lux.lux
+++ b/stdlib/source/lux.lux
@@ -25,9 +25,9 @@
           (+1 [["lux" "doc"] (+5 "Your standard, run-of-the-mill integer numbers.")]
               (+0)))))
 
-(_lux_def Real
-  (+12 ["lux" "Real"]
-       (+0 "#Real" (+0)))
+(_lux_def Frac
+  (+12 ["lux" "Frac"]
+       (+0 "#Frac" (+0)))
   (+1 [["lux" "type?"] (+0 true)]
       (+1 [["lux" "export?"] (+0 true)]
           (+1 [["lux" "doc"] (+5 "Your standard, run-of-the-mill floating-point numbers.")]
@@ -212,7 +212,7 @@
 ##   (#NatA Nat)
 ##   (#IntA Int)
 ##   (#DegA Deg)
-##   (#RealA Real)
+##   (#FracA Frac)
 ##   (#TextA Text)
 ##   (#IdentA Ident)
 ##   (#ListA (List Ann-Value))
@@ -231,8 +231,8 @@
                                Int
                                (#Sum ## #DegA
                                 Deg
-                                (#Sum ## #RealA
-                                 Real
+                                (#Sum ## #FracA
+                                 Frac
                                  (#Sum ## #TextA
                                   Text
                                   (#Sum ## #IdentA
@@ -249,7 +249,7 @@
                                                   (#Cons (+5 "NatA")
                                                          (#Cons (+5 "IntA")
                                                                 (#Cons (+5 "DegA")
-                                                                       (#Cons (+5 "RealA")
+                                                                       (#Cons (+5 "FracA")
                                                                               (#Cons (+5 "TextA")
                                                                                      (#Cons (+5 "IdentA")
                                                                                             (#Cons (+5 "ListA")
@@ -380,7 +380,7 @@
 ##   (#Nat Nat)
 ##   (#Int Int)
 ##   (#Deg Deg)
-##   (#Real Real)
+##   (#Frac Frac)
 ##   (#Text Text)
 ##   (#Symbol Text Text)
 ##   (#Tag Text Text)
@@ -404,8 +404,8 @@
                          Int
                          (#Sum ## "lux;Deg"
                           Deg
-                          (#Sum ## "lux;Real"
-                           Real
+                          (#Sum ## "lux;Frac"
+                           Frac
                            (#Sum ## "lux;Text"
                             Text
                             (#Sum ## "lux;Symbol"
@@ -424,7 +424,7 @@
                                         (#Cons (#TextA "Nat")
                                                (#Cons (#TextA "Int")
                                                       (#Cons (#TextA "Deg")
-                                                             (#Cons (#TextA "Real")
+                                                             (#Cons (#TextA "Frac")
                                                                     (#Cons (#TextA "Text")
                                                                            (#Cons (#TextA "Symbol")
                                                                                   (#Cons (#TextA "Tag")
@@ -732,9 +732,9 @@
     (_lux_function _ value (_meta (#Deg value))))
   #Nil)
 
-(_lux_def real$
-  (_lux_: (#Function Real Code)
-    (_lux_function _ value (_meta (#Real value))))
+(_lux_def frac$
+  (_lux_: (#Function Frac Code)
+    (_lux_function _ value (_meta (#Frac value))))
   #Nil)
 
 (_lux_def text$
@@ -1778,8 +1778,8 @@
     [_ [_ (#Deg value)]]
     (return (wrap-meta (form$ (list (tag$ ["lux" "Deg"]) (deg$ value)))))
     
-    [_ [_ (#Real value)]]
-    (return (wrap-meta (form$ (list (tag$ ["lux" "Real"]) (real$ value)))))
+    [_ [_ (#Frac value)]]
+    (return (wrap-meta (form$ (list (tag$ ["lux" "Frac"]) (frac$ value)))))
 
     [_ [_ (#Text value)]]
     (return (wrap-meta (form$ (list (tag$ ["lux" "Text"]) (text$ value)))))
@@ -2121,16 +2121,16 @@
        (_lux_proc [<category> "="] [subject test])))]
 
   [ Nat "nat"  n.= n.< n.<= n.> n.>=
-   "Natural equality." "Natural less-than." "Natural less-than-equal." "Natural greater-than." "Natural greater-than-equal."]
+   "Nat(ural) equality." "Nat(ural) less-than." "Nat(ural) less-than-equal." "Nat(ural) greater-than." "Nat(ural) greater-than-equal."]
 
   [ Int "int"  i.= i.< i.<= i.> i.>=
-   "Integer equality." "Integer less-than." "Integer less-than-equal." "Integer greater-than." "Integer greater-than-equal."]
+   "Int(eger) equality." "Int(eger) less-than." "Int(eger) less-than-equal." "Int(eger) greater-than." "Int(eger) greater-than-equal."]
   
   [ Deg "deg"  d.= d.< d.<= d.> d.>=
-   "Degree equality." "Degree less-than." "Degree less-than-equal." "Degree greater-than." "Degree greater-than-equal."]
+   "Deg(ree) equality." "Deg(ree) less-than." "Deg(ree) less-than-equal." "Deg(ree) greater-than." "Deg(ree) greater-than-equal."]
 
-  [Real "real" r.= r.< r.<= r.> r.>=
-   "Real equality." "Real less-than." "Real less-than-equal." "Real greater-than." "Real greater-than-equal."]
+  [Frac "frac" f.= f.< f.<= f.> f.>=
+   "Frac(tion) equality." "Frac(tion) less-than." "Frac(tion) less-than-equal." "Frac(tion) greater-than." "Frac(tion) greater-than-equal."]
   )
 
 (do-template [<type> <name> <op> <doc>]
@@ -2157,11 +2157,11 @@
   [ Deg d./ [ "deg" "/"] "Deg(ree) division."]
   [ Deg d.% [ "deg" "%"] "Deg(ree) remainder."]
   
-  [Real r.+ ["real" "+"] "Real addition."]
-  [Real r.- ["real" "-"] "Real substraction."]
-  [Real r.* ["real" "*"] "Real multiplication."]
-  [Real r./ ["real" "/"] "Real division."]
-  [Real r.% ["real" "%"] "Real remainder."]
+  [Frac f.+ ["frac" "+"] "Frac(tion) addition."]
+  [Frac f.- ["frac" "-"] "Frac(tion) substraction."]
+  [Frac f.* ["frac" "*"] "Frac(tion) multiplication."]
+  [Frac f./ ["frac" "/"] "Frac(tion) division."]
+  [Frac f.% ["frac" "%"] "Frac(tion) remainder."]
   )
 
 (do-template [<type> <name> <op> <doc>]
@@ -2191,8 +2191,8 @@
   [d.min  Deg d.< "Deg(ree) minimum."]
   [d.max  Deg d.> "Deg(ree) maximum."]
   
-  [r.min Real r.< "Real minimum."]
-  [r.max Real r.> "Real minimum."]
+  [f.min Frac f.< "Frac minimum."]
+  [f.max Frac f.> "Frac minimum."]
   )
 
 (def:''' (Bool/encode x)
@@ -2252,10 +2252,10 @@
            (|> value (i./ 10) Int/abs)
            (|> value (i.% 10) Int/abs (_lux_:! Nat) digit-to-text)))))
 
-(def:''' (Real/encode x)
+(def:''' (Frac/encode x)
   #Nil
-  (-> Real Text)
-  (_lux_proc ["real" "encode"] [x]))
+  (-> Frac Text)
+  (_lux_proc ["frac" "encode"] [x]))
 
 (def:''' (multiple? div n)
   #Nil
@@ -2686,8 +2686,8 @@
     [_ (#Deg value)]
     (_lux_proc ["io" "error"] ["Undefined behavior."])
     
-    [_ (#Real value)]
-    (Real/encode value)
+    [_ (#Frac value)]
+    (Frac/encode value)
 
     [_ (#Text value)]
     ($_ Text/append "\"" value "\"")
@@ -2916,8 +2916,8 @@
     [_ (#Deg value)]
     (return (form$ (list (tag$ ["lux" "DegA"]) (deg$ value))))
 
-    [_ (#Real value)]
-    (return (form$ (list (tag$ ["lux" "RealA"]) (real$ value))))
+    [_ (#Frac value)]
+    (return (form$ (list (tag$ ["lux" "FracA"]) (frac$ value))))
 
     [_ (#Text value)]
     (return (form$ (list (tag$ ["lux" "TextA"]) (text$ value))))
@@ -4877,8 +4877,8 @@
      (-> <from> <to>)
      (_lux_proc <proc> [n]))]
 
-  [real-to-int Real Int  ["real" "to-int"]]
-  [int-to-real Int  Real ["int" "to-real"]]
+  [frac-to-int Frac Int  ["frac" "to-int"]]
+  [int-to-frac Int  Frac ["int" "to-frac"]]
   )
 
 (def: (find-baseline-column ast)
@@ -4891,7 +4891,7 @@
      [#Nat]
      [#Int]
      [#Deg]
-     [#Real]
+     [#Frac]
      [#Text]
      [#Symbol]
      [#Tag])
@@ -4958,8 +4958,8 @@
 
   [int-to-nat ["int" "to-nat"] Int Nat]
   [nat-to-int ["nat" "to-int"] Nat Int]
-  [real-to-deg ["real" "to-deg"] Real Deg]
-  [deg-to-real ["deg" "to-real"] Deg Real]
+  [frac-to-deg ["frac" "to-deg"] Frac Deg]
+  [deg-to-frac ["deg" "to-frac"] Deg Frac]
   )
 
 (def: (repeat n x)
@@ -5008,7 +5008,7 @@
     ([#Bool   Bool/encode]
      [#Nat    Nat/encode]
      [#Int    Int/encode]
-     [#Real   Real/encode]
+     [#Frac   Frac/encode]
      [#Text   Text/encode]
      [#Symbol Ident/encode]
      [#Tag    Tag/encode])
@@ -5208,7 +5208,7 @@
 (def: (place-tokens label tokens target)
   (-> Text (List Code) Code (Maybe (List Code)))
   (case target
-    (^or [_ (#Bool _)] [_ (#Nat _)] [_ (#Int _)] [_ (#Deg _)] [_ (#Real _)] [_ (#Text _)] [_ (#Tag _)])
+    (^or [_ (#Bool _)] [_ (#Nat _)] [_ (#Int _)] [_ (#Deg _)] [_ (#Frac _)] [_ (#Text _)] [_ (#Tag _)])
     (#Some (list target))
 
     [_ (#Symbol [prefix name])]
@@ -5257,7 +5257,7 @@
                              [(bool true)                             "true"       [_ (#;Bool true)]]
                              [(bool false)                            "false"      [_ (#;Bool false)]]
                              [(int 123)                               "123"        [_ (#;Int 123)]]
-                             [(real 123.0)                            "123.0"      [_ (#;Real 123.0)]]
+                             [(frac 123.0)                            "123.0"      [_ (#;Frac 123.0)]]
                              [(text "\n")                             "\"\\n\""    [_ (#;Text "\n")]]
                              [(tag ["yolo" "lol"])                    "#yolo;lol"  [_ (#;Tag ["yolo" "lol"])]]
                              [(symbol ["yolo" "lol"])                 "yolo;lol"   [_ (#;Symbol ["yolo" "lol"])]]
@@ -5302,7 +5302,7 @@
      ["Nat"]
      ["Int"]
      ["Deg"]
-     ["Real"]
+     ["Frac"]
      ["Text"])
     
