- Implemented Nat functionality in pure Lux.

15 files changed, 29 insertions, 687 deletions

diff --git a/new-luxc/source/luxc/lang/extension/analysis/common.lux b/new-luxc/source/luxc/lang/extension/analysis/common.lux
index c63d063cd..1d4429e09 100644
--- a/new-luxc/source/luxc/lang/extension/analysis/common.lux
+++ b/new-luxc/source/luxc/lang/extension/analysis/common.lux
@@ -209,22 +209,6 @@
           (install "arithmetic-right-shift" (binary Int Nat Int))
           )))
 
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary Nat Nat Nat))
-          (install "-" (binary Nat Nat Nat))
-          (install "*" (binary Nat Nat Nat))
-          (install "/" (binary Nat Nat Nat))
-          (install "%" (binary Nat Nat Nat))
-          (install "=" (binary Nat Nat Bool))
-          (install "<" (binary Nat Nat Bool))
-          (install "min" (nullary Nat))
-          (install "max" (nullary Nat))
-          (install "to-int" (unary Nat Int))
-          (install "char" (unary Nat Text)))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -239,7 +223,8 @@
           (install "min" (nullary Int))
           (install "max" (nullary Int))
           (install "to-nat" (unary Int Nat))
-          (install "to-frac" (unary Int Frac)))))
+          (install "to-frac" (unary Int Frac))
+          (install "char" (unary Int Text)))))
 
 (def: deg-procs
   Bundle
@@ -453,7 +438,6 @@
       (|> (dict.new text.Hash<Text>)
           (dict.merge lux-procs)
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/js/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/js/procedure/common.jvm.lux
index 14e37efb8..f9e00be2a 100644
--- a/new-luxc/source/luxc/lang/translation/js/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/js/procedure/common.jvm.lux
@@ -210,9 +210,6 @@
      Nullary
      (<encode> <const>))]
 
-  [nat//min                 0                           runtimeT.int]
-  [nat//max                -1                           runtimeT.int]
-
   [int//min                Long::MIN_VALUE              runtimeT.int]
   [int//max                Long::MAX_VALUE              runtimeT.int]
   
@@ -238,12 +235,6 @@
   [int//div        runtimeT.int///]
   [int//rem        runtimeT.int//%]
   
-  [nat//add        runtimeT.int//+]
-  [nat//sub        runtimeT.int//-]
-  [nat//mul        runtimeT.int//*]
-  [nat//div        runtimeT.nat///]
-  [nat//rem        runtimeT.nat//%]
-
   [deg//add        runtimeT.int//+]
   [deg//sub        runtimeT.int//-]
   [deg//mul        runtimeT.deg//*]
@@ -275,21 +266,10 @@
      Binary
      (format <cmp> "(" subjectJS "," paramJS ")"))]
 
-  [nat//= runtimeT.int//=]
-  [nat//< runtimeT.nat//<]
   [int//= runtimeT.int//=]
   [int//< runtimeT.int//<]
   [deg//= runtimeT.int//=]
-  [deg//< runtimeT.nat//<]
-  )
-
-(do-template [<name>]
-  [(def: (<name> inputJS)
-     Unary
-     inputJS)]
-
-  [nat//to-int]
-  [int//to-nat]
+  [deg//< runtimeT.int//<]
   )
 
 (def: (frac//encode inputJS)
@@ -314,7 +294,7 @@
   [text//hash   runtimeT.text//hash]
   )
 
-(def: (nat//char inputJS)
+(def: (int//char inputJS)
   Unary
   (format "String.fromCharCode" "(" (int//to-frac inputJS) ")"))
 
@@ -479,22 +459,6 @@
           (install "arithmetic-right-shift" (binary bit//arithmetic-right-shift))
           )))
 
