From 68b37de7281d31470263d0e06bc72b1c5b6c2e32 Mon Sep 17 00:00:00 2001
From: Eduardo Julian
Date: Wed, 24 Jul 2019 21:18:30 -0400
Subject: Got rid of the "Number" abstraction.

---
 stdlib/source/lux/abstract/number.lux             | 14 ----
 stdlib/source/lux/data/number/complex.lux         | 71 +++++++----------
 stdlib/source/lux/data/number/frac.lux            | 94 ++++++++++++-----------
 stdlib/source/lux/data/number/int.lux             | 63 ++++++++-------
 stdlib/source/lux/data/number/nat.lux             | 32 ++++----
 stdlib/source/lux/data/number/ratio.lux           | 76 +++++++++---------
 stdlib/source/lux/data/number/rev.lux             |  5 +-
 stdlib/source/lux/time/duration.lux               |  4 +-
 stdlib/source/lux/type/unit.lux                   |  9 +--
 stdlib/source/test/lux/abstract/number.lux        | 46 -----------
 stdlib/source/test/lux/data/color.lux             |  4 +-
 stdlib/source/test/lux/data/number/complex.lux    | 13 ++--
 stdlib/source/test/lux/data/number/frac.lux       |  2 -
 stdlib/source/test/lux/data/number/int.lux        |  2 -
 stdlib/source/test/lux/data/number/nat.lux        |  2 -
 stdlib/source/test/lux/data/number/ratio.lux      |  2 -
 stdlib/source/test/lux/data/number/rev.lux        |  1 -
 stdlib/source/test/lux/macro/poly/equivalence.lux | 41 +++++-----
 stdlib/source/test/lux/math.lux                   |  6 +-
 stdlib/source/test/lux/world/file.lux             |  2 +-
 20 files changed, 203 insertions(+), 286 deletions(-)
 delete mode 100644 stdlib/source/lux/abstract/number.lux
 delete mode 100644 stdlib/source/test/lux/abstract/number.lux

(limited to 'stdlib')

diff --git a/stdlib/source/lux/abstract/number.lux b/stdlib/source/lux/abstract/number.lux
deleted file mode 100644
index b3a314ba5..000000000
--- a/stdlib/source/lux/abstract/number.lux
+++ /dev/null
@@ -1,14 +0,0 @@
-(.module:
-  lux)
-
-(`` (signature: #export (Number n)
-      {#.doc "Everything that should be expected of a number type."}
-
-      (~~ (template [<name>]
-            [(: (-> n n n) <name>)]
-            [+] [-] [*] [/] [%]))
-
-      (~~ (template [<name>]
-            [(: (-> n n) <name>)]
-            [negate] [signum] [abs]))
-      ))
diff --git a/stdlib/source/lux/data/number/complex.lux b/stdlib/source/lux/data/number/complex.lux
index 064a3a847..8b9be426f 100644
--- a/stdlib/source/lux/data/number/complex.lux
+++ b/stdlib/source/lux/data/number/complex.lux
@@ -3,8 +3,7 @@
    ["." math]
    [abstract
     [equivalence (#+ Equivalence)]
-    number
-    codec
+    [codec (#+ Codec)]
     ["M" monad (#+ Monad do)]]
    [control
     ["p" parser
@@ -12,7 +11,7 @@
    [data
     ["." maybe]
     [number
-     ["." frac ("#;." number)]]
+     ["." frac]]
     ["." text ("#;." monoid)]
     [collection
      ["." list ("#;." functor)]]]
@@ -65,19 +64,19 @@
 (structure: #export equivalence (Equivalence Complex)
   (def: = ..=))
 
-(def: #export negate
-  (-> Complex Complex)
-  (|>> (update@ #real frac;negate)
-       (update@ #imaginary frac;negate)))
+(template [<name> <transform>]
+  [(def: #export <name>
+     (-> Complex Complex)
+     (|>> (update@ #real <transform>)
+          (update@ #imaginary <transform>)))]
 
-(def: #export signum
-  (-> Complex Complex)
-  (|>> (update@ #real frac;signum)
-       (update@ #imaginary frac;signum)))
+  [negate frac.negate]
+  [signum frac.signum]
+  )
 
 (def: #export conjugate
   (-> Complex Complex)
-  (update@ #imaginary frac;negate))
+  (update@ #imaginary frac.negate))
 
 (def: #export (*' param input)
   (-> Frac Complex Complex)
@@ -100,8 +99,8 @@
 (def: #export (/ param input)
   (-> Complex Complex Complex)
   (let [(^slots [#real #imaginary]) param]
-    (if (f/< (frac;abs imaginary)
-             (frac;abs real))
+    (if (f/< (frac.abs imaginary)
+             (frac.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))
@@ -131,7 +130,7 @@
   (let [(^slots [#real #imaginary]) subject]
     {#real (f/* (math.cosh imaginary)
                 (math.cos real))
-     #imaginary (frac;negate (f/* (math.sinh imaginary)
+     #imaginary (frac.negate (f/* (math.sinh imaginary)
                                   (math.sin real)))}))
 