     (#Named _ type')
@@ -5324,7 +5324,7 @@
        ["Nat"  Nat  nat$]
        ["Int"  Int  int$]
        ["Deg"  Deg  deg$]
-       ["Real" Real real$]
+       ["Frac" Frac frac$]
        ["Text" Text text$])
       
       _
@@ -5362,7 +5362,7 @@
     ))
 
 (macro: #export (^~ tokens)
-  {#;doc (doc "Use global defs with simple values, such as text, int, real and bool in place of literals in patterns."
+  {#;doc (doc "Use global defs with simple values, such as text, int, frac and bool in place of literals in patterns."
               "The definitions must be properly-qualified (though you may use one of the short-cuts Lux provides)."
               (def: (empty?' node)
                 (All [K V] (-> (Node K V) Bool))
diff --git a/stdlib/source/lux/control/concatenative.lux b/stdlib/source/lux/control/concatenative.lux
index a0854ffcf..61a6ddbd0 100644
--- a/stdlib/source/lux/control/concatenative.lux
+++ b/stdlib/source/lux/control/concatenative.lux
@@ -2,7 +2,7 @@
            n.+ n.- n.* n./ n.% n.= n.< n.<= n.> n.>=
            i.+ i.- i.* i./ i.% i.= i.< i.<= i.> i.>=
            d.+ d.- d.* d./ d.% d.= d.< d.<= d.> d.>=
-           r.+ r.- r.* r./ r.% r.= r.< r.<= r.> r.>=]
+           f.+ f.- f.* f./ f.% f.= f.< f.<= f.> f.>=]
   (lux (control ["p" parser "p/" Monad<Parser>]
                 [monad])
        (data [text]
@@ -98,7 +98,7 @@
   (case command
     (^or [_ (#;Bool _)]
          [_ (#;Nat _)]  [_ (#;Int _)]
-         [_ (#;Deg _)]  [_ (#;Real _)]
+         [_ (#;Deg _)]  [_ (#;Frac _)]
          [_ (#;Text _)]
          [_ (#;Tag _)]  (^ [_ (#;Form (list [_ (#;Tag _)]))]))
     (` (;;push (~ command)))
@@ -231,16 +231,16 @@
   [Deg Bool d.>  ;d.>]
   [Deg Bool d.>= ;d.>=]
 
-  [Real Real r.+  ;r.+]
-  [Real Real r.-  ;r.-]
-  [Real Real r.*  ;r.*]
-  [Real Real r./  ;r./]
-  [Real Real r.%  ;r.%]
-  [Real Bool r.=  ;r.=]
-  [Real Bool r.<  ;r.<]
-  [Real Bool r.<= ;r.<=]
-  [Real Bool r.>  ;r.>]
-  [Real Bool r.>= ;r.>=]
+  [Frac Frac f.+  ;f.+]
+  [Frac Frac f.-  ;f.-]
+  [Frac Frac f.*  ;f.*]
+  [Frac Frac f./  ;f./]
+  [Frac Frac f.%  ;f.%]
+  [Frac Bool f.=  ;f.=]
+  [Frac Bool f.<  ;f.<]
+  [Frac Bool f.<= ;f.<=]
+  [Frac Bool f.>  ;f.>]
+  [Frac Bool f.>= ;f.>=]
   )
 
 (def: #export if
diff --git a/stdlib/source/lux/data/color.lux b/stdlib/source/lux/data/color.lux
index f4799726f..61ee1249a 100644
--- a/stdlib/source/lux/data/color.lux
+++ b/stdlib/source/lux/data/color.lux
@@ -8,18 +8,18 @@
 (def: rgb Nat +256)
 (def: top Nat (n.dec rgb))
 
-(def: nat-to-real (-> Nat Real) (|>. nat-to-int int-to-real))
-(def: real-to-nat (-> Real Nat) (|>. real-to-int int-to-nat))
+(def: nat-to-frac (-> Nat Frac) (|>. nat-to-int int-to-frac))
+(def: frac-to-nat (-> Frac Nat) (|>. frac-to-int int-to-nat))
 
-(def: rgb-factor Real (nat-to-real top))
+(def: rgb-factor Frac (nat-to-frac top))
 
 (def: scale-down
-  (-> Nat Real)
-  (|>. nat-to-real (r./ rgb-factor)))
+  (-> Nat Frac)
+  (|>. nat-to-frac (f./ rgb-factor)))
 
 (def: scale-up
-  (-> Real Nat)
-  (|>. (r.* rgb-factor) real-to-nat))
+  (-> Frac Nat)
+  (|>. (f.* rgb-factor) frac-to-nat))
 
 (opaque: #export Color {}
   {#red Nat
@@ -46,115 +46,115 @@
   )
 
 (def: #export (to-hsl color)
-  (-> Color [Real Real Real])
+  (-> Color [Frac Frac Frac])
   (let [[red green blue] (unpack color)
         red (scale-down red)
         green (scale-down green)
         blue (scale-down blue)
-        max ($_ r.max red green blue)
-        min ($_ r.min red green blue)
-        luminance (|> (r.+ max min) (r./ 2.0))]
-    (if (r.= max min)
+        max ($_ f.max red green blue)
+        min ($_ f.min red green blue)
+        luminance (|> (f.+ max min) (f./ 2.0))]
+    (if (f.= max min)
       ## Achromatic
       [0.0 0.0 luminance]
       ## Chromatic
-      (let [diff (|> max (r.- min))
+      (let [diff (|> max (f.- min))
             saturation (|> diff
-                           (r./ (if (r.> 0.5 luminance)
-                                  (|> 2.0 (r.- max) (r.- min))
-                                  (|> max (r.+ min)))))
-            hue' (cond (r.= red max)
-                       (|> green (r.- blue) (r./ diff)
-                           (r.+ (if (r.< blue green) 6.0 0.0)))
+                           (f./ (if (f.> 0.5 luminance)
+                                  (|> 2.0 (f.- max) (f.- min))
+                                  (|> max (f.+ min)))))
+            hue' (cond (f.= red max)
+                       (|> green (f.- blue) (f./ diff)
+                           (f.+ (if (f.< blue green) 6.0 0.0)))
                        
-                       (r.= green max)
-                       (|> blue (r.- red) (r./ diff)
-                           (r.+ 2.0))
+                       (f.= green max)
+                       (|> blue (f.- red) (f./ diff)
+                           (f.+ 2.0))
                        
-                       ## (r.= blue max)
-                       (|> red (r.- green) (r./ diff)
-                           (r.+ 4.0)))]
-        [(|> hue' (r./ 6.0))
+                       ## (f.= blue max)
+                       (|> red (f.- green) (f./ diff)
+                           (f.+ 4.0)))]
+        [(|> hue' (f./ 6.0))
          saturation
          luminance]))))
 
 (def: (hue-to-rgb p q t)
-  (-> Real Real Real Real)
-  (let [t (cond (r.< 0.0 t) (r.+ 1.0 t)
-                (r.> 1.0 t) (r.- 1.0 t)
+  (-> Frac Frac Frac Frac)
+  (let [t (cond (f.< 0.0 t) (f.+ 1.0 t)
+                (f.> 1.0 t) (f.- 1.0 t)
                 ## else
                 t)
-        f2/3 (r./ 3.0 2.0)]
-    (cond (r.< (r./ 6.0 1.0) t)
-          (|> q (r.- p) (r.* 6.0) (r.* t) (r.+ p))
+        f2/3 (f./ 3.0 2.0)]
+    (cond (f.< (f./ 6.0 1.0) t)
+          (|> q (f.- p) (f.* 6.0) (f.* t) (f.+ p))
           
-          (r.< (r./ 2.0 1.0) t)
+          (f.< (f./ 2.0 1.0) t)
           q
           
-          (r.< f2/3 t)
-          (|> q (r.- p) (r.* (|> f2/3 (r.- t))) (r.* 6.0) (r.+ p))
+          (f.< f2/3 t)
+          (|> q (f.- p) (f.* (|> f2/3 (f.- t))) (f.* 6.0) (f.+ p))
           
           ## else
           p)))
 
 (def: #export (from-hsl [hue saturation luminance])
-  (-> [Real Real Real] Color)
-  (if (r.= 0.0 saturation)
+  (-> [Frac Frac Frac] Color)
+  (if (f.= 0.0 saturation)
     ## Achromatic
     (let [intensity (scale-up luminance)]
       (color [intensity intensity intensity]))
     ## Chromatic
-    (let [q (if (r.< 0.5 luminance)
-              (|> saturation (r.+ 1.0) (r.* luminance))
-              (|> luminance (r.+ saturation) (r.- (r.* saturation luminance))))
-          p (|> luminance (r.* 2.0) (r.- q))
-          third (|> 1.0 (r./ 3.0))]
-      (color [(scale-up (|> hue (r.+ third) (hue-to-rgb p q)))
+    (let [q (if (f.< 0.5 luminance)
+              (|> saturation (f.+ 1.0) (f.* luminance))
+              (|> luminance (f.+ saturation) (f.- (f.* saturation luminance))))
+          p (|> luminance (f.* 2.0) (f.- q))
+          third (|> 1.0 (f./ 3.0))]
+      (color [(scale-up (|> hue (f.+ third) (hue-to-rgb p q)))
               (scale-up (|> hue (hue-to-rgb p q)))
-              (scale-up (|> hue (r.- third) (hue-to-rgb p q)))]))))
+              (scale-up (|> hue (f.- third) (hue-to-rgb p q)))]))))
 
 (def: #export (to-hsb color)
-  (-> Color [Real Real Real])
+  (-> Color [Frac Frac Frac])
   (let [[red green blue] (unpack color)
         red (scale-down red)
         green (scale-down green)
         blue (scale-down blue)
-        max ($_ r.max red green blue)
-        min ($_ r.min red green blue)
+        max ($_ f.max red green blue)
+        min ($_ f.min red green blue)
         brightness max
-        diff (|> max (r.- min))
-        saturation (if (r.= 0.0 max)
+        diff (|> max (f.- min))
+        saturation (if (f.= 0.0 max)
                      0.0
-                     (|> diff (r./ max)))]
-    (if (r.= max min)
+                     (|> diff (f./ max)))]
+    (if (f.= max min)
       ## Achromatic
       [0.0 saturation brightness]
       ## Chromatic
-      (let [hue (cond (r.= red max)
-                      (|> green (r.- blue) (r./ diff)
-                          (r.+ (if (r.< blue green) 6.0 0.0)))
-
-                      (r.= green max)
-                      (|> blue (r.- red) (r./ diff)
-                          (r.+ 2.0))
-
-                      ## (r.= blue max)
-                      (|> red (r.- green) (r./ diff)
-                          (r.+ 4.0)))]
-        [(|> hue (r./ 6.0))
+      (let [hue (cond (f.= red max)
+                      (|> green (f.- blue) (f./ diff)
+                          (f.+ (if (f.< blue green) 6.0 0.0)))
+
+                      (f.= green max)
+                      (|> blue (f.- red) (f./ diff)
+                          (f.+ 2.0))
+
+                      ## (f.= blue max)
+                      (|> red (f.- green) (f./ diff)
+                          (f.+ 4.0)))]
+        [(|> hue (f./ 6.0))
          saturation
          brightness]))))
 