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//=))
-          (install "<" (binary nat//<))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary nat//to-int))
-          (install "char" (unary nat//char)))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -508,8 +472,8 @@
           (install "<" (binary int//<))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary int//to-nat))
-          (install "to-frac" (unary int//to-frac)))))
+          (install "to-frac" (unary int//to-frac))
+          (install "char" (unary int//char)))))
 
 (def: deg-procs
   Bundle
@@ -638,7 +602,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/js/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/js/runtime.jvm.lux
index afb3cd538..5fab92941 100644
--- a/new-luxc/source/luxc/lang/translation/js/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/js/runtime.jvm.lux
@@ -584,99 +584,6 @@
           __int///
           __int//%))
 
-(runtime: nat//< "ltN64"
-  (let [high (function (_ i64) (format "(" i64 "." //.int-high-field ")"))
-        low (function (_ i64) (format "(" i64 "." //.int-low-field ")"))
-        i32 (function (_ word) (format "(" word " >>> 0)"))]
-    (js.function @ (list "subject" "parameter")
-      (list (js.return! (js.or (js.> (i32 (high "subject"))
-                                     (i32 (high "parameter")))
-                               (js.and (js.= (high "subject")
-                                             (high "parameter"))
-                                       (js.> (i32 (low "subject"))
-                                             (i32 (low "parameter"))))))))))
-
-(def: (<N param subject)
-  (-> Expression Expression Expression)
-  (js.apply nat//< (list subject param)))
-
-(def: (<=N param subject)
-  (-> Expression Expression Expression)
-  (js.or (js.apply nat//< (list subject param))
-         (js.apply int//= (list subject param))))
-
-(def: (>N param subject)
-  (-> Expression Expression Expression)
-  (js.apply nat//< (list param subject)))
-
-(def: (>=N param subject)
-  (-> Expression Expression Expression)
-  (js.or (js.apply nat//< (list param subject))
-         (js.apply int//= (list subject param))))
-
-(runtime: nat/// "divN64"
-  (let [negative? (function (_ value)
-                    (js.apply int//< (list value int//zero)))
-        valid-division-check [(=I int//zero "parameter")
-                              (js.throw! (js.string "Cannot divide by zero!"))]
-        short-circuit-check [(=I int//zero "subject")
-                             (js.return! int//zero)]]
-    (js.function @ (list "subject" "parameter")
-      (list (js.cond! (list valid-division-check
-                            short-circuit-check
-
-                            [(>N "subject" "parameter")
-                             (js.return! int//zero)]
-
-                            [(>N (js.apply bit//logical-right-shift
-                                           (list "subject" (js.number 1.0)))
-                                 "parameter")
-                             (js.return! int//one)])
-                      (js.block! (list (js.var! "result" (#.Some int//zero))
-                                       (js.var! "remainder" (#.Some "subject"))
-                                       (js.while! (>=N "parameter" "remainder")
-                                                  (let [rough-estimate (js.apply "Math.floor" (list (js./ (js.apply int//to-number (list "parameter"))
-                                                                                                          (js.apply int//to-number (list "remainder")))))
-                                                        log2 (js./ "Math.LN2"
-                                                                   (js.apply "Math.log" (list "approximate")))
-                                                        approx-result (js.apply int//from-number (list "approximate"))
-                                                        approx-remainder (js.apply int//* (list "approximate_result" "parameter"))]
-                                                    (list (js.var! "approximate" (#.Some (js.apply "Math.max" (list (js.number 1.0)
-                                                                                                                    rough-estimate))))
-                                                          (js.var! "log2" (#.Some (js.apply "Math.ceil" (list log2))))
-                                                          (js.var! "delta" (#.Some (js.? (js.<= (js.number 48.0) "log2")
-                                                                                         (js.number 1.0)
-                                                                                         (js.apply "Math.pow" (list (js.number 2.0)
-                                                                                                                    (js.- (js.number 48.0)
-                                                                                                                          "log2"))))))
-                                                          (js.var! "approximate_result" (#.Some approx-result))
-                                                          (js.var! "approximate_remainder" (#.Some approx-remainder))
-                                                          (js.while! (js.or (negative? "approximate_remainder")
-                                                                            (>N "remainder"
-                                                                                "approximate_remainder"))
-                                                                     (list (js.set! "approximate" (js.- "delta" "approximate"))
-                                                                           (js.set! "approximate_result" approx-result)
-                                                                           (js.set! "approximate_remainder" approx-remainder)))
-                                                          (js.block! (list (js.set! "result" (js.apply int//+ (list "result"
-                                                                                                                    (js.? (=I int//zero "approximate_result")
-                                                                                                                          int//one
-                                                                                                                          "approximate_result"))))
-                                                                           (js.set! "remainder" (js.apply int//- (list "remainder" "approximate_remainder"))))))))
-                                       (js.return! "result")))
-                      )))))
-
-(runtime: nat//% "remN64"
-  (js.function @ (list "subject" "parameter")
-    (list (let [flat (js.apply int//* (list (js.apply nat/// (list "subject" "parameter"))
-                                            "parameter"))]
-            (js.return! (js.apply int//- (list "subject" flat)))))))
-
-(def: runtime//nat
-  Runtime
-  (format __nat//<
-          __nat///
-          __nat//%))
-
 (runtime: deg//* "mulD64"
   (format "(function " @ "(l,r) {"
           "var lL = " int//from-number "(l.L);"
@@ -900,7 +807,6 @@
           runtime//adt
           runtime//bit
           runtime//int
-          runtime//nat
           runtime//deg
           runtime//text
           runtime//array
diff --git a/new-luxc/source/luxc/lang/translation/jvm/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/jvm/procedure/common.jvm.lux
index 3a5cc9b70..05a38eb2f 100644
--- a/new-luxc/source/luxc/lang/translation/jvm/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/jvm/procedure/common.jvm.lux
@@ -267,18 +267,11 @@
 