 (def: #export (cosh subject)
@@ -179,36 +178,20 @@
 (def: #export (abs subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    (complex (if (f/< (frac;abs imaginary)
-                      (frac;abs real))
+    (complex (if (f/< (frac.abs imaginary)
+                      (frac.abs real))
                (if (f/= +0.0 imaginary)
-                 (frac;abs real)
+                 (frac.abs real)
                  (let [q (f// imaginary real)]
                    (f/* (math.pow +0.5 (f/+ +1.0 (f/* q q)))
-                        (frac;abs imaginary))))
+                        (frac.abs imaginary))))
                (if (f/= +0.0 real)
-                 (frac;abs imaginary)
+                 (frac.abs imaginary)
                  (let [q (f// real imaginary)]
                    (f/* (math.pow +0.5 (f/+ +1.0 (f/* q q)))
-                        (frac;abs real))))
+                        (frac.abs real))))
                ))))
 
-(structure: #export number (Number Complex)
-  (def: + ..+)
-  (def: - ..-)
-  (def: * ..*)
-  (def: / ../)
-  (def: % ..%)
-  (def: (negate x)
-    (|> x
-        (update@ #real frac;negate)
-        (update@ #imaginary frac;negate)))
-  (def: abs ..abs)
-  (def: (signum x)
-    (|> x
-        (update@ #real frac;signum)
-        (update@ #imaginary frac;signum))))
-
 (def: #export (exp subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject
@@ -233,17 +216,17 @@
 
 (def: (copy-sign sign magnitude)
   (-> Frac Frac Frac)
-  (f/* (frac;signum sign) magnitude))
+  (f/* (frac.signum sign) magnitude))
 
 (def: #export (root2 (^@ input (^slots [#real #imaginary])))
   (-> Complex Complex)
-  (let [t (|> input ..abs (get@ #real) (f/+ (frac;abs real)) (f// +2.0) (math.pow +0.5))]
+  (let [t (|> input ..abs (get@ #real) (f/+ (frac.abs real)) (f// +2.0) (math.pow +0.5))]
     (if (f/>= +0.0 real)
       {#real t
        #imaginary (f// (f/* +2.0 t)
                        imaginary)}
       {#real (f// (f/* +2.0 t)
-                  (frac;abs imaginary))
+                  (frac.abs imaginary))
        #imaginary (f/* t (copy-sign imaginary +1.0))})))
 
 (def: #export (root2-1z input)
@@ -252,18 +235,18 @@
 
 (def: #export (reciprocal (^slots [#real #imaginary]))
   (-> Complex Complex)
-  (if (f/< (frac;abs imaginary)
-           (frac;abs real))
+  (if (f/< (frac.abs imaginary)
+           (frac.abs real))
     (let [q (f// imaginary real)
           scale (f// (|> real (f/* q) (f/+ imaginary))
                      +1.0)]
       {#real (f/* q scale)
-       #imaginary (frac;negate scale)})
+       #imaginary (frac.negate scale)})
     (let [q (f// real imaginary)
           scale (f// (|> imaginary (f/* q) (f/+ real))
                      +1.0)]
       {#real scale
-       #imaginary (|> scale frac;negate (f/* q))})))
+       #imaginary (|> scale frac.negate (f/* q))})))
 
 (def: #export (acos input)
   (-> Complex Complex)
diff --git a/stdlib/source/lux/data/number/frac.lux b/stdlib/source/lux/data/number/frac.lux
index 6fb8f3831..ce7fb08bf 100644
--- a/stdlib/source/lux/data/number/frac.lux
+++ b/stdlib/source/lux/data/number/frac.lux
@@ -2,11 +2,10 @@
   [lux #*
    [abstract
     [hash (#+ Hash)]
-    [number (#+ Number)]
     [monoid (#+ Monoid)]
     [equivalence (#+ Equivalence)]
-    ["." order (#+ Order)]
-    [codec (#+ Codec)]]
+    [codec (#+ Codec)]
+    ["." order (#+ Order)]]
    [control
     ["." try (#+ Try)]]
    [data
@@ -25,31 +24,39 @@
   (def: &equivalence ..equivalence)
   (def: < f/<))
 
-(structure: #export number (Number Frac)
-  (def: + f/+)
-  (def: - f/-)
-  (def: * f/*)
-  (def: / f//)
-  (def: % f/%)
-  (def: negate (f/* -1.0))
-  (def: (abs x)
-    (if (f/< +0.0 x)
-      (f/* -1.0 x)
-      x))
-  (def: (signum x)
-    (cond (f/= +0.0 x) +0.0
-          (f/< +0.0 x) -1.0
-          ## else
-          +1.0))
-  )
+(def: #export + (-> Frac Frac Frac) f/+)
+
+(def: #export - (-> Frac Frac Frac) f/-)
+
+(def: #export * (-> Frac Frac Frac) f/*)
+
+(def: #export / (-> Frac Frac Frac) f//)
+
+(def: #export % (-> Frac Frac Frac) f/%)
+
+(def: #export negate (-> Frac Frac) (f/* -1.0))
+
+(def: #export (abs x)
+  (-> Frac Frac)
+  (if (f/< +0.0 x)
+    (..* -1.0 x)
+    x))
+
+(def: #export (signum x)
+  (-> Frac Frac)
+  (cond (f/= +0.0 x) +0.0
+        (f/< +0.0 x) -1.0
+        ## else
+        +1.0))
+
 
 (template [<name> <compose> <identity>]
   [(structure: #export <name> (Monoid Frac)
      (def: identity <identity>)
      (def: compose <compose>))]
 
-  [addition       f/+   +0.0]
-  [multiplication f/*   +1.0]
+  [addition       ..+   +0.0]
+  [multiplication ..*   +1.0]
   [maximum        f/max ("lux f64 min")]
   [minimum        f/min ("lux f64 max")]
   )
@@ -58,7 +65,7 @@
   [(def: #export <name>
      {#.doc <doc>}
      Frac
-     (f// +0.0 <numerator>))]
+     (../ +0.0 <numerator>))]
 