 (def: #export (from-hsb [hue saturation brightness])
-  (-> [Real Real Real] Color)
-  (let [hue (|> hue (r.* 6.0))
+  (-> [Frac Frac Frac] Color)
+  (let [hue (|> hue (f.* 6.0))
         i (math;floor hue)
-        f (|> hue (r.- i))
-        p (|> 1.0 (r.- saturation) (r.* brightness))
-        q (|> 1.0 (r.- (r.* f saturation)) (r.* brightness))
-        t (|> 1.0 (r.- (|> 1.0 (r.- f) (r.* saturation))) (r.* brightness))
+        f (|> hue (f.- i))
+        p (|> 1.0 (f.- saturation) (f.* brightness))
+        q (|> 1.0 (f.- (f.* f saturation)) (f.* brightness))
+        t (|> 1.0 (f.- (|> 1.0 (f.- f) (f.* saturation))) (f.* brightness))
         v brightness
-        mod (|> i (r.% 6.0) real-to-nat)
+        mod (|> i (f.% 6.0) frac-to-nat)
         red (case mod +0 v +1 q +2 p +3 p +4 t +5 v _ (undefined))
         green (case mod +0 t +1 v +2 v +3 q +4 p +5 p _ (undefined))
         blue (case mod +0 p +1 p +2 t +3 v +4 v +5 q _ (undefined))]
@@ -163,51 +163,51 @@
             (scale-up blue)])))
 
 (def: #export (to-cmyk color)
-  (-> Color [Real Real Real Real])
+  (-> Color [Frac Frac Frac Frac])
   (let [[red green blue] (unpack color)
         red (scale-down red)
         green (scale-down green)
         blue (scale-down blue)
-        key (|> 1.0 (r.- ($_ r.max red green blue)))
-        f (if (r.< 1.0 key)
-            (|> 1.0 (r./ (|> 1.0 (r.- key))))
+        key (|> 1.0 (f.- ($_ f.max red green blue)))
+        f (if (f.< 1.0 key)
+            (|> 1.0 (f./ (|> 1.0 (f.- key))))
             0.0)
-        cyan (|> 1.0 (r.- red) (r.- key) (r.* f))
-        magenta (|> 1.0 (r.- green) (r.- key) (r.* f))
-        yellow (|> 1.0 (r.- blue) (r.- key) (r.* f))]
+        cyan (|> 1.0 (f.- red) (f.- key) (f.* f))
+        magenta (|> 1.0 (f.- green) (f.- key) (f.* f))
+        yellow (|> 1.0 (f.- blue) (f.- key) (f.* f))]
     [cyan magenta yellow key]))
 
 (def: #export (from-cmyk [cyan magenta yellow key])
-  (-> [Real Real Real Real] Color)
-  (if (r.= 1.0 key)
+  (-> [Frac Frac Frac Frac] Color)
+  (if (f.= 1.0 key)
     (color [+0 +0 +0])
-    (let [red (|> (|> 1.0 (r.- cyan))
-                  (r.* (|> 1.0 (r.- key))))
-          green (|> (|> 1.0 (r.- magenta))
-                    (r.* (|> 1.0 (r.- key))))
-          blue (|> (|> 1.0 (r.- yellow))
-                   (r.* (|> 1.0 (r.- key))))]
+    (let [red (|> (|> 1.0 (f.- cyan))
+                  (f.* (|> 1.0 (f.- key))))
+          green (|> (|> 1.0 (f.- magenta))
+                    (f.* (|> 1.0 (f.- key))))
+          blue (|> (|> 1.0 (f.- yellow))
+                   (f.* (|> 1.0 (f.- key))))]
       (color [(scale-up red) (scale-up green) (scale-up blue)]))))
 
 (def: (normalize ratio)
-  (-> Real Real)
-  (cond (r.> 1.0 ratio)
-        (r.% 1.0 ratio)
+  (-> Frac Frac)
+  (cond (f.> 1.0 ratio)
+        (f.% 1.0 ratio)
 
-        (r.< 0.0 ratio)
-        (|> 1.0 (r.+ (r.% 1.0 ratio)))
+        (f.< 0.0 ratio)
+        (|> 1.0 (f.+ (f.% 1.0 ratio)))
 
         ## else
         ratio))
 
 (def: #export (interpolate ratio end start)
-  (-> Real Color Color Color)
+  (-> Frac Color Color Color)
   (let [dS (normalize ratio)
-        dE (|> 1.0 (r.- dS))
+        dE (|> 1.0 (f.- dS))
         interpolate' (: (-> Nat Nat Nat)
                         (function [end start]
-                          (real-to-nat (r.+ (r.* dE (nat-to-real end))
-                                            (r.* dS (nat-to-real start))))))
+                          (frac-to-nat (f.+ (f.* dE (nat-to-frac end))
+                                            (f.* dS (nat-to-frac start))))))
         [redS greenS blueS] (unpack start)
         [redE greenE blueE] (unpack end)]
     (color [(interpolate' redE redS)
@@ -219,7 +219,7 @@
 
 (do-template [<name> <target>]
   [(def: #export (<name> ratio color)
-     (-> Real Color Color)
+     (-> Frac Color Color)
      (interpolate ratio <target> color))]
 
   [darker   black]
@@ -236,16 +236,16 @@
 
 (do-template [<name> <op>]
   [(def: #export (<name> ratio color)
-     (-> Real Color Color)
+     (-> Frac Color Color)
      (let [[hue saturation luminance] (to-hsl color)]
        (from-hsl [hue
                   (|> saturation
-                      (r.* (|> 1.0 (<op> (normalize ratio))))
-                      (r.min 1.0))
+                      (f.* (|> 1.0 (<op> (normalize ratio))))
+                      (f.min 1.0))
                   luminance])))]
 
-  [saturate    r.+]
-  [de-saturate r.-]
+  [saturate    f.+]
+  [de-saturate f.-]
   )
 
 (def: #export (gray-scale color)
@@ -258,12 +258,12 @@
      (-> Color [Color Color Color])
      (let [[hue saturation luminance] (to-hsl color)]
        [color
-        (from-hsl [(|> hue (r.+ <1>) normalize) saturation luminance])
-        (from-hsl [(|> hue (r.+ <2>) normalize) saturation luminance])]))]
+        (from-hsl [(|> hue (f.+ <1>) normalize) saturation luminance])
+        (from-hsl [(|> hue (f.+ <2>) normalize) saturation luminance])]))]
 
-  [triad            (|> 1.0 (r./ 3.0)) (|> 2.0 (r./ 3.0))]
-  [clash            (|> 1.0 (r./ 4.0)) (|> 3.0 (r./ 4.0))]
-  [split-complement (|> 1.0 (r./ 5.0)) (|> 3.0 (r./ 5.0))]
+  [triad            (|> 1.0 (f./ 3.0)) (|> 2.0 (f./ 3.0))]
+  [clash            (|> 1.0 (f./ 4.0)) (|> 3.0 (f./ 4.0))]
+  [split-complement (|> 1.0 (f./ 5.0)) (|> 3.0 (f./ 5.0))]
   )
 
 (do-template [<name> <1> <2> <3>]
@@ -271,22 +271,22 @@
      (-> Color [Color Color Color Color])
      (let [[hue saturation luminance] (to-hsl color)]
        [color
-        (from-hsl [(|> hue (r.+ <1>) normalize) saturation luminance])
-        (from-hsl [(|> hue (r.+ <2>) normalize) saturation luminance])
-        (from-hsl [(|> hue (r.+ <3>) normalize) saturation luminance])]))]
+        (from-hsl [(|> hue (f.+ <1>) normalize) saturation luminance])
+        (from-hsl [(|> hue (f.+ <2>) normalize) saturation luminance])
+        (from-hsl [(|> hue (f.+ <3>) normalize) saturation luminance])]))]
 
-  [square   (|> 1.0 (r./ 4.0))  (|> 2.0 (r./ 4.0))  (|> 3.0 (r./ 4.0))]
-  [tetradic (|> 2.0 (r./ 12.0)) (|> 6.0 (r./ 12.0)) (|> 8.0 (r./ 12.0))]
+  [square   (|> 1.0 (f./ 4.0))  (|> 2.0 (f./ 4.0))  (|> 3.0 (f./ 4.0))]
+  [tetradic (|> 2.0 (f./ 12.0)) (|> 6.0 (f./ 12.0)) (|> 8.0 (f./ 12.0))]
   )
 
 (def: #export (analogous results slice color)
-  (-> Nat Real Color (List Color))
+  (-> Nat Frac Color (List Color))
   (if (n.= +0 results)
     (list)
     (let [[hue saturation luminance] (to-hsl color)
           slice (normalize slice)]
       (L/map (function [idx]
-               (from-hsl [(|> idx nat-to-real (r.* slice) (r.+ hue) normalize)
+               (from-hsl [(|> idx nat-to-frac (f.* slice) (f.+ hue) normalize)
                           saturation
                           luminance]))
              (list;n.range +0 (n.dec results))))))
@@ -296,11 +296,11 @@
   (if (n.= +0 results)
     (list)
     (let [[hue saturation brightness] (to-hsb color)
-          slice (|> 1.0 (r./ (nat-to-real results)))]
+          slice (|> 1.0 (f./ (nat-to-frac results)))]
       (|> (list;n.range +0 (n.dec results))
-          (L/map (|>. nat-to-real
-                      (r.* slice)
-                      (r.+ brightness)
+          (L/map (|>. nat-to-frac
+                      (f.* slice)
+                      (f.+ brightness)
                       normalize
                       [hue saturation]
                       from-hsb))))))
diff --git a/stdlib/source/lux/data/format/css.lux b/stdlib/source/lux/data/format/css.lux
index a5adfb928..e4ca7e3cd 100644
--- a/stdlib/source/lux/data/format/css.lux
+++ b/stdlib/source/lux/data/format/css.lux
@@ -74,7 +74,7 @@
 
 (do-template [<name> <suffix>]
   [(def: #export (<name> value)
-     (-> Real Value)
+     (-> Frac Value)
      (format (%r value) <suffix>))]
 