 (def: deg-method $.Method nat-method)
 
-(def: compare-nat-method
-  $.Method
-  ($t.method (list $t.long $t.long) (#.Some $t.int) (list)))
-
 (do-template [<name> <const> <type>]
   [(def: (<name> _)
      Nullary
      (|>> <const> ($i.wrap <type>)))]
 
-  [nat//min                ($i.long 0)                              #$.Long]
-  [nat//max                ($i.long -1)                             #$.Long]
-
   [int//min                ($i.long Long::MIN_VALUE)                #$.Long]
   [int//max                ($i.long Long::MAX_VALUE)                #$.Long]
   
@@ -307,12 +300,6 @@
   [int//div        #$.Long   $i.LDIV]
   [int//rem        #$.Long   $i.LREM]
   
-  [nat//add        #$.Long   $i.LADD]
-  [nat//sub        #$.Long   $i.LSUB]
-  [nat//mul        #$.Long   $i.LMUL]
-  [nat//div        #$.Long   ($i.INVOKESTATIC hostL.runtime-class "div_nat" nat-method false)]
-  [nat//rem        #$.Long   ($i.INVOKESTATIC hostL.runtime-class "rem_nat" nat-method false)]
-
   [frac//add       #$.Double $i.DADD]
   [frac//sub       #$.Double $i.DSUB]
   [frac//mul       #$.Double $i.DMUL]
@@ -340,10 +327,9 @@
      [<eq>  0]
      [<lt> -1])]
 
-  [nat//eq  nat//lt  ($i.unwrap #$.Long)   ($i.INVOKESTATIC hostL.runtime-class "compare_nat" compare-nat-method false)]
   [int//eq  int//lt  ($i.unwrap #$.Long)   $i.LCMP]
   [frac//eq frac//lt ($i.unwrap #$.Double) $i.DCMPG]
-  [deg//eq  deg//lt  ($i.unwrap #$.Long)   ($i.INVOKESTATIC hostL.runtime-class "compare_nat" compare-nat-method false)]
+  [deg//eq  deg//lt  ($i.unwrap #$.Long)   $i.LCMP]
   )
 