   [not-a-number      +0.0 "Not a number."]
   [positive-infinity +1.0 "Positive infinity."]
@@ -95,16 +102,16 @@
      (def: (encode value)
        (let [whole (frac-to-int value)
              whole-part (:: <int> encode whole)
-             decimal (:: ..number abs (f/% +1.0 value))
+             decimal (|> value (..% +1.0) ..abs)
              decimal-part (if (f/= +0.0 decimal)
                             ".0"
                             (loop [dec-left decimal
                                    output ""]
                               (if (f/= +0.0 dec-left)
                                 ("lux text concat" "." output)
-                                (let [shifted (f/* <base> dec-left)
-                                      digit-idx (|> shifted (f/% <base>) frac-to-int .nat)]
-                                  (recur (f/% +1.0 shifted)
+                                (let [shifted (..* <base> dec-left)
+                                      digit-idx (|> shifted (..% <base>) frac-to-int .nat)]
+                                  (recur (..% +1.0 shifted)
                                          ("lux text concat" output ("lux text clip" digit-idx (inc digit-idx) <char-set>)))))))]
          ("lux text concat" whole-part decimal-part)))
 
@@ -125,16 +132,16 @@
                                (if (n/= 0 muls-left)
                                  output
                                  (recur (dec muls-left)
-                                        (f/* <base> output))))
-                   adjusted-decimal (|> decimal int-to-frac (f// div-power))
+                                        (..* <base> output))))
+                   adjusted-decimal (|> decimal int-to-frac (../ div-power))
                    dec-rev (case (:: //rev.hex decode ("lux text concat" "." decimal-part))
                              (#try.Success dec-rev)
                              dec-rev
 
                              (#try.Failure error)
                              (error! error))]
-               (#try.Success (f/+ (int-to-frac whole)
-                                  (f/* sign adjusted-decimal))))
+               (#try.Success (..+ (int-to-frac whole)
+                                  (..* sign adjusted-decimal))))
 
              _
              (#try.Failure ("lux text concat" <error> repr))))
@@ -282,7 +289,7 @@
 (template [<struct> <error> <from> <to>]
   [(structure: #export <struct> (Codec Text Frac)
      (def: (encode value)
-       (let [sign (:: ..number signum value)
+       (let [sign (..signum value)
              raw-bin (:: ..binary encode value)
              dot-idx (maybe.assume ("lux text index" 0 "." raw-bin))
              whole-part ("lux text clip" (if (f/= -1.0 sign) 1 0) dot-idx raw-bin)
@@ -324,7 +331,7 @@
 
 (def: (log2 input)
   (-> Frac Frac)
-  (f// (math.log +2.0)
+  (../ (math.log +2.0)
        (math.log input)))
 
 (def: double-bias Nat 1023)
@@ -355,7 +362,7 @@
              ..negative-infinity-bits
 
              (f/= +0.0 input)
-             (let [reciprocal (f// input +1.0)]
+             (let [reciprocal (../ input +1.0)]
                (if (f/= positive-infinity reciprocal)
                  ## Positive zero
                  ..positive-zero-bits
@@ -363,16 +370,17 @@
                  ..negative-zero-bits))
 
              ## else
-             (let [sign (:: ..number signum input)
-                   input (:: ..number abs input)
+             (let [input (..abs input)
                    exponent (math.floor (log2 input))
                    exponent-mask (|> 1 (//i64.left-shift exponent-size) dec) 
                    mantissa (|> input
                                 ## Normalize
-                                (f// (math.pow exponent +2.0))
+                                (../ (math.pow exponent +2.0))
                                 ## Make it int-equivalent
-                                (f/* (math.pow +52.0 +2.0)))
-                   sign-bit (if (f/= -1.0 sign) 1 0)
+                                (..* (math.pow +52.0 +2.0)))
+                   sign-bit (if (f/= -1.0 (..signum input))
+                              1
+                              0)
                    exponent-bits (|> exponent frac-to-int .nat (n/+ double-bias) (//i64.and exponent-mask))
                    mantissa-bits (|> mantissa frac-to-int .nat)]
                ($_ //i64.or
@@ -407,20 +415,20 @@
           (and (n/= 0 E) (n/= 0 M))
           (if (n/= 0 S)
             +0.0
-            (f/* -1.0 +0.0))
+            (..* -1.0 +0.0))
 
           ## else
           (let [normalized (|> M (//i64.set mantissa-size)
                                .int int-to-frac
-                               (f// (math.pow +52.0 +2.0)))
+                               (../ (math.pow +52.0 +2.0)))
                 power (math.pow (|> E (n/- double-bias)
                                     .int int-to-frac)
                                 +2.0)
-                shifted (f/* power
+                shifted (..* power
                              normalized)]
             (if (n/= 0 S)
               shifted
-              (f/* -1.0 shifted))))))
+              (..* -1.0 shifted))))))
 