   [em "em"]
diff --git a/stdlib/source/lux/data/format/json.lux b/stdlib/source/lux/data/format/json.lux
index 379e3b23b..847b5fa0f 100644
--- a/stdlib/source/lux/data/format/json.lux
+++ b/stdlib/source/lux/data/format/json.lux
@@ -11,7 +11,7 @@
        (data [bool]
              [text "text/" Eq<Text> Monoid<Text>]
              (text ["l" lexer])
-             [number "real/" Codec<Text,Real> "nat/" Codec<Text,Nat>]
+             [number "frac/" Codec<Text,Frac> "nat/" Codec<Text,Nat>]
              maybe
              ["R" result]
              [sum]
@@ -32,7 +32,7 @@
 
   [Null    Unit]
   [Boolean Bool]
-  [Number  Real]
+  [Number  Frac]
   [String  Text]
   )
 
@@ -72,7 +72,7 @@
         [_ (<ast-tag> value)]
         (wrap (list (` (: JSON (<json-tag> (~ (<ctor> value))))))))
       ([#;Bool code;bool            #Boolean]
-       [#;Real code;real            #Number]
+       [#;Frac code;frac            #Number]
        [#;Text code;text            #String])
 
       [_ (#;Tag ["" "null"])]
@@ -190,7 +190,7 @@
         [(<tag> x') (<tag> y')]
         (:: <struct> = x' y'))
       ([#Boolean bool;Eq<Bool>]
-       [#Number  number;Eq<Real>]
+       [#Number  number;Eq<Frac>]
        [#String  text;Eq<Text>])
 
       [(#Array xs) (#Array ys)]
diff --git a/stdlib/source/lux/data/format/json/codec.lux b/stdlib/source/lux/data/format/json/codec.lux
index 8a50757bf..d6d888c0e 100644
--- a/stdlib/source/lux/data/format/json/codec.lux
+++ b/stdlib/source/lux/data/format/json/codec.lux
@@ -12,7 +12,7 @@
              [bit]
              [text "text/" Eq<Text> Monoid<Text>]
              (text ["l" lexer])
-             [number "real/" Codec<Text,Real> "nat/" Codec<Text,Nat>]
+             [number "frac/" Codec<Text,Frac> "nat/" Codec<Text,Nat>]
              maybe
              ["R" result]
              [sum]
@@ -38,7 +38,7 @@
   [(def: <name> (-> <type> Text) <codec>)]
 
   [show-boolean ..;Boolean (:: bool;Codec<Text,Bool> encode)]
-  [show-number  ..;Number (:: number;Codec<Text,Real> encode)]
+  [show-number  ..;Number (:: number;Codec<Text,Frac> encode)]
   [show-string  ..;String text;encode])
 
 (def: (show-array show-json elems)
@@ -114,7 +114,7 @@
               signed?' (l;this? "-")
               offset (l;many l;decimal)]
              (wrap ($_ text/append mark (if signed?' "-" "") offset))))]
-    (case (real/decode ($_ text/append (if signed? "-" "") digits "." decimals exp))
+    (case (frac/decode ($_ text/append (if signed? "-" "") digits "." decimals exp))
       (#R;Error message)
       (p;fail message)
       
@@ -185,8 +185,8 @@
   L/map)
 
 (def: tag
-  (-> Nat Real)
-  (|>. nat-to-int int-to-real))
+  (-> Nat Frac)
+  (|>. nat-to-int int-to-frac))
 
 (def: #hidden (rec-encode non-rec)
   (All [a] (-> (-> (-> a JSON)
@@ -202,15 +202,15 @@
   (def: (encode input)
     (let [high (|> input (bit;and high-mask) (bit;unsigned-shift-right +32))
           low (bit;and low-mask input)]
-      (..;array (vector (|> high nat-to-int int-to-real #..;Number)
-                        (|> low nat-to-int int-to-real #..;Number)))))
+      (..;array (vector (|> high nat-to-int int-to-frac #..;Number)
+                        (|> low nat-to-int int-to-frac #..;Number)))))
   (def: (decode input)
     (<| (../reader;run input)
         (do p;Monad<Parser>
           [high ../reader;number
            low ../reader;number])
-        (wrap (n.+ (|> high real-to-int int-to-nat (bit;shift-left +32))
-                   (|> low real-to-int int-to-nat))))))
+        (wrap (n.+ (|> high frac-to-int int-to-nat (bit;shift-left +32))
+                   (|> low frac-to-int int-to-nat))))))
 
 (struct: #hidden _ (Codec JSON Int)
   (def: encode (|>. int-to-nat (:: Codec<JSON,Nat> encode)))
@@ -229,7 +229,7 @@
                [Bool poly;bool ..;boolean]
                [Nat  poly;nat  (:: ;;Codec<JSON,Nat> (~' encode))]
                [Int  poly;int  (:: ;;Codec<JSON,Int> (~' encode))]
-               [Real poly;real ..;number]
+               [Frac poly;frac ..;number]
                [Text poly;text ..;string])
      <time> (do-template [<type> <codec>]
               [(do @
@@ -284,7 +284,7 @@
                           (case (~ g!input)
                             (~@ (L/join (L/map (function [[tag g!encode]]
                                                  (list (` ((~ (code;nat tag)) (~ g!input)))
-                                                       (` (..;json [(~ (code;real (;;tag tag)))
+                                                       (` (..;json [(~ (code;frac (;;tag tag)))
                                                                     ((~ g!encode) (~ g!input))]))))
                                                (list;enumerate members))))))))))
           (do @
@@ -336,7 +336,7 @@
                [Bool poly;bool ../reader;boolean]
                [Nat  poly;nat  (p;codec ;;Codec<JSON,Nat> ../reader;any)]
                [Int  poly;int  (p;codec ;;Codec<JSON,Int> ../reader;any)]
-               [Real poly;real ../reader;number]
+               [Frac poly;frac ../reader;number]
                [Text poly;text ../reader;string])
      <time> (do-template [<type> <codec>]
               [(do @
@@ -381,7 +381,7 @@
                         ($_ p;alt
                             (~@ (L/map (function [[tag memberC]]
                                          (` (|> (~ memberC)
-                                                (p;after (../reader;number! (~ (code;real (;;tag tag)))))
+                                                (p;after (../reader;number! (~ (code;frac (;;tag tag)))))
                                                 ../reader;array)))
                                        (list;enumerate members))))))))
           (do @
@@ -418,18 +418,18 @@
               (type: Variant
                 (#Case0 Bool)
                 (#Case1 Text)
-                (#Case2 Real))
+                (#Case2 Frac))
 
               (type: Record
                 {#unit Unit
                  #bool Bool
-                 #real Real
+                 #frac Frac
                  #text Text
-                 #maybe (Maybe Real)
-                 #list (List Real)
+                 #maybe (Maybe Frac)
+                 #list (List Frac)
                  #variant Variant
-                 #tuple [Bool Real Text]
-                 #dict (Dict Text Real)})
+                 #tuple [Bool Frac Text]
+                 #dict (Dict Text Frac)})
 
               (derived: (Codec<JSON,?> Record)))}
   (with-gensyms [g!inputs]
diff --git a/stdlib/source/lux/data/format/json/reader.lux b/stdlib/source/lux/data/format/json/reader.lux
index 83713bcf3..1b26d746d 100644
--- a/stdlib/source/lux/data/format/json/reader.lux
+++ b/stdlib/source/lux/data/format/json/reader.lux
@@ -8,7 +8,7 @@
                 ["p" parser "p/" Monad<Parser>])
        (data [bool]
              [text "text/" Monoid<Text>]
-             [number "real/" Codec<Text,Real> "nat/" Codec<Text,Nat>]
+             [number "frac/" Codec<Text,Frac> "nat/" Codec<Text,Nat>]
              ["R" result]
              (coll [list]
                    [vector]
@@ -63,7 +63,7 @@
 
   [null    Unit #..;Null    "null"]
   [boolean Bool #..;Boolean "boolean"]
-  [number  Real #..;Number  "number"]
+  [number  Frac #..;Number  "number"]
   [string  Text #..;String  "string"]
   )
 
@@ -96,7 +96,7 @@
          (fail ($_ text/append "JSON value is not a " <desc> ".")))))]
 
   [boolean? boolean! Bool bool;Eq<Bool>   (:: bool;Codec<Text,Bool> encode)   #..;Boolean "boolean" id]
-  [number?  number!  Real number;Eq<Real> (:: number;Codec<Text,Real> encode) #..;Number  "number"  id]
+  [number?  number!  Frac number;Eq<Frac> (:: number;Codec<Text,Frac> encode) #..;Number  "number"  id]
   [string?  string!  Text text;Eq<Text>   text;encode                         #..;String  "string"  id]
   )
 
diff --git a/stdlib/source/lux/data/number.lux b/stdlib/source/lux/data/number.lux
index 783e9bc55..713ee943f 100644
--- a/stdlib/source/lux/data/number.lux
+++ b/stdlib/source/lux/data/number.lux
@@ -19,7 +19,7 @@
   [ Nat n.=]
   [ Int i.=]
   [ Deg d.=]
-  [Real r.=]
+  [Frac f.=]
   )
 
 (do-template [<type> <eq> <lt> <lte> <gt> <gte>]
@@ -33,7 +33,7 @@
   [ Nat Eq<Nat>  n.< n.<= n.> n.>=]
   [ Int Eq<Int>  i.< i.<= i.> i.>=]
   [Deg  Eq<Deg>  d.< d.<= d.> d.>=]
-  [Real Eq<Real> r.< r.<= r.> r.>=]
+  [Frac Eq<Frac> f.< f.<= f.> f.>=]
   )
 
 (struct: #export _ (Number Nat)
@@ -70,7 +70,7 @@
      )]
 
   [ Int  Order<Int> i.+ i.- i.* i./ i.% i.= i.<   0   1   -1]
-  [Real Order<Real> r.+ r.- r.* r./ r.% r.= r.< 0.0 1.0 -1.0]
+  [Frac Order<Frac> f.+ f.- f.* f./ f.% f.= f.< 0.0 1.0 -1.0]
   )
 
 (struct: #export _ (Number Deg)
@@ -93,7 +93,7 @@
 
   [Nat Order<Nat> n.inc n.dec]
   [Int Order<Int> i.inc i.dec]
-  [Real Order<Real> (r.+ (_lux_proc [ "real" "smallest-value"] [])) (r.- (_lux_proc [ "real" "smallest-value"] []))]
+  [Frac Order<Frac> (f.+ (_lux_proc [ "frac" "smallest-value"] [])) (f.- (_lux_proc [ "frac" "smallest-value"] []))]
   [Deg Order<Deg> (d.+ (_lux_proc [ "deg" "min-value"] [])) (d.- (_lux_proc [ "deg" "min-value"] []))]
   )
 
@@ -105,7 +105,7 @@
 
   [ Nat Enum<Nat>  (_lux_proc [ "nat" "max-value"] []) (_lux_proc [ "nat" "min-value"] [])]
   [ Int Enum<Int>  (_lux_proc [ "int" "max-value"] []) (_lux_proc [ "int" "min-value"] [])]
-  [Real Enum<Real> (_lux_proc ["real" "max-value"] []) (_lux_proc ["real" "min-value"] [])]
+  [Frac Enum<Frac> (_lux_proc ["frac" "max-value"] []) (_lux_proc ["frac" "min-value"] [])]
   [ Deg Enum<Deg>  (_lux_proc [ "deg" "max-value"] []) (_lux_proc [ "deg" "min-value"] [])]
   )
 