 (do-template [<name> <prepare> <transform>]
@@ -351,12 +337,9 @@
      Unary
      (|>> inputI <prepare> <transform>))]
 
-  [nat//to-int id id]
-  [nat//char ($i.unwrap #$.Long)
-   ((|>> $i.L2I $i.I2C ($i.INVOKESTATIC "java.lang.Character" "toString" ($t.method (list $t.char) (#.Some $String) (list)) false)))]
-  
-  [int//to-nat id id]
   [int//to-frac ($i.unwrap #$.Long) (<| ($i.wrap #$.Double) $i.L2D)]
+  [int//char ($i.unwrap #$.Long)
+   ((|>> $i.L2I $i.I2C ($i.INVOKESTATIC "java.lang.Character" "toString" ($t.method (list $t.char) (#.Some $String) (list)) false)))]
 
   [frac//to-int ($i.unwrap #$.Double) (<| ($i.wrap #$.Long) $i.D2L)]
   [frac//to-deg ($i.unwrap #$.Double)
@@ -623,22 +606,6 @@
           (install "arithmetic-right-shift" (binary bit//arithmetic-right-shift))
           )))
 
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//eq))
-          (install "<" (binary nat//lt))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary nat//to-int))
-          (install "char" (unary nat//char)))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -652,8 +619,8 @@
           (install "<" (binary int//lt))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary int//to-nat))
-          (install "to-frac" (unary int//to-frac)))))
+          (install "to-frac" (unary int//to-frac))
+          (install "char" (unary int//char)))))
 
 (def: deg-procs
   Bundle
@@ -782,7 +749,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/jvm/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/jvm/runtime.jvm.lux
index b394a7f53..58ed736ab 100644
--- a/new-luxc/source/luxc/lang/translation/jvm/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/jvm/runtime.jvm.lux
@@ -167,94 +167,6 @@
   $.Inst
   ($i.INVOKESTATIC hostL.runtime-class "force_text" ($t.method (list $Object) (#.Some $String) (list)) false))
 