 (structure: #export hash (Hash Frac)
   (def: &equivalence ..equivalence)
diff --git a/stdlib/source/lux/data/number/int.lux b/stdlib/source/lux/data/number/int.lux
index c924ba9fe..9e1299ae2 100644
--- a/stdlib/source/lux/data/number/int.lux
+++ b/stdlib/source/lux/data/number/int.lux
@@ -2,18 +2,17 @@
   [lux #*
    [abstract
     [hash (#+ Hash)]
-    [number (#+ Number)]
     [enum (#+ Enum)]
     [interval (#+ Interval)]
     [monoid (#+ Monoid)]
     [equivalence (#+ Equivalence)]
-    ["." order (#+ Order)]
-    [codec (#+ Codec)]]
+    [codec (#+ Codec)]
+    ["." order (#+ Order)]]
    [control
     ["." try (#+ Try)]]
    [data
-    ["." maybe]
-    [text (#+ Char)]]]
+    [text (#+ Char)]
+    ["." maybe]]]
   [//
    ["." nat]])
 
@@ -34,23 +33,31 @@
   (def: top +9,223,372,036,854,775,807)
   (def: bottom -9,223,372,036,854,775,808))
 
-(structure: #export number (Number Int)
-  (def: + i/+)
-  (def: - i/-)
-  (def: * i/*)
-  (def: / i//)
-  (def: % i/%)
-  (def: negate (i/* -1))
-  (def: (abs x)
-    (if (i/< +0 x)
-      (i/* -1 x)
-      x))
-  (def: (signum x)
-    (cond (i/= +0 x) +0
-          (i/< +0 x) -1
-          ## else
-          +1))
-  )
+(def: #export + (-> Int Int Int) i/+)
+
+(def: #export - (-> Int Int Int) i/-)
+
+(def: #export * (-> Int Int Int) i/*)
+
+(def: #export / (-> Int Int Int) i//)
+
+(def: #export % (-> Int Int Int) i/%)
+
+(def: #export negate (-> Int Int) (i/* -1))
+
+(def: #export (abs x)
+  (-> Int Int)
+  (if (i/< +0 x)
+    (i/* -1 x)
+    x))
+
+(def: #export (signum x)
+  (-> Int Int)
+  (cond (i/= +0 x) +0
+        (i/< +0 x) -1
+        ## else
+        +1))
+
 
 (template [<name> <compose> <identity>]
   [(structure: #export <name> (Monoid Int)
@@ -63,13 +70,13 @@
   [minimum        i/min (:: ..interval top)]
   )
 
-(def: (int;sign!! value)
+(def: (sign!! value)
   (-> Int Text)
   (if (i/< +0 value)
     "-"
     "+"))
 
-(def: (int;sign?? representation)
+(def: (sign?? representation)
   (-> Text (Maybe Int))
   (case ("lux text char" 0 representation)
     (^ (char "-"))
@@ -100,12 +107,12 @@
      (def: (encode value)
        (if (i/= +0 value)
          "+0"
-         (loop [input (|> value (i// <base>) (:: ..number abs))
-                output (|> value (i/% <base>) (:: ..number abs) .nat
+         (loop [input (|> value (i// <base>) ..abs)
+                output (|> value (i/% <base>) ..abs .nat
                            <to-character>
                            maybe.assume)]
            (if (i/= +0 input)
-             ("lux text concat" (int;sign!! value) output)
+             ("lux text concat" (sign!! value) output)
              (let [digit (maybe.assume (<to-character> (.nat (i/% <base> input))))]
                (recur (i// <base> input)
                       ("lux text concat" digit output)))))))
@@ -113,7 +120,7 @@
      (def: (decode repr)
        (let [input-size ("lux text size" repr)]
          (if (n/> 1 input-size)
-           (case (int;sign?? repr)
+           (case (sign?? repr)
              (#.Some sign)
              (int-decode-loop input-size repr sign <base> <to-value> <error>)
 
diff --git a/stdlib/source/lux/data/number/nat.lux b/stdlib/source/lux/data/number/nat.lux
index 0a5b94f0a..a7c804f65 100644
--- a/stdlib/source/lux/data/number/nat.lux
+++ b/stdlib/source/lux/data/number/nat.lux
@@ -2,7 +2,6 @@
   [lux #*
    [abstract
     [hash (#+ Hash)]
-    [number (#+ Number)]
     [enum (#+ Enum)]
     [interval (#+ Interval)]
     [monoid (#+ Monoid)]
@@ -33,26 +32,23 @@
   (def: top (.nat -1))
   (def: bottom 0))
 
-(structure: #export number (Number Nat)
-  (def: + n/+)
-  (def: - n/-)
-  (def: * n/*)
-  (def: / n//)
-  (def: % n/%)
-  (def: (negate value) (n/- value 0))
-  (def: abs function.identity)
-  (def: (signum x)
-    (case x
-      0 0
-      _ 1)))
+(def: #export + (-> Nat Nat Nat) n/+)
+
+(def: #export - (-> Nat Nat Nat) n/-)
+
+(def: #export * (-> Nat Nat Nat) n/*)
+
+(def: #export / (-> Nat Nat Nat) n//)
+
+(def: #export % (-> Nat Nat Nat) n/%)
 
 (template [<name> <compose> <identity>]
   [(structure: #export <name> (Monoid Nat)
      (def: identity <identity>)
      (def: compose <compose>))]
 
-  [addition       n/+   0]
-  [multiplication n/*   1]
+  [addition       ..+   0]
+  [multiplication ..*   1]
   [minimum        n/min (:: ..interval top)]
   [maximum        n/max (:: ..interval bottom)]
   )
@@ -174,9 +170,9 @@
      (def: (encode value)
        (loop [input value
               output ""]
-         (let [digit (maybe.assume (<to-character> (n/% <base> input)))
+         (let [digit (maybe.assume (<to-character> (..% <base> input)))
                output' ("lux text concat" digit output)]
-           (case (n// <base> input)
+           (case (../ <base> input)
              0
              output'
 