@@ -122,10 +122,10 @@
   [ Mul@Monoid<Int>  Int 1                          i.*]
   [ Max@Monoid<Int>  Int (:: Interval<Int> bottom)  i.max]
   [ Min@Monoid<Int>  Int (:: Interval<Int> top)     i.min]
-  [Add@Monoid<Real> Real 0.0                        r.+]
-  [Mul@Monoid<Real> Real 1.0                        r.*]
-  [Max@Monoid<Real> Real (:: Interval<Real> bottom) r.max]
-  [Min@Monoid<Real> Real (:: Interval<Real> top)    r.min]
+  [Add@Monoid<Frac> Frac 0.0                        f.+]
+  [Mul@Monoid<Frac> Frac 1.0                        f.*]
+  [Max@Monoid<Frac> Frac (:: Interval<Frac> bottom) f.max]
+  [Min@Monoid<Frac> Frac (:: Interval<Frac> top)    f.min]
   [ Add@Monoid<Deg>  Deg (:: Interval<Deg> bottom)  d.+]
   [ Mul@Monoid<Deg>  Deg (:: Interval<Deg> top)     d.*]
   [ Max@Monoid<Deg>  Deg (:: Interval<Deg> bottom)  d.max]
@@ -135,8 +135,8 @@
 (do-template [<name> <const> <doc>]
   [(def: #export <name>
      {#;doc <doc>}
-     Real
-     (_lux_proc ["real" <const>] []))]
+     Frac
+     (_lux_proc ["frac" <const>] []))]
 
   [not-a-number      "not-a-number"      "Not-a-number."]
   [positive-infinity "positive-infinity" "Positive infinity."]
@@ -144,15 +144,15 @@
   )
 
 (def: #export (not-a-number? number)
-  {#;doc "Tests whether a real is actually not-a-number."}
-  (-> Real Bool)
-  (not (r.= number number)))
+  {#;doc "Tests whether a frac is actually not-a-number."}
+  (-> Frac Bool)
+  (not (f.= number number)))
 
-(def: #export (real? value)
-  (-> Real Bool)
+(def: #export (frac? value)
+  (-> Frac Bool)
   (not (or (not-a-number? value)
-           (r.= positive-infinity value)
-           (r.= negative-infinity value))))
+           (f.= positive-infinity value)
+           (f.= negative-infinity value))))
 
 (do-template [<type> <encoder> <decoder> <error>]
   [(struct: #export _ (Codec Text <type>)
@@ -167,7 +167,7 @@
          #;None
          (#R;Error <error>))))]
 
-  [Real ["real" "encode"] ["real" "decode"] "Could not decode Real"]
+  [Frac ["frac" "encode"] ["frac" "decode"] "Could not decode Frac"]
   )
 
 ## [Values & Syntax]
@@ -302,21 +302,21 @@
   )
 
 (do-template [<struct> <int> <base> <char-set> <error>]
-  [(struct: #export <struct> (Codec Text Real)
+  [(struct: #export <struct> (Codec Text Frac)
      (def: (encode value)
-       (let [whole (real-to-int value)
+       (let [whole (frac-to-int value)
              whole-part (:: <int> encode whole)
-             decimal (:: Number<Real> abs (r.% 1.0 value))
-             decimal-part (if (r.= 0.0 decimal)
+             decimal (:: Number<Frac> abs (f.% 1.0 value))
+             decimal-part (if (f.= 0.0 decimal)
                             ".0"
                             (loop [dec-left decimal
                                    output ""]
-                              (if (r.= 0.0 dec-left)
+                              (if (f.= 0.0 dec-left)
                                 (_lux_proc ["text" "append"] ["." output])
-                                (let [shifted (r.* <base> dec-left)
-                                      digit (|> shifted (r.% <base>) real-to-int int-to-nat
+                                (let [shifted (f.* <base> dec-left)
+                                      digit (|> shifted (f.% <base>) frac-to-int int-to-nat
                                                 (get-char <char-set>) assume)]
-                                  (recur (r.% 1.0 shifted)
+                                  (recur (f.% 1.0 shifted)
                                          (_lux_proc ["text" "append"] [output digit]))))))]
          (_lux_proc ["text" "append"] [whole-part decimal-part])))
 
@@ -337,16 +337,16 @@
                                (if (n.= +0 muls-left)
                                  output
                                  (recur (n.dec muls-left)
-                                        (r.* <base> output))))
-                   adjusted-decimal (|> decimal int-to-real (r./ div-power))
+                                        (f.* <base> output))))
+                   adjusted-decimal (|> decimal int-to-frac (f./ div-power))
                    dec-deg (case (:: Hex@Codec<Text,Deg> decode (_lux_proc ["text" "append"] ["." decimal-part]))
                              (#R;Success dec-deg)
                              dec-deg
 
                              (#R;Error error)
                              (error! error))]
-               (#R;Success (r.+ (int-to-real whole)
-                                (r.* sign adjusted-decimal))))
+               (#R;Success (f.+ (int-to-frac whole)
+                                (f.* sign adjusted-decimal))))
 
              _
              (#R;Error (_lux_proc ["text" "append"] [<error> repr]))))
@@ -354,7 +354,7 @@
          _
          (#R;Error (_lux_proc ["text" "append"] [<error> repr])))))]
 
-  [Binary@Codec<Text,Real> Binary@Codec<Text,Int> 2.0 "01" "Invalid binary syntax: "]
+  [Binary@Codec<Text,Frac> Binary@Codec<Text,Int> 2.0 "01" "Invalid binary syntax: "]
   )
 
 (def: (segment-digits chunk-size digits)
@@ -493,13 +493,13 @@
   )
 
 (do-template [<struct> <error> <from> <to>]
-  [(struct: #export <struct> (Codec Text Real)
+  [(struct: #export <struct> (Codec Text Frac)
      (def: (encode value)
-       (let [sign (:: Number<Real> signum value)
-             raw-bin (:: Binary@Codec<Text,Real> encode value)
+       (let [sign (:: Number<Frac> signum value)
+             raw-bin (:: Binary@Codec<Text,Frac> encode value)
              dot-idx (assume (_lux_proc ["text" "index"] [raw-bin "." +0]))
              whole-part (assume (_lux_proc ["text" "clip"] [raw-bin
-                                                            (if (r.= -1.0 sign) +1 +0)
+                                                            (if (f.= -1.0 sign) +1 +0)
                                                             dot-idx]))
              decimal-part (assume (_lux_proc ["text" "clip"] [raw-bin (n.inc dot-idx) (_lux_proc ["text" "size"] [raw-bin])]))
              hex-output (|> (<from> false decimal-part)
@@ -507,7 +507,7 @@
                             (_lux_proc ["text" "append"])
                             [(<from> true whole-part)]
                             (_lux_proc ["text" "append"])
-                            [(if (r.= -1.0 sign) "-" "")]
+                            [(if (f.= -1.0 sign) "-" "")]
                             (_lux_proc ["text" "append"]))]
          hex-output))
 
@@ -520,16 +520,16 @@
                     1.0)]
          (case (_lux_proc ["text" "index"] [repr "." +0])
            (#;Some split-index)
-           (let [whole-part (assume (_lux_proc ["text" "clip"] [repr (if (r.= -1.0 sign) +1 +0) split-index]))
+           (let [whole-part (assume (_lux_proc ["text" "clip"] [repr (if (f.= -1.0 sign) +1 +0) split-index]))
                  decimal-part (assume (_lux_proc ["text" "clip"] [repr (n.inc split-index) (_lux_proc ["text" "size"] [repr])]))
                  as-binary (|> (<to> decimal-part)
                                ["."]
                                (_lux_proc ["text" "append"])
                                [(<to> whole-part)]
                                (_lux_proc ["text" "append"])
-                               [(if (r.= -1.0 sign) "-" "")]
+                               [(if (f.= -1.0 sign) "-" "")]
                                (_lux_proc ["text" "append"]))]
-             (case (:: Binary@Codec<Text,Real> decode as-binary)
+             (case (:: Binary@Codec<Text,Frac> decode as-binary)
                (#R;Error _)
                (#R;Error (_lux_proc ["text" "append"] [<error> repr]))
 
@@ -539,11 +539,11 @@
            _
            (#R;Error (_lux_proc ["text" "append"] [<error> repr]))))))]
 
-  [Octal@Codec<Text,Real> "Invalid octaladecimal syntax: " binary-to-octal octal-to-binary]
-  [Hex@Codec<Text,Real>   "Invalid hexadecimal syntax: "   binary-to-hex   hex-to-binary]
+  [Octal@Codec<Text,Frac> "Invalid octaladecimal syntax: " binary-to-octal octal-to-binary]
+  [Hex@Codec<Text,Frac>   "Invalid hexadecimal syntax: "   binary-to-hex   hex-to-binary]
   )
 
-(do-template [<macro> <nat> <int> <deg> <real> <error> <doc>]
+(do-template [<macro> <nat> <int> <deg> <frac> <error> <doc>]
   [(macro: #export (<macro> tokens state)
      {#;doc <doc>}
      (case tokens
@@ -561,8 +561,8 @@
          (#R;Success [state (list [meta (#;Deg value)])])
 
          (^multi (#R;Error _)
-                 [(:: <real> decode repr) (#R;Success value)])
-         (#R;Success [state (list [meta (#;Real value)])])
+                 [(:: <frac> decode repr) (#R;Success value)])
+         (#R;Success [state (list [meta (#;Frac value)])])
 
          _
          (#R;Error <error>))
@@ -570,17 +570,17 @@
        _
        (#R;Error <error>)))]
 
-  [bin Binary@Codec<Text,Nat> Binary@Codec<Text,Int> Binary@Codec<Text,Deg> Binary@Codec<Text,Real>
+  [bin Binary@Codec<Text,Nat> Binary@Codec<Text,Int> Binary@Codec<Text,Deg> Binary@Codec<Text,Frac>
    "Invalid binary syntax."
-   (doc "Given syntax for a binary number, generates a Nat, an Int, a Deg or a Real."
+   (doc "Given syntax for a binary number, generates a Nat, an Int, a Deg or a Frac."
         (bin "11001001"))]
-  [oct Octal@Codec<Text,Nat>  Octal@Codec<Text,Int>  Octal@Codec<Text,Deg>  Octal@Codec<Text,Real>
+  [oct Octal@Codec<Text,Nat>  Octal@Codec<Text,Int>  Octal@Codec<Text,Deg>  Octal@Codec<Text,Frac>
    "Invalid octal syntax."
-   (doc "Given syntax for a octal number, generates a Nat, an Int, a Deg or a Real."
+   (doc "Given syntax for a octal number, generates a Nat, an Int, a Deg or a Frac."
         (oct "615243"))]
-  [hex Hex@Codec<Text,Nat>    Hex@Codec<Text,Int>    Hex@Codec<Text,Deg>    Hex@Codec<Text,Real>
+  [hex Hex@Codec<Text,Nat>    Hex@Codec<Text,Int>    Hex@Codec<Text,Deg>    Hex@Codec<Text,Frac>
    "Invalid hexadecimal syntax."
-   (doc "Given syntax for a hexadecimal number, generates a Nat, an Int, a Deg or a Real."
+   (doc "Given syntax for a hexadecimal number, generates a Nat, an Int, a Deg or a Frac."
         (hex "deadBEEF"))]
   )
 