-(def: nat-methods
-  $.Def
-  (let [compare-nat-method ($t.method (list $t.long $t.long) (#.Some $t.int) (list))
-        less-thanI (function (_ @where) (|>> ($i.INVOKESTATIC hostL.runtime-class "compare_nat" compare-nat-method false) ($i.IFLT @where)))
-        $BigInteger ($t.class "java.math.BigInteger" (list))
-        upcast-method ($t.method (list $t.long) (#.Some $BigInteger) (list))
-        div-method ($t.method (list $t.long $t.long) (#.Some $t.long) (list))
-        upcastI ($i.INVOKESTATIC hostL.runtime-class "_toUnsignedBigInteger" upcast-method false)
-        downcastI ($i.INVOKEVIRTUAL "java.math.BigInteger" "longValue" ($t.method (list) (#.Some $t.long) (list)) false)]
-    (|>> ($d.method #$.Public $.staticM "_toUnsignedBigInteger" upcast-method
-                    (let [upcastI ($i.INVOKESTATIC "java.math.BigInteger" "valueOf" upcast-method false)
-                          discernI (function (_ @where) (|>> ($i.LLOAD +0) ($i.long 0) $i.LCMP ($i.IFGE @where)))
-                          prepare-upperI (|>> ($i.LLOAD +0) ($i.int 32) $i.LUSHR
-                                              upcastI
-                                              ($i.int 32) ($i.INVOKEVIRTUAL "java.math.BigInteger" "shiftLeft" ($t.method (list $t.int) (#.Some $BigInteger) (list)) false))
-                          prepare-lowerI (|>> ($i.LLOAD +0) ($i.int 32) $i.LSHL
-                                              ($i.int 32)   $i.LUSHR
-                                              upcastI)]
-                      (<| $i.with-label (function (_ @simple))
-                          (|>> (discernI @simple)
-                               ## else
-                               prepare-upperI
-                               prepare-lowerI
-                               ($i.INVOKEVIRTUAL "java.math.BigInteger" "add" ($t.method (list $BigInteger) (#.Some $BigInteger) (list)) false)
-                               $i.ARETURN
-                               ## then
-                               ($i.label @simple)
-                               ($i.LLOAD +0)
-                               upcastI
-                               $i.ARETURN))))
-         ($d.method #$.Public $.staticM "compare_nat" compare-nat-method
-                    (let [shiftI (|>> ($i.GETSTATIC "java.lang.Long" "MIN_VALUE" $t.long) $i.LADD)]
-                      (|>> ($i.LLOAD +0) shiftI
-                           ($i.LLOAD +2) shiftI
-                           $i.LCMP
-                           $i.IRETURN)))
-         ($d.method #$.Public $.staticM "div_nat" div-method
-                    (let [is-param-largeI (function (_ @where) (|>> ($i.LLOAD +2) ($i.long 0) $i.LCMP ($i.IFLT @where)))
-                          is-subject-smallI (function (_ @where) (|>> ($i.LLOAD +0) ($i.long 0) $i.LCMP ($i.IFGT @where)))
-                          small-division (|>> ($i.LLOAD +0) ($i.LLOAD +2) $i.LDIV $i.LRETURN)
-                          big-divisionI ($i.INVOKEVIRTUAL "java.math.BigInteger" "divide" ($t.method (list $BigInteger) (#.Some $BigInteger) (list)) false)]
-                      (<| $i.with-label (function (_ @is-zero))
-                          $i.with-label (function (_ @param-is-large))
-                          $i.with-label (function (_ @subject-is-small))
-                          (|>> (is-param-largeI @param-is-large)
-                               ## Param is not too large
-                               (is-subject-smallI @subject-is-small)
-                               ## Param is small, but subject is large
-                               ($i.LLOAD +0) upcastI
-                               ($i.LLOAD +2) upcastI
-                               big-divisionI downcastI $i.LRETURN
-                               ## Both param and subject are small,
-                               ## and can thus be divided normally.
-                               ($i.label @subject-is-small)
-                               small-division
-                               ## Param is too large. Cannot simply divide.
-                               ## Depending on the result of the
-                               ## comparison, a result will be determined.
-                               ($i.label @param-is-large)
-                               ($i.LLOAD +0) ($i.LLOAD +2) (less-thanI @is-zero)
-                               ## Greater-than or equals
-                               ($i.long 1) $i.LRETURN
-                               ## Less than
-                               ($i.label @is-zero)
-                               ($i.long 0) $i.LRETURN))))
-         ($d.method #$.Public $.staticM "rem_nat" div-method
-                    (let [is-subject-largeI (function (_ @where) (|>> ($i.LLOAD +0) ($i.long 0) $i.LCMP ($i.IFLE @where)))
-                          is-param-largeI (function (_ @where) (|>> ($i.LLOAD +2) ($i.long 0) $i.LCMP ($i.IFLE @where)))
-                          small-remainderI (|>> ($i.LLOAD +0) ($i.LLOAD +2) $i.LREM $i.LRETURN)
-                          big-remainderI ($i.INVOKEVIRTUAL "java.math.BigInteger" "remainder" ($t.method (list $BigInteger) (#.Some $BigInteger) (list)) false)]
-                      (<| $i.with-label (function (_ @large-number))
-                          $i.with-label (function (_ @subject-is-smaller-than-param))
-                          (|>> (is-subject-largeI @large-number)
-                               (is-param-largeI @large-number)
-                               small-remainderI
-
-                               ($i.label @large-number)
-                               ($i.LLOAD +0) ($i.LLOAD +2) (less-thanI @subject-is-smaller-than-param)
-                               
-                               ($i.LLOAD +0) upcastI
-                               ($i.LLOAD +2) upcastI
-                               big-remainderI downcastI $i.LRETURN
-                               
-                               ($i.label @subject-is-smaller-than-param)
-                               ($i.LLOAD +0)
-                               $i.LRETURN))))
-         )))
-
 (def: frac-shiftI $.Inst ($i.double (math.pow 32.0 2.0)))
 