@@ -195,7 +191,7 @@
 
                  (#.Some digit-value)
                  (recur (inc idx)
-                        (|> output (n/* <base>) (n/+ digit-value))))
+                        (|> output (..* <base>) (..+ digit-value))))
                (#try.Success output)))
            (#try.Failure ("lux text concat" <error> repr))))))]
 
diff --git a/stdlib/source/lux/data/number/ratio.lux b/stdlib/source/lux/data/number/ratio.lux
index 5709b5724..09d81d20d 100644
--- a/stdlib/source/lux/data/number/ratio.lux
+++ b/stdlib/source/lux/data/number/ratio.lux
@@ -1,10 +1,10 @@
-(.module: {#.doc "Rational numbers."}
+(.module:
+  {#.doc "Rational numbers."}
   [lux #*
    [abstract
     [equivalence (#+ Equivalence)]
     [order (#+ Order)]
     [monoid (#+ Monoid)]
-    [number (#+ Number)]
     [codec (#+ Codec)]
     [monad (#+ do)]]
    [control
@@ -55,51 +55,45 @@
       (n/< parameter' subject')))
   )
 
-(def: (- parameter subject)
+(def: #export (+ parameter subject)
+  (-> Ratio Ratio Ratio)
   (let [[parameter' subject'] (..equalize parameter subject)]
-    (normalize [(n/- parameter' subject')
+    (normalize [(n/+ parameter' subject')
                 (n/* (get@ #denominator parameter)
                      (get@ #denominator subject))])))
 
-(structure: #export number
-  (Number Ratio)
-  
-  (def: (+ parameter subject)
-    (let [[parameter' subject'] (..equalize parameter subject)]
-      (normalize [(n/+ parameter' subject')
-                  (n/* (get@ #denominator parameter)
-                       (get@ #denominator subject))])))
-
-  (def: - ..-)
-
-  (def: (* parameter subject)
-    (normalize [(n/* (get@ #numerator parameter)
-                     (get@ #numerator subject))
+(def: #export (- parameter subject)
+  (-> Ratio Ratio Ratio)
+  (let [[parameter' subject'] (..equalize parameter subject)]
+    (normalize [(n/- parameter' subject')
                 (n/* (get@ #denominator parameter)
-                     (get@ #denominator subject))]))
+                     (get@ #denominator subject))])))
 
-  (def: (/ parameter subject)
-    (let [[parameter' subject'] (..equalize parameter subject)]
-      (normalize [subject' parameter'])))
+(def: #export (* parameter subject)
+  (-> Ratio Ratio Ratio)
+  (normalize [(n/* (get@ #numerator parameter)
+                   (get@ #numerator subject))
+              (n/* (get@ #denominator parameter)
+                   (get@ #denominator subject))]))
 
-  (def: (% parameter subject)
-    (let [[parameter' subject'] (..equalize parameter subject)
-          quot (n// parameter' subject')]
-      (..- (update@ #numerator (n/* quot) parameter)
-           subject)))
+(def: #export (/ parameter subject)
+  (-> Ratio Ratio Ratio)
+  (let [[parameter' subject'] (..equalize parameter subject)]
+    (normalize [subject' parameter'])))
 
-  (def: (negate (^slots [#numerator #denominator]))
-    {#numerator denominator
-     #denominator numerator})
-  
-  (def: abs function.identity)
-  
-  (def: (signum x)
-    {#numerator 1
-     #denominator 1})
-  )
+(def: #export (% parameter subject)
+  (-> Ratio Ratio Ratio)
+  (let [[parameter' subject'] (..equalize parameter subject)
+        quot (n// parameter' subject')]
+    (..- (update@ #numerator (n/* quot) parameter)
+         subject)))
+
+(def: #export (reciprocal (^slots [#numerator #denominator]))
+  (-> Ratio Ratio)
+  {#numerator denominator
+   #denominator numerator})
 
-(def: separator Text ":")
+(def: separator ":")
 
 (structure: #export codec (Codec Text Ratio)
   (def: (encode (^slots [#numerator #denominator]))
@@ -131,9 +125,9 @@
      (Monoid Ratio)
 
      (def: identity (..ratio <identity>))
-     (def: compose (:: ..number <compose>))
+     (def: compose <compose>)
      )]
   