@@ -771,8 +771,8 @@
     ))
 
 (def: (log2 input)
-  (-> Real Real)
-  (r./ (_lux_proc ["math" "log"] [2.0])
+  (-> Frac Frac)
+  (f./ (_lux_proc ["math" "log"] [2.0])
        (_lux_proc ["math" "log"] [input])))
 
 (def: double-bias Nat +1023)
@@ -780,38 +780,38 @@
 (def: mantissa-size Nat +52)
 (def: exponent-size Nat +11)
 
-(def: #export (real-to-bits input)
-  (-> Real Nat)
+(def: #export (frac-to-bits input)
+  (-> Frac Nat)
   (cond (not-a-number? input)
         (hex "+7FF7FFFFFFFFFFFF")
 
-        (r.= positive-infinity input)
+        (f.= positive-infinity input)
         (hex "+7FF0000000000000")
 
-        (r.= negative-infinity input)
+        (f.= negative-infinity input)
         (hex "+FFF0000000000000")
 
-        (r.= 0.0 input)
-        (let [reciprocal (r./ input 1.0)]
-          (if (r.= positive-infinity reciprocal)
+        (f.= 0.0 input)
+        (let [reciprocal (f./ input 1.0)]
+          (if (f.= positive-infinity reciprocal)
             ## Positive zero
             (hex "+0000000000000000")
             ## Negative zero
             (hex "+8000000000000000")))
 
         ## else
-        (let [sign (:: Number<Real> signum input)
-              input (:: Number<Real> abs input)
+        (let [sign (:: Number<Frac> signum input)
+              input (:: Number<Frac> abs input)
               exponent (_lux_proc ["math" "floor"] [(log2 input)])
               exponent-mask (|> +1 (bit;shift-left exponent-size) n.dec) 
               mantissa (|> input
                            ## Normalize
-                           (r./ (_lux_proc ["math" "pow"] [2.0 exponent]))
+                           (f./ (_lux_proc ["math" "pow"] [2.0 exponent]))
                            ## Make it int-equivalent
-                           (r.* (_lux_proc ["math" "pow"] [2.0 52.0])))
-              sign-bit (if (r.= -1.0 sign) +1 +0)
-              exponent-bits (|> exponent real-to-int int-to-nat (n.+ double-bias) (bit;and exponent-mask))
-              mantissa-bits (|> mantissa real-to-int int-to-nat)]
+                           (f.* (_lux_proc ["math" "pow"] [2.0 52.0])))
+              sign-bit (if (f.= -1.0 sign) +1 +0)
+              exponent-bits (|> exponent frac-to-int int-to-nat (n.+ double-bias) (bit;and exponent-mask))
+              mantissa-bits (|> mantissa frac-to-int int-to-nat)]
           ($_ bit;or
               (bit;shift-left +63 sign-bit)
               (bit;shift-left mantissa-size exponent-bits)
@@ -829,8 +829,8 @@
   [sign     sign-mask     +1            (n.+ exponent-size mantissa-size)]
   )
 
-(def: #export (bits-to-real input)
-  (-> Nat Real)
+(def: #export (bits-to-frac input)
+  (-> Nat Frac)
   (let [S (sign input)
         E (exponent input)
         M (mantissa input)]
@@ -844,20 +844,20 @@
           (and (n.= +0 E) (n.= +0 M))
           (if (n.= +0 S)
             0.0
-            (r.* -1.0 0.0))
+            (f.* -1.0 0.0))
 
           ## else
           (let [normalized (|> M (bit;set mantissa-size)
-                               nat-to-int int-to-real
-                               (r./ (_lux_proc ["math" "pow"] [2.0 52.0])))
+                               nat-to-int int-to-frac
+                               (f./ (_lux_proc ["math" "pow"] [2.0 52.0])))
                 power (|> E (n.- double-bias)
-                          nat-to-int int-to-real
+                          nat-to-int int-to-frac
                           [2.0] (_lux_proc ["math" "pow"]))
-                shifted (r.* power
+                shifted (f.* power
                              normalized)]
             (if (n.= +0 S)
               shifted
-              (r.* -1.0 shifted))))))
+              (f.* -1.0 shifted))))))
 
 ## [Hash]
 (struct: #export _ (Hash Nat)
@@ -868,10 +868,10 @@
   (def: eq Eq<Int>)
   (def: hash int-to-nat))
 
-(struct: #export _ (Hash Real)
-  (def: eq Eq<Real>)
+(struct: #export _ (Hash Frac)
+  (def: eq Eq<Frac>)
   
-  (def: hash real-to-bits))
+  (def: hash frac-to-bits))
 
 (struct: #export _ (Hash Deg)
   (def: eq Eq<Deg>)
diff --git a/stdlib/source/lux/data/number/complex.lux b/stdlib/source/lux/data/number/complex.lux
index a3a2fe217..3b8fb7f00 100644
--- a/stdlib/source/lux/data/number/complex.lux
+++ b/stdlib/source/lux/data/number/complex.lux
@@ -6,7 +6,7 @@
                 codec
                 ["M" monad #+ do Monad]
                 ["p" parser])
-       (data [number "r/" Number<Real> Codec<Text,Real>]
+       (data [number "f/" Number<Frac> Codec<Text,Frac>]
              [text "text/" Monoid<Text>]
              text/format
              ["R" result]
@@ -20,8 +20,8 @@
 ## https://github.com/apache/commons-math/blob/master/src/main/java/org/apache/commons/math4/complex/Complex.java
 
 (type: #export Complex
-  {#real Real
-   #imaginary Real})
+  {#real Frac
+   #imaginary Frac})
 
 (syntax: #export (complex real [?imaginary (p;opt s;any)])
   {#;doc (doc "Complex literals."
@@ -44,9 +44,9 @@
 
 (def: #export (c.= param input)
   (-> Complex Complex Bool)
-  (and (r.= (get@ #real param)
+  (and (f.= (get@ #real param)
             (get@ #real input))
-       (r.= (get@ #imaginary param)
+       (f.= (get@ #imaginary param)
             (get@ #imaginary input))))
 
 (do-template [<name> <op>]
@@ -57,8 +57,8 @@
       #imaginary (<op> (get@ #imaginary param)
                        (get@ #imaginary input))})]
 
-  [c.+ r.+]
-  [c.- r.-]
+  [c.+ f.+]
+  [c.- f.-]
   )
 
 (struct: #export _ (Eq Complex)
@@ -66,55 +66,55 @@
 
 (def: #export c.negate
   (-> Complex Complex)
-  (|>. (update@ #real r/negate)
-       (update@ #imaginary r/negate)))
+  (|>. (update@ #real f/negate)
+       (update@ #imaginary f/negate)))
 
 (def: #export c.signum
   (-> Complex Complex)
-  (|>. (update@ #real r/signum)
-       (update@ #imaginary r/signum)))
+  (|>. (update@ #real f/signum)
+       (update@ #imaginary f/signum)))
 
 (def: #export conjugate
   (-> Complex Complex)
-  (update@ #imaginary r/negate))
+  (update@ #imaginary f/negate))
 
 (def: #export (c.*' param input)
-  (-> Real Complex Complex)
-  {#real (r.* param
+  (-> Frac Complex Complex)
+  {#real (f.* param
               (get@ #real input))
-   #imaginary (r.* param
+   #imaginary (f.* param
                    (get@ #imaginary input))})
 
 (def: #export (c.* param input)
   (-> Complex Complex Complex)
-  {#real (r.- (r.* (get@ #imaginary param)
+  {#real (f.- (f.* (get@ #imaginary param)
                    (get@ #imaginary input))
-              (r.* (get@ #real param)
+              (f.* (get@ #real param)
                    (get@ #real input)))
-   #imaginary (r.+ (r.* (get@ #real param)
+   #imaginary (f.+ (f.* (get@ #real param)
                         (get@ #imaginary input))
-                   (r.* (get@ #imaginary param)
+                   (f.* (get@ #imaginary param)
                         (get@ #real input)))})
 
 (def: #export (c./ param input)
   (-> Complex Complex Complex)
   (let [(^slots [#real #imaginary]) param]
-    (if (r.< (r/abs imaginary)
-             (r/abs real))
-      (let [quot (r./ imaginary real)
-            denom (|> real (r.* quot) (r.+ imaginary))]
-        {#real (|> (get@ #real input) (r.* quot) (r.+ (get@ #imaginary input)) (r./ denom))
-         #imaginary (|> (get@ #imaginary input) (r.* quot) (r.- (get@ #real input)) (r./ denom))})
-      (let [quot (r./ real imaginary)
-            denom (|> imaginary (r.* quot) (r.+ real))]
-        {#real (|> (get@ #imaginary input) (r.* quot) (r.+ (get@ #real input)) (r./ denom))
-         #imaginary (|> (get@ #imaginary input) (r.- (r.* quot (get@ #real input))) (r./ denom))}))))
+    (if (f.< (f/abs imaginary)
+             (f/abs real))
+      (let [quot (f./ imaginary real)
+            denom (|> real (f.* quot) (f.+ imaginary))]
+        {#real (|> (get@ #real input) (f.* quot) (f.+ (get@ #imaginary input)) (f./ denom))
+         #imaginary (|> (get@ #imaginary input) (f.* quot) (f.- (get@ #real input)) (f./ denom))})
+      (let [quot (f./ real imaginary)
+            denom (|> imaginary (f.* quot) (f.+ real))]
+        {#real (|> (get@ #imaginary input) (f.* quot) (f.+ (get@ #real input)) (f./ denom))
+         #imaginary (|> (get@ #imaginary input) (f.- (f.* quot (get@ #real input))) (f./ denom))}))))
 
 (def: #export (c./' param subject)
-  (-> Real Complex Complex)
+  (-> Frac Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    {#real (r./ param real)
-     #imaginary (r./ param imaginary)}))
+    {#real (f./ param real)
+     #imaginary (f./ param imaginary)}))
 
 (def: #export (c.% param input)
   (-> Complex Complex Complex)
@@ -128,68 +128,68 @@
 (def: #export (cos subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    {#real (r.* (math;cosh imaginary)
+    {#real (f.* (math;cosh imaginary)
                 (math;cos real))
-     #imaginary (r.* (math;sinh imaginary)
-                     (r/negate (math;sin real)))}))
+     #imaginary (f.* (math;sinh imaginary)
+                     (f/negate (math;sin real)))}))
 
 (def: #export (cosh subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    {#real (r.* (math;cos imaginary)
+    {#real (f.* (math;cos imaginary)
                 (math;cosh real))
-     #imaginary (r.* (math;sin imaginary)
+     #imaginary (f.* (math;sin imaginary)
                      (math;sinh real))}))
 