 (def: frac-methods
@@ -620,7 +532,6 @@
     [_ (wrap [])
      #let [bytecode ($d.class #$.V1_6 #$.Public $.finalC hostL.runtime-class (list) ["java.lang.Object" (list)] (list)
                               (|>> adt-methods
-                                   nat-methods
                                    frac-methods
                                    deg-methods
                                    text-methods
diff --git a/new-luxc/source/luxc/lang/translation/lua/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/lua/procedure/common.jvm.lux
index bdba05a9d..a9849b557 100644
--- a/new-luxc/source/luxc/lang/translation/lua/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/lua/procedure/common.jvm.lux
@@ -197,9 +197,6 @@
      Nullary
      (<encode> <const>))]
 
-  [nat//min                 0                           lua.int]
-  [nat//max                -1                           lua.int]
-
   [frac//smallest          Double::MIN_VALUE            lua.float]
   [frac//min               (f/* -1.0 Double::MAX_VALUE) lua.float]
   [frac//max               Double::MAX_VALUE            lua.float]
@@ -238,12 +235,6 @@
   [int//div        lua.//]
   [int//rem        lua.%]
   
-  [nat//add        lua.+]
-  [nat//sub        lua.-]
-  [nat//mul        lua.*]
-  [nat//div        runtimeT.nat///]
-  [nat//rem        runtimeT.nat//%]
-
   [deg//add        lua.+]
   [deg//sub        lua.-]
   [deg//mul        runtimeT.deg//*]
@@ -275,21 +266,10 @@
      Binary
      (<cmp> paramO subjectO))]
 
-  [nat//= lua.=]
-  [nat//< runtimeT.nat//<]
   [int//= lua.=]
   [int//< lua.<]
   [deg//= lua.=]
-  [deg//< runtimeT.nat//<]
-  )
-
-(do-template [<name>]
-  [(def: (<name> inputO)
-     Unary
-     inputO)]
-
-  [nat//to-int]
-  [int//to-nat]
+  [deg//< lua.<]
   )
 
 (def: frac//encode
@@ -320,7 +300,7 @@
   [text//hash   runtimeT.text//hash]
   )
 
-(def: nat//char
+(def: int//char
   Unary
   (|>> (list) (lua.apply "string.char")))
 
@@ -466,22 +446,6 @@
           (install "arithmetic-right-shift" (binary bit//arithmetic-right-shift))
           )))
 
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//=))
-          (install "<" (binary nat//<))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary nat//to-int))
-          (install "char" (unary nat//char)))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -495,8 +459,8 @@
           (install "<" (binary int//<))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary int//to-nat))
-          (install "to-frac" (unary int//to-frac)))))
+          (install "to-frac" (unary int//to-frac))
+          (install "char" (unary int//char)))))
 
 (def: deg-procs
   Bundle
@@ -620,7 +584,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/lua/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/lua/runtime.jvm.lux
index 64253b1c3..cd5d0c090 100644
--- a/new-luxc/source/luxc/lang/translation/lua/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/lua/runtime.jvm.lux
@@ -197,36 +197,6 @@
   (format @@bit//count
           @@bit//logical-right-shift))
 