-  [0 + addition]
-  [1 * multiplication]
+  [0 ..+ addition]
+  [1 ..* multiplication]
   )
diff --git a/stdlib/source/lux/data/number/rev.lux b/stdlib/source/lux/data/number/rev.lux
index f57137c88..0633d5c0b 100644
--- a/stdlib/source/lux/data/number/rev.lux
+++ b/stdlib/source/lux/data/number/rev.lux
@@ -2,13 +2,12 @@
   [lux #*
    [abstract
     [hash (#+ Hash)]
-    [number (#+ Number)]
     [enum (#+ Enum)]
     [interval (#+ Interval)]
     [monoid (#+ Monoid)]
     [equivalence (#+ Equivalence)]
-    ["." order (#+ Order)]
-    [codec (#+ Codec)]]
+    [codec (#+ Codec)]
+    ["." order (#+ Order)]]
    [control
     ["." function]
     ["." try (#+ Try)]]
diff --git a/stdlib/source/lux/time/duration.lux b/stdlib/source/lux/time/duration.lux
index 8a5611d16..a82ae6bed 100644
--- a/stdlib/source/lux/time/duration.lux
+++ b/stdlib/source/lux/time/duration.lux
@@ -13,7 +13,7 @@
    [data
     [number
      ["." nat ("#@." decimal)]
-     ["." int ("#@." decimal number)]]
+     ["." int]]
     ["." text ("#@." monoid)]]
    [type
     abstract]])
@@ -106,7 +106,7 @@
     (let [signed? (negative? duration)
           [days time-left] [(query day duration) (frame day duration)]
           days (if signed?
-                 (int@abs days)
+                 (int.abs days)
                  days)
           time-left (if signed?
                       (..inverse time-left)
diff --git a/stdlib/source/lux/type/unit.lux b/stdlib/source/lux/type/unit.lux
index dd8b467bf..dbf356488 100644
--- a/stdlib/source/lux/type/unit.lux
+++ b/stdlib/source/lux/type/unit.lux
@@ -11,7 +11,7 @@
      ["s" code (#+ Parser)]]]
    [data
     [number
-     ["r" ratio (#+ Ratio)]]
+     ["." ratio (#+ Ratio)]]
     [text
      ["%" format (#+ format)]]]
    ["." macro
@@ -95,7 +95,7 @@
 (syntax: #export (scale:
                    {export csr.export}
                    {name s.local-identifier}
-                   {(^slots [#r.numerator #r.denominator]) ratio^}
+                   {(^slots [#ratio.numerator #ratio.denominator]) ratio^}
                    {annotations (p.default cs.empty-annotations csr.annotations)})
   (let [g!scale (code.local-identifier name)]
     (wrap (list (` (type: (~+ (csw.export export)) ((~ g!scale) (~' u))
@@ -144,9 +144,8 @@
 
 (def: #export (re-scale from to quantity)
   (All [si so u] (-> (Scale si) (Scale so) (Qty (si u)) (Qty (so u))))
-  (let [[numerator denominator] (:: r.number /
-                                    (:: from ratio)
-                                    (:: to ratio))]
+  (let [[numerator denominator] (ratio./ (:: from ratio)
+                                         (:: to ratio))]
     (|> quantity
         out
         (i/* (.int numerator))
diff --git a/stdlib/source/test/lux/abstract/number.lux b/stdlib/source/test/lux/abstract/number.lux
deleted file mode 100644
index e04ad3124..000000000
--- a/stdlib/source/test/lux/abstract/number.lux
+++ /dev/null
@@ -1,46 +0,0 @@
-(.module:
-  [lux #*
-   ["_" test (#+ Test)]
-   [abstract/monad (#+ do)]
-   [data
-    [text
-     ["%" format (#+ format)]]]
-   [math
-    ["r" random (#+ Random)]]]
-  {1
-   ["." / (#+ Number)
-    [//
-     ["." order (#+ Order)]]]})
-
-(def: #export (spec (^@ order (^open "/@.")) (^open "/@.") gen-sample)
-  (All [a] (-> (Order a) (Number a) (Random a) Test))
-  (do r.monad
-    [#let [non-zero (r.filter (function (_ sample)
-                                (|> sample (/@+ sample) (/@= sample) not))
-                              gen-sample)]
-     parameter non-zero
-     subject non-zero]
-    (<| (_.context (%.name (name-of /.Number)))
-        ($_ _.and
-            (_.test "Addition and subtraction are inverse functions."
-                    (|> subject (/@+ parameter) (/@- parameter) (/@= subject)))
-            (_.test "Multiplication and division are inverse functions."
-                    (|> subject (/@* parameter) (/@/ parameter) (/@= subject)))
-            (_.test "Modulus fills all the information division misses."
-                    (let [modulus (/@% parameter subject)
-                          multiple (/@- modulus subject)
-                          factor (/@/ parameter multiple)]
-                      (|> parameter (/@* factor) (/@+ modulus) (/@= subject))))
-            (_.test "Negation flips the sign of a number and mimics subtraction."
-                    (let [unsigned? (/@= (/@signum parameter)
-                                         (/@signum (/@negate parameter)))]
-                      (or unsigned?
-                          (/@= (/@+ (/@negate parameter) subject)
-                               (/@- parameter subject)))))
-            (_.test "The absolute value is always positive."
-                    (let [unsigned? (/@= parameter
-                                         (/@negate parameter))]
-                      (if unsigned?
-                        (/@= subject (/@abs subject))
-                        (order.>= order subject (/@abs subject)))))
-            ))))
diff --git a/stdlib/source/test/lux/data/color.lux b/stdlib/source/test/lux/data/color.lux
index 86abba0a3..ee3bdffb1 100644
--- a/stdlib/source/test/lux/data/color.lux
+++ b/stdlib/source/test/lux/data/color.lux
@@ -9,7 +9,7 @@
    [data
     ["%" text/format (#+ format)]
     [number
-     ["." frac ("#@." number)]]]
+     ["." frac]]]
    ["." math
     ["r" random (#+ Random)]]]
   {1
@@ -100,6 +100,6 @@
                                 (saturation gray'ed))
                            (|> (luminance gray'ed)
                                (f/- (luminance mediocre))
-                               frac@abs
+                               frac.abs
                                (f/<= error-margin)))))
             ))))
diff --git a/stdlib/source/test/lux/data/number/complex.lux b/stdlib/source/test/lux/data/number/complex.lux
index 6d7689582..52e43a77e 100644
--- a/stdlib/source/test/lux/data/number/complex.lux
+++ b/stdlib/source/test/lux/data/number/complex.lux
@@ -8,11 +8,10 @@
      [/
       ["$." equivalence]
       ["$." order]
-      ["$." number]
       ["$." codec]]}]
    [data
     [number
-     ["." frac ("#@." number)]]
+     ["." frac]]
     [collection
      ["." list ("#@." functor)]]]
    ["." math
@@ -24,9 +23,9 @@
 