 (def: #export (sin subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    {#real (r.* (math;cosh imaginary)
+    {#real (f.* (math;cosh imaginary)
                 (math;sin real))
-     #imaginary (r.* (math;sinh imaginary)
+     #imaginary (f.* (math;sinh imaginary)
                      (math;cos real))}))
 
 (def: #export (sinh subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    {#real (r.* (math;cos imaginary)
+    {#real (f.* (math;cos imaginary)
                 (math;sinh real))
-     #imaginary (r.* (math;sin imaginary)
+     #imaginary (f.* (math;sin imaginary)
                      (math;cosh real))}))
 
 (def: #export (tan subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject
-        r2 (r.* 2.0 real)
-        i2 (r.* 2.0 imaginary)
-        d (r.+ (math;cos r2) (math;cosh i2))]
-    {#real (r./ d (math;sin r2))
-     #imaginary (r./ d (math;sinh i2))}))
+        r2 (f.* 2.0 real)
+        i2 (f.* 2.0 imaginary)
+        d (f.+ (math;cos r2) (math;cosh i2))]
+    {#real (f./ d (math;sin r2))
+     #imaginary (f./ d (math;sinh i2))}))
 
 (def: #export (tanh subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject
-        r2 (r.* 2.0 real)
-        i2 (r.* 2.0 imaginary)
-        d (r.+ (math;cosh r2) (math;cos i2))]
-    {#real (r./ d (math;sinh r2))
-     #imaginary (r./ d (math;sin i2))}))
+        r2 (f.* 2.0 real)
+        i2 (f.* 2.0 imaginary)
+        d (f.+ (math;cosh r2) (math;cos i2))]
+    {#real (f./ d (math;sinh r2))
+     #imaginary (f./ d (math;sin i2))}))
 
 (def: #export (c.abs subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    (complex (if (r.< (r/abs imaginary)
-                      (r/abs real))
-               (if (r.= 0.0 imaginary)
-                 (r/abs real)
-                 (let [q (r./ imaginary real)]
-                   (r.* (math;root2 (r.+ 1.0 (r.* q q)))
-                        (r/abs imaginary))))
-               (if (r.= 0.0 real)
-                 (r/abs imaginary)
-                 (let [q (r./ real imaginary)]
-                   (r.* (math;root2 (r.+ 1.0 (r.* q q)))
-                        (r/abs real))))
+    (complex (if (f.< (f/abs imaginary)
+                      (f/abs real))
+               (if (f.= 0.0 imaginary)
+                 (f/abs real)
+                 (let [q (f./ imaginary real)]
+                   (f.* (math;root2 (f.+ 1.0 (f.* q q)))
+                        (f/abs imaginary))))
+               (if (f.= 0.0 real)
+                 (f/abs imaginary)
+                 (let [q (f./ real imaginary)]
+                   (f.* (math;root2 (f.+ 1.0 (f.* q q)))
+                        (f/abs real))))
                ))))
 
 (struct: #export _ (Number Complex)
@@ -200,20 +200,20 @@
   (def: % c.%)
   (def: (negate x)
     (|> x
-        (update@ #real r/negate)
-        (update@ #imaginary r/negate)))
+        (update@ #real f/negate)
+        (update@ #imaginary f/negate)))
   (def: abs c.abs)
   (def: (signum x)
     (|> x
-        (update@ #real r/signum)
-        (update@ #imaginary r/signum))))
+        (update@ #real f/signum)
+        (update@ #imaginary f/signum))))
 
 (def: #export (exp subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject
         r-exp (math;exp real)]
-    {#real (r.* r-exp (math;cos imaginary))
-     #imaginary (r.* r-exp (math;sin imaginary))}))
+    {#real (f.* r-exp (math;cos imaginary))
+     #imaginary (f.* r-exp (math;sin imaginary))}))
 
 (def: #export (log subject)
   (-> Complex Complex)
@@ -227,23 +227,23 @@
      (|> input log (<op> param) exp))]
 
   [pow  Complex c.*]
-  [pow' Real    c.*']
+  [pow' Frac    c.*']
   )
 
 (def: (copy-sign sign magnitude)
-  (-> Real Real Real)
-  (r.* (r/signum sign) magnitude))
+  (-> Frac Frac Frac)
+  (f.* (f/signum sign) magnitude))
 
 (def: #export (root2 (^@ input (^slots [#real #imaginary])))
   (-> Complex Complex)
-  (let [t (|> input c.abs (get@ #real) (r.+ (r/abs real)) (r./ 2.0) math;root2)]
-    (if (r.>= 0.0 real)
+  (let [t (|> input c.abs (get@ #real) (f.+ (f/abs real)) (f./ 2.0) math;root2)]
+    (if (f.>= 0.0 real)
       {#real t
-       #imaginary (r./ (r.* 2.0 t)
+       #imaginary (f./ (f.* 2.0 t)
                        imaginary)}
-      {#real (r./ (r.* 2.0 t)
-                  (r/abs imaginary))
-       #imaginary (r.* t (copy-sign imaginary 1.0))})))
+      {#real (f./ (f.* 2.0 t)
+                  (f/abs imaginary))
+       #imaginary (f.* t (copy-sign imaginary 1.0))})))
 
 (def: #export (root2-1z input)
   (-> Complex Complex)
@@ -251,18 +251,18 @@
 
 (def: #export (reciprocal (^slots [#real #imaginary]))
   (-> Complex Complex)
-  (if (r.< (r/abs imaginary)
-           (r/abs real))
-    (let [q (r./ imaginary real)
-          scale (r./ (|> real (r.* q) (r.+ imaginary))
+  (if (f.< (f/abs imaginary)
+           (f/abs real))
+    (let [q (f./ imaginary real)
+          scale (f./ (|> real (f.* q) (f.+ imaginary))
                      1.0)]
-      {#real (r.* q scale)
-       #imaginary (r/negate scale)})
-    (let [q (r./ real imaginary)
-          scale (r./ (|> imaginary (r.* q) (r.+ real))
+      {#real (f.* q scale)
+       #imaginary (f/negate scale)})
+    (let [q (f./ real imaginary)
+          scale (f./ (|> imaginary (f.* q) (f.+ real))
                      1.0)]
       {#real scale
-       #imaginary (|> scale r/negate (r.* q))})))
+       #imaginary (|> scale f/negate (f.* q))})))
 
 (def: #export (acos input)
   (-> Complex Complex)
@@ -288,32 +288,32 @@
       (c.* (c./ (complex 2.0) i))))
 
 (def: #export (argument (^slots [#real #imaginary]))
-  (-> Complex Real)
+  (-> Complex Frac)
   (math;atan2 real imaginary))
 
 (def: #export (nth-roots nth input)
   (-> Nat Complex (List Complex))
   (if (n.= +0 nth)
     (list)
-    (let [r-nth (|> nth nat-to-int int-to-real)
-          nth-root-of-abs (|> input c.abs (get@ #real) (math;pow (r./ r-nth 1.0)))
-          nth-phi (|> input argument (r./ r-nth))
-          slice (|> math;pi (r.* 2.0) (r./ r-nth))]
+    (let [r-nth (|> nth nat-to-int int-to-frac)
+          nth-root-of-abs (|> input c.abs (get@ #real) (math;pow (f./ r-nth 1.0)))
+          nth-phi (|> input argument (f./ r-nth))
+          slice (|> math;pi (f.* 2.0) (f./ r-nth))]
       (|> (list;n.range +0 (n.dec nth))
           (L/map (function [nth']
-                   (let [inner (|> nth' nat-to-int int-to-real
-                                   (r.* slice)
-                                   (r.+ nth-phi))
-                         real (r.* nth-root-of-abs
+                   (let [inner (|> nth' nat-to-int int-to-frac
+                                   (f.* slice)
+                                   (f.+ nth-phi))
+                         real (f.* nth-root-of-abs
                                    (math;cos inner))
-                         imaginary (r.* nth-root-of-abs
+                         imaginary (f.* nth-root-of-abs
                                         (math;sin inner))]
                      {#real real
                       #imaginary imaginary})))))))
 
 (struct: #export _ (Codec Text Complex)
   (def: (encode (^slots [#real #imaginary]))
-    ($_ text/append "(" (r/encode real) ", " (r/encode imaginary) ")"))
+    ($_ text/append "(" (f/encode real) ", " (f/encode imaginary) ")"))
 
   (def: (decode input)
     (case (do maybe;Monad<Maybe>
@@ -324,8 +324,8 @@
 
       (#;Some [r' i'])
       (do R;Monad<Result>
-        [r (r/decode (text;trim r'))
-         i (r/decode (text;trim i'))]
+        [r (f/decode (text;trim r'))
+         i (f/decode (text;trim i'))]
         (wrap {#real r
                #imaginary i}))
       )))
diff --git a/stdlib/source/lux/data/text/format.lux b/stdlib/source/lux/data/text/format.lux
index 37e5e7cb6..db33bdc05 100644
--- a/stdlib/source/lux/data/text/format.lux
+++ b/stdlib/source/lux/data/text/format.lux
@@ -42,7 +42,7 @@
   [%n        Nat               (:: number;Codec<Text,Nat> encode)]
   [%i        Int               (:: number;Codec<Text,Int> encode)]
   [%d        Deg               (:: number;Codec<Text,Deg> encode)]
-  [%r        Real              (:: number;Codec<Text,Real> encode)]
+  [%r        Frac              (:: number;Codec<Text,Frac> encode)]
   [%t        Text              text;encode]
   [%ident    Ident             (:: ident;Codec<Text,Ident> encode)]
   [%code     Code              code;to-text]
diff --git a/stdlib/source/lux/host.js.lux b/stdlib/source/lux/host.js.lux
index 2a6aa45f4..258de1b8d 100644
--- a/stdlib/source/lux/host.js.lux
+++ b/stdlib/source/lux/host.js.lux
@@ -21,7 +21,7 @@
   [(type: #export <name> <type>)]
 
   [String  Text]
-  [Number  Real]
+  [Number  Frac]
   [Boolean Bool]
   )
 
@@ -39,7 +39,7 @@
 (syntax: #export (get field-name type object)
   {#;doc (doc "A way to get fields from objects."
               (get "ceil" (ref "Math"))
-              (get "ceil" (-> Real Real) (ref "Math")))}
+              (get "ceil" (-> Frac Frac) (ref "Math")))}
   (wrap (list (` (:! (~ type)
                      (;_lux_proc ["js" "get-field"] [(~ object) (~ field-name)]))))))
 