-(runtime: (nat//< param subject)
-  (lua.return! (lua.apply "math.ult" (list subject param))))
-
-(runtime: (nat/// param subject)
-  (lua.if! (lua.< (lua.int 0) param)
-           (lua.if! (nat//< param subject)
-                    (lua.return! (lua.int 0))
-                    (lua.return! (lua.int 1)))
-           (lua.block! (list (lua.local! "quotient" (#.Some (|> subject
-                                                                (lua.bit-shr (lua.int 1))
-                                                                (lua.// param)
-                                                                (lua.bit-shl (lua.int 1)))))
-                             (lua.local! "remainder" (#.Some (lua.- (lua.* param "quotient")
-                                                                    subject)))
-                             (lua.if! (lua.not (nat//< param "remainder"))
-                                      (lua.return! (lua.+ (lua.int 1) "quotient"))
-                                      (lua.return! "quotient"))))))
-
-(runtime: (nat//% param subject)
-  (let [flat (|> subject
-                 (nat/// param)
-                 (lua.* param))]
-    (lua.return! (lua.- flat subject))))
-
-(def: runtime//nat
-  Runtime
-  (format @@nat//<
-          @@nat///
-          @@nat//%))
-
 (runtime: deg//low-mask
   (|> (lua.int 1)
       (lua.bit-shl (lua.int 32))
@@ -477,7 +447,6 @@
   (format runtime//lux
           runtime//adt
           runtime//bit
-          runtime//nat
           runtime//deg
           runtime//text
           runtime//array
diff --git a/new-luxc/source/luxc/lang/translation/python/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/python/procedure/common.jvm.lux
index c201c417c..69b4aede4 100644
--- a/new-luxc/source/luxc/lang/translation/python/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/python/procedure/common.jvm.lux
@@ -228,9 +228,6 @@
      Nullary
      (<encode> <const>))]
 
-  [nat//min                 0                           python.int]
-  [nat//max                -1                           python.int]
-
   [frac//smallest          Double::MIN_VALUE            python.float]
   [frac//min               (f/* -1.0 Double::MAX_VALUE) python.float]
   [frac//max               Double::MAX_VALUE            python.float]
@@ -269,10 +266,6 @@
   [int//sub        python.-]
   [int//mul        python.*]
 
-  [nat//add        python.+]
-  [nat//sub        python.-]
-  [nat//mul        python.*]
-
   [deg//add        python.+]
   [deg//sub        python.-]
   [deg//rem        python.-]
@@ -288,9 +281,6 @@
   [int//div        python./]
   [int//rem        python.%]
   
-  [nat//div        runtimeT.nat///]
-  [nat//rem        runtimeT.nat//%]
-
   [deg//mul        runtimeT.deg//*]
   [deg//div        runtimeT.deg///]
   [deg//reciprocal python./]
@@ -318,14 +308,11 @@
      Binary
      (<cmp> paramO subjectO))]
 
-  [nat//= python.=]
-  [nat//< runtimeT.nat//<]
-
   [int//= python.=]
   [int//< python.<]
 
   [deg//= python.=]
-  [deg//< runtimeT.nat//<]
+  [deg//< python.<]
   )
 
 (def: (apply1 func)
@@ -347,22 +334,6 @@
                               (python.global "float"))]
   )
 
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//=))
-          (install "<" (binary nat//<))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary id))
-          (install "char" (unary (apply1 (python.global "chr")))))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -376,8 +347,8 @@
           (install "<" (binary int//<))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary id))
-          (install "to-frac" (unary (apply1 (python.global "float")))))))
+          (install "to-frac" (unary (apply1 (python.global "float"))))
+          (install "char" (unary (apply1 (python.global "chr")))))))
 
 (def: deg-procs
   Bundle
@@ -558,7 +529,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/python/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/python/runtime.jvm.lux
index 65e864d91..3457cc49b 100644
--- a/new-luxc/source/luxc/lang/translation/python/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/python/runtime.jvm.lux
@@ -285,45 +285,6 @@
 (def: high (-> Expression Expression) (bit//logical-right-shift (python.int 32)))
 (def: low  (-> Expression Expression) (python.bit-and full-32-bits))
 