 (def: (within? margin standard value)
   (-> Frac Complex Complex Bit)
-  (let [real-dist (frac@abs (f/- (get@ #/.real standard)
+  (let [real-dist (frac.abs (f/- (get@ #/.real standard)
                                  (get@ #/.real value)))
-        imgn-dist (frac@abs (f/- (get@ #/.imaginary standard)
+        imgn-dist (frac.abs (f/- (get@ #/.imaginary standard)
                                  (get@ #/.imaginary value)))]
     (and (f/< margin real-dist)
          (f/< margin imgn-dist))))
@@ -70,8 +69,8 @@
         (_.test "Absolute value of complex >= absolute value of any of the parts."
                 (let [r+i (/.complex real imaginary)
                       abs (get@ #/.real (/.abs r+i))]
-                  (and (f/>= (frac@abs real) abs)
-                       (f/>= (frac@abs imaginary) abs))))
+                  (and (f/>= (frac.abs real) abs)
+                       (f/>= (frac.abs imaginary) abs))))
         (_.test "The absolute value of a complex number involving a NaN on either dimension, results in a NaN value."
                 (and (frac.not-a-number? (get@ #/.real (/.abs (/.complex frac.not-a-number imaginary))))
                      (frac.not-a-number? (get@ #/.real (/.abs (/.complex real frac.not-a-number))))))
@@ -130,7 +129,7 @@
                 (let [cx (/.conjugate x)]
                   (and (f/= (get@ #/.real x)
                             (get@ #/.real cx))
-                       (f/= (frac@negate (get@ #/.imaginary x))
+                       (f/= (frac.negate (get@ #/.imaginary x))
                             (get@ #/.imaginary cx)))))
         (_.test "The reciprocal functions is its own inverse."
                 (|> x /.reciprocal /.reciprocal (within? margin-of-error x)))
diff --git a/stdlib/source/test/lux/data/number/frac.lux b/stdlib/source/test/lux/data/number/frac.lux
index 9edc0f921..736f82457 100644
--- a/stdlib/source/test/lux/data/number/frac.lux
+++ b/stdlib/source/test/lux/data/number/frac.lux
@@ -8,7 +8,6 @@
      [/
       ["$." equivalence]
       ["$." order]
-      ["$." number]
       ["$." monoid]
       ["$." codec]]}]
    [math
@@ -24,7 +23,6 @@
         (`` ($_ _.and
                 ($equivalence.spec /.equivalence gen-frac)
                 ($order.spec /.order gen-frac)
-                ($number.spec /.order /.number gen-frac)
                 (~~ (template [<monoid>]
                       [(<| (_.context (%.name (name-of <monoid>)))
                            ($monoid.spec /.equivalence <monoid> gen-frac))]
diff --git a/stdlib/source/test/lux/data/number/int.lux b/stdlib/source/test/lux/data/number/int.lux
index 4fa93051b..7d11f0a03 100644
--- a/stdlib/source/test/lux/data/number/int.lux
+++ b/stdlib/source/test/lux/data/number/int.lux
@@ -8,7 +8,6 @@
      [/
       ["$." equivalence]
       ["$." order]
-      ["$." number]
       ["$." enum]
       ["$." interval]
       ["$." monoid]
@@ -25,7 +24,6 @@
       (`` ($_ _.and
               ($equivalence.spec /.equivalence r.int)
               ($order.spec /.order r.int)
-              ($number.spec /.order /.number (:: r.monad map (i/% +1,000,000) r.int))
               ($enum.spec /.enum r.int)
               ($interval.spec /.interval r.int)
               (~~ (template [<monoid>]
diff --git a/stdlib/source/test/lux/data/number/nat.lux b/stdlib/source/test/lux/data/number/nat.lux
index dda227223..9a7f5907c 100644
--- a/stdlib/source/test/lux/data/number/nat.lux
+++ b/stdlib/source/test/lux/data/number/nat.lux
@@ -8,7 +8,6 @@
      [/
       ["$." equivalence]
       ["$." order]
-      ["$." number]
       ["$." enum]
       ["$." interval]
       ["$." monoid]
@@ -25,7 +24,6 @@
       (`` ($_ _.and
               ($equivalence.spec /.equivalence r.nat)
               ($order.spec /.order r.nat)
-              ($number.spec /.order /.number (:: r.monad map (n/% 1,000,000) r.nat))
               ($enum.spec /.enum r.nat)
               ($interval.spec /.interval r.nat)
               (~~ (template [<monoid>]
diff --git a/stdlib/source/test/lux/data/number/ratio.lux b/stdlib/source/test/lux/data/number/ratio.lux
index 160a4fa53..f2162681d 100644
--- a/stdlib/source/test/lux/data/number/ratio.lux
+++ b/stdlib/source/test/lux/data/number/ratio.lux
@@ -8,7 +8,6 @@
      [/
       ["$." equivalence]
       ["$." order]
-      ["$." number]
       ["$." monoid]
       ["$." codec]]}]
    [math
@@ -33,7 +32,6 @@
       (`` ($_ _.and
               ($equivalence.spec /.equivalence ..ratio)
               ($order.spec /.order ..ratio)
-              ($number.spec /.order /.number ..ratio)
               (~~ (template [<monoid>]
                     [(<| (_.context (%.name (name-of <monoid>)))
                          ($monoid.spec /.equivalence <monoid> ..ratio))]
diff --git a/stdlib/source/test/lux/data/number/rev.lux b/stdlib/source/test/lux/data/number/rev.lux
index 37df07567..1a0bc4571 100644
--- a/stdlib/source/test/lux/data/number/rev.lux
+++ b/stdlib/source/test/lux/data/number/rev.lux
@@ -8,7 +8,6 @@
      [/
       ["$." equivalence]
       ["$." order]
-      ["$." number]
       ["$." enum]
       ["$." interval]
       ["$." monoid]
diff --git a/stdlib/source/test/lux/macro/poly/equivalence.lux b/stdlib/source/test/lux/macro/poly/equivalence.lux
index ef46b9063..c6dcd4687 100644
--- a/stdlib/source/test/lux/macro/poly/equivalence.lux
+++ b/stdlib/source/test/lux/macro/poly/equivalence.lux
@@ -1,16 +1,17 @@
 (.module:
   [lux #*
    ["%" data/text/format (#+ format)]
-   ["r" math/random (#+ Random)]
    ["_" test (#+ Test)]
-   [abstract/monad (#+ do)]
+   [math
+    ["." random (#+ Random)]]
    [abstract
+    [monad (#+ do)]
     [equivalence (#+ Equivalence)]]
    [data
     ["." bit]
     ["." maybe]
     [number
-     ["." int ("#@." number)]]
+     ["." int]]
     ["." text]
     [collection
      ["." list]]]
@@ -40,25 +41,25 @@
    #recursive Recursive})
 