@@ -55,7 +55,7 @@
 (syntax: #export (ref [name s;text] [type (p;opt s;any)])
   {#;doc (doc "A way to refer to JavaScript variables."
               (ref "document")
-              (ref "Math.ceil" (-> Real Real)))}
+              (ref "Math.ceil" (-> Frac Frac)))}
   (wrap (list (` (:! (~ (default (' ;;Object) type))
                      (;_lux_proc ["js" "ref"] [(~ (code;text name))]))))))
 
diff --git a/stdlib/source/lux/host.jvm.lux b/stdlib/source/lux/host.jvm.lux
index a735a8570..42a076b8f 100644
--- a/stdlib/source/lux/host.jvm.lux
+++ b/stdlib/source/lux/host.jvm.lux
@@ -276,8 +276,8 @@
      ["short"   ;Int]
      ["int"     ;Int]
      ["long"    ;Int]
-     ["float"   ;Real]
-     ["double"  ;Real]
+     ["float"   ;Frac]
+     ["double"  ;Frac]
      ["void"    ;Unit])
 
     _
diff --git a/stdlib/source/lux/macro.lux b/stdlib/source/lux/macro.lux
index 88e2b4d91..a7a5d22cd 100644
--- a/stdlib/source/lux/macro.lux
+++ b/stdlib/source/lux/macro.lux
@@ -167,7 +167,7 @@
 
   [get-bool-ann  #;BoolA  Bool]
   [get-int-ann   #;IntA   Int]
-  [get-real-ann  #;RealA  Real]
+  [get-frac-ann  #;FracA  Frac]
   [get-text-ann  #;TextA  Text]
   [get-ident-ann #;IdentA Ident]
   [get-list-ann  #;ListA  (List Ann-Value)]
diff --git a/stdlib/source/lux/macro/code.lux b/stdlib/source/lux/macro/code.lux
index 2755ae6f5..a171d74d5 100644
--- a/stdlib/source/lux/macro/code.lux
+++ b/stdlib/source/lux/macro/code.lux
@@ -13,7 +13,7 @@
 ##   (#;Bool Bool)
 ##   (#;Nat Nat)
 ##   (#;Int Int)
-##   (#;Real Real)
+##   (#;Frac Frac)
 ##   (#;Text Text)
 ##   (#;Symbol Text Text)
 ##   (#;Tag Text Text)
@@ -37,7 +37,7 @@
   [nat    Nat               #;Nat]
   [int    Int               #;Int]
   [deg    Deg               #;Deg]
-  [real   Real              #;Real]
+  [frac   Frac              #;Frac]
   [text   Text              #;Text]
   [symbol Ident             #;Symbol]
   [tag    Ident             #;Tag]
@@ -66,7 +66,7 @@
        [#;Nat    Eq<Nat>]
        [#;Int    Eq<Int>]
        [#;Deg    Eq<Deg>]
-       [#;Real   Eq<Real>]
+       [#;Frac   Eq<Frac>]
        [#;Text   Eq<Text>]
        [#;Symbol Eq<Ident>]
        [#;Tag    Eq<Ident>])
@@ -102,7 +102,7 @@
      [#;Nat    Codec<Text,Nat>]
      [#;Int    Codec<Text,Int>]
      [#;Deg    Codec<Text,Deg>]
-     [#;Real   Codec<Text,Real>]
+     [#;Frac   Codec<Text,Frac>]
      [#;Symbol Codec<Text,Ident>])
 
     [_ (#;Text value)]
diff --git a/stdlib/source/lux/macro/poly.lux b/stdlib/source/lux/macro/poly.lux
index 995cc023a..bc8d5d375 100644
--- a/stdlib/source/lux/macro/poly.lux
+++ b/stdlib/source/lux/macro/poly.lux
@@ -131,7 +131,7 @@
   [nat  "Nat"  (#;Host "#Nat" #;Nil)]
   [int  "Int"  (#;Host "#Int" #;Nil)]
   [deg  "Deg"  (#;Host "#Deg" #;Nil)]
-  [real "Real" (#;Host "#Real" #;Nil)]
+  [frac "Frac" (#;Host "#Frac" #;Nil)]
   [text "Text" (#;Host "#Text" #;Nil)]
   )
 
@@ -146,7 +146,7 @@
                          nat
                          int
                          deg
-                         real
+                         frac
                          text))
       (#R;Error error)
       (p;fail error)
diff --git a/stdlib/source/lux/macro/poly/eq.lux b/stdlib/source/lux/macro/poly/eq.lux
index b4d1a5231..45013ebb8 100644
--- a/stdlib/source/lux/macro/poly/eq.lux
+++ b/stdlib/source/lux/macro/poly/eq.lux
@@ -43,7 +43,7 @@
                [poly;nat  number;Eq<Nat>]
                [poly;int  number;Eq<Int>]
                [poly;deg  number;Eq<Deg>]
-               [poly;real number;Eq<Real>]
+               [poly;frac number;Eq<Frac>]
                [poly;text text;Eq<Text>])
      <time> (do-template [<type> <eq>]
               [(do @
diff --git a/stdlib/source/lux/macro/syntax.lux b/stdlib/source/lux/macro/syntax.lux
index f56c84e1b..4a05041f6 100644
--- a/stdlib/source/lux/macro/syntax.lux
+++ b/stdlib/source/lux/macro/syntax.lux
@@ -58,7 +58,7 @@
   [   nat   Nat    #;Nat  number;Eq<Nat> "nat"]
   [   int   Int    #;Int  number;Eq<Int> "int"]
   [  deg    Deg    #;Deg  number;Eq<Deg> "deg"]
-  [  real  Real   #;Real number;Eq<Real> "real"]
+  [  frac  Frac   #;Frac number;Eq<Frac> "frac"]
   [  text  Text   #;Text   text;Eq<Text> "text"]
   [symbol Ident #;Symbol ident;Eq<Ident> "symbol"]
   [   tag Ident    #;Tag ident;Eq<Ident> "tag"]
diff --git a/stdlib/source/lux/math.lux b/stdlib/source/lux/math.lux
index e5e06bd16..73c37d598 100644
--- a/stdlib/source/lux/math.lux
+++ b/stdlib/source/lux/math.lux
@@ -11,7 +11,7 @@
 ## [Values]
 (do-template [<name> <value>]
   [(def: #export <name>
-     Real
+     Frac
      (_lux_proc ["math" <value>] []))]
 
   [e  "e"]
@@ -20,12 +20,12 @@
 
 (def: #export tau
   {#;doc "The same as 2*PI."}
-  Real
+  Frac
   6.28318530717958647692)
 
 (do-template [<name> <method>]
   [(def: #export (<name> input)
-     (-> Real Real)
+     (-> Frac Frac)
      (_lux_proc ["math" <method>] [input]))]
 
   [cos   "cos"]
@@ -53,7 +53,7 @@
 
 (do-template [<name> <method>]
   [(def: #export (<name> param subject)
-     (-> Real Real Real)
+     (-> Frac Frac Frac)
      (_lux_proc ["math" <method>] [subject param]))]
 
   [atan2 "atan2"]
@@ -61,7 +61,7 @@
   )
 
 (def: #export (log' base input)
-  (r./ (log base)
+  (f./ (log base)
        (log input)))
 
 (def: #export (factorial n)
@@ -73,8 +73,8 @@
       (recur (n.* n acc) (n.dec n)))))
 
 (def: #export (hypotenuse catA catB)
-  (-> Real Real Real)
-  (root2 (r.+ (pow 2.0 catA)
+  (-> Frac Frac Frac)
+  (root2 (f.+ (pow 2.0 catA)
               (pow 2.0 catB))))
 
 (def: #export (gcd a b)
@@ -109,7 +109,7 @@
           (p/map code;nat s;nat)
           (p/map code;int s;int)
           (p/map code;deg s;deg)
-          (p/map code;real s;real)
+          (p/map code;frac s;frac)
           (p/map code;text s;text)
           (p/map code;symbol s;symbol)
           (p/map code;tag s;tag))
diff --git a/stdlib/source/lux/math/logic/fuzzy.lux b/stdlib/source/lux/math/logic/fuzzy.lux
index c3677649b..84e217d6b 100644
--- a/stdlib/source/lux/math/logic/fuzzy.lux
+++ b/stdlib/source/lux/math/logic/fuzzy.lux
@@ -82,7 +82,7 @@
        (<descending> from to)))]
 
   [d.ascending d.descending d.gradient Deg  d.< d.> d.<= d.>= d.- d./ id]
-  [r.ascending r.descending r.gradient Real r.< r.> r.<= r.>= r.- r./ real-to-deg]
+  [f.ascending f.descending f.gradient Frac f.< f.> f.<= f.>= f.- f./ frac-to-deg]
   )
 
 (do-template [<triangle> <trapezoid> <type> <ascending> <descending> <lt>]
@@ -107,22 +107,22 @@
        (undefined)))]
 
   [d.triangle d.trapezoid Deg  d.ascending d.descending d.<]
-  [r.triangle r.trapezoid Real r.ascending r.descending r.<]
+  [f.triangle f.trapezoid Frac f.ascending f.descending f.<]
   )
 
 (def: #export (gaussian deviation center)
-  (-> Real Real (Fuzzy Real))
+  (-> Frac Frac (Fuzzy Frac))
   (function [elem]
-    (let [scale (|> deviation (math;pow 2.0) (r.* 2.0))
+    (let [scale (|> deviation (math;pow 2.0) (f.* 2.0))
           membership (|> elem
-                         (r.- center)
+                         (f.- center)
                          (math;pow 2.0)
-                         (r.* -1.0)
-                         (r./ scale)
+                         (f.* -1.0)
+                         (f./ scale)
                          math;exp)]
-      (if (r.= 1.0 membership)
+      (if (f.= 1.0 membership)
         &;~true
-        (real-to-deg membership)))))
+        (frac-to-deg membership)))))
 
 (def: #export (cut treshold set)
   (All [a] (-> Deg (Fuzzy a) (Fuzzy a)))
diff --git a/stdlib/source/lux/math/random.lux b/stdlib/source/lux/math/random.lux
index 376dd9192..7a0c2963d 100644
--- a/stdlib/source/lux/math/random.lux
+++ b/stdlib/source/lux/math/random.lux
@@ -84,20 +84,20 @@
     (let [[prng output] (prng [])]
       [prng (bit;unsigned-shift-right (n.- n +64) output)])))
 
-(def: #export real
-  (Random Real)
+(def: #export frac
+  (Random Frac)
   (do Monad<Random>
     [left (bits +26)
      right (bits +27)]
     (wrap (|> right
               (n.+ (bit;shift-left +27 left))
               nat-to-int
-              int-to-real
-              (r./ (|> +1 (bit;shift-left +53) nat-to-int int-to-real))))))
+              int-to-frac
+              (f./ (|> +1 (bit;shift-left +53) nat-to-int int-to-frac))))))
 
 (def: #export deg
   (Random Deg)
-  (:: Monad<Random> map real-to-deg real))
+  (:: Monad<Random> map frac-to-deg frac))
 
 (def: #export (text' char-gen size)
   (-> (Random Nat) Nat (Random Text))
@@ -121,7 +121,7 @@
        (wrap (<ctor> left right))))]
 
   [ratio   r;Ratio   r;ratio   nat]
-  [complex c;Complex c;complex real]
+  [complex c;Complex c;complex frac]
   )
 
 (def: #export (seq left right)
-- 
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