 (def: gen-recursive
-  (r.Random Recursive)
-  (r.rec (function (_ gen-recursive)
-           (r.or r.frac
-                 (r.and r.frac gen-recursive)))))
+  (Random Recursive)
+  (random.rec (function (_ gen-recursive)
+                (random.or random.frac
+                           (random.and random.frac gen-recursive)))))
 
 (def: gen-record
-  (r.Random Record)
-  (do r.monad
-    [size (:: @ map (n/% 2) r.nat)
-     #let [gen-int (|> r.int (:: @ map (|>> int@abs (i/% +1,000,000))))]]
-    ($_ r.and
-        r.bit
+  (Random Record)
+  (do random.monad
+    [size (:: @ map (n/% 2) random.nat)
+     #let [gen-int (|> random.int (:: @ map (|>> int.abs (i/% +1,000,000))))]]
+    ($_ random.and
+        random.bit
         gen-int
-        r.frac
-        (r.unicode size)
-        (r.maybe gen-int)
-        (r.list size gen-int)
-        ($_ r.or r.bit gen-int r.frac)
-        ($_ r.and gen-int r.frac (r.unicode size))
+        random.frac
+        (random.unicode size)
+        (random.maybe gen-int)
+        (random.list size gen-int)
+        ($_ random.or random.bit gen-int random.frac)
+        ($_ random.and gen-int random.frac (random.unicode size))
         gen-recursive)))
 
 (derived: equivalence (/.equivalence Record))
@@ -66,7 +67,7 @@
 (def: #export test
   Test
   (<| (_.context (%.name (name-of /._)))
-      (do r.monad
+      (do random.monad
         [sample gen-record
          #let [(^open "/@.") ..equivalence]]
         (_.test "Every instance equals itself."
diff --git a/stdlib/source/test/lux/math.lux b/stdlib/source/test/lux/math.lux
index 88dc6d420..46b5171ee 100644
--- a/stdlib/source/test/lux/math.lux
+++ b/stdlib/source/test/lux/math.lux
@@ -7,7 +7,7 @@
    [data
     ["." bit ("#@." equivalence)]
     [number
-     ["." frac ("#@." number)]]]]
+     ["." frac]]]]
   {1
    ["." /]}
   ["." / #_
@@ -20,7 +20,7 @@
 (def: (within? margin-of-error standard value)
   (-> Frac Frac Frac Bit)
   (f/< margin-of-error
-       (frac@abs (f/- standard value))))
+       (frac.abs (f/- standard value))))
 
 (def: margin Frac +0.0000001)
 
@@ -61,7 +61,7 @@
                     (_.test "The round will be an integer value, and will be < or > or = the original."
                             (let [round'd (/.round sample)]
                               (and (|> round'd frac-to-int int-to-frac (f/= round'd))
-                                   (f/<= +1.0 (frac@abs (f/- sample round'd))))))
+                                   (f/<= +1.0 (frac.abs (f/- sample round'd))))))
                     )))
           (<| (_.context "Exponentials and logarithms")
               (do r.monad
diff --git a/stdlib/source/test/lux/world/file.lux b/stdlib/source/test/lux/world/file.lux
index 808a09e0e..2659183af 100644
--- a/stdlib/source/test/lux/world/file.lux
+++ b/stdlib/source/test/lux/world/file.lux
@@ -71,7 +71,7 @@
         [file-size (|> r.nat (:: @ map (|>> (n/% 100) (n/max 10))))
          dataL (_binary.binary file-size)
          dataR (_binary.binary file-size)
-         new-modified (|> r.int (:: @ map (|>> (:: int.number abs)
+         new-modified (|> r.int (:: @ map (|>> int.abs
                                                truncate-millis
                                                duration.from-millis
                                                instant.absolute)))]
-- 
cgit v1.2.3