-(runtime: (nat//< param subject)
-  (with-vars [ph sh]
-    ($_ python.then!
-        (python.set! (list ph) (..high param))
-        (python.set! (list sh) (..high subject))
-        (python.return! (python.or (python.< (@@ ph) (@@ sh))
-                                   (python.and (python.= (@@ ph) (@@ sh))
-                                               (python.< (low param) (low subject))))))))
-
-(runtime: (nat/// param subject)
-  (with-vars [quotient remainder]
-    (python.if! (python.< (python.int 0) param)
-                (python.if! (nat//< param subject)
-                            (python.return! (python.int 0))
-                            (python.return! (python.int 1)))
-                ($_ python.then!
-                    (python.set! (list quotient) (|> subject
-                                                     (python.bit-shr (python.int 1))
-                                                     (python./ param)
-                                                     (python.bit-shl (python.int 1))))
-                    (let [remainder (python.- (python.* param (@@ quotient))
-                                              subject)]
-                      (python.if! (python.not (nat//< param remainder))
-                                  (python.return! (python.+ (python.int 1) (@@ quotient)))
-                                  (python.return! (@@ quotient))))))))
-
-(runtime: (nat//% param subject)
-  (let [flat (|> subject
-                 (nat/// param)
-                 (python.* param))]
-    (python.return! (|> subject (python.- flat)))))
-
-(def: runtime//nat
-  Runtime
-  ($_ python.then!
-      @@nat//<
-      @@nat///
-      @@nat//%))
-
 (runtime: (deg//* param subject)
   (with-vars [$sL $sH $pL $pH $bottom $middle $top]
     ($_ python.then!
@@ -561,7 +522,6 @@
       runtime//lux
       runtime//adt
       runtime//bit
-      runtime//nat
       runtime//deg
       runtime//frac
       runtime//text
diff --git a/new-luxc/source/luxc/lang/translation/r/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/r/procedure/common.jvm.lux
index a9e661130..9554abc86 100644
--- a/new-luxc/source/luxc/lang/translation/r/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/r/procedure/common.jvm.lux
@@ -229,9 +229,6 @@
      Nullary
      <expression>)]
 
-  [nat//min runtimeT.int//zero]
-  [nat//max runtimeT.int//-one]
-
   [int//min runtimeT.int//min]
   [int//max runtimeT.int//max]
 
@@ -260,12 +257,6 @@
   [int//div        runtimeT.int///]
   [int//rem        runtimeT.int//%]
 
-  [nat//add        runtimeT.int//+]
-  [nat//sub        runtimeT.int//-]
-  [nat//mul        runtimeT.int//*]
-  [nat//div        runtimeT.nat///]
-  [nat//rem        runtimeT.nat//%]
-
   [deg//add        runtimeT.int//+]
   [deg//sub        runtimeT.int//-]
   [deg//rem        runtimeT.int//-]
@@ -297,14 +288,11 @@
      Binary
      (<cmp> paramO subjectO))]
 
-  [nat//= runtimeT.int//=]
-  [nat//< runtimeT.nat//<]
-
   [int//= runtimeT.int//=]
   [int//< runtimeT.int//<]
 
   [deg//= runtimeT.int//=]
-  [deg//< runtimeT.nat//<]
+  [deg//< runtimeT.int//<]
   )
 
 (def: (apply1 func)
@@ -312,23 +300,7 @@
   (function (_ value)
     (r.apply (list value) func)))
 
-(def: nat//char (|>> runtimeT.int64-low (apply1 (r.global "intToUtf8"))))
-
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//=))
-          (install "<" (binary nat//<))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary id))
-          (install "char" (unary nat//char)))))
+(def: int//char (|>> runtimeT.int64-low (apply1 (r.global "intToUtf8"))))
 
 (def: int-procs
   Bundle
@@ -343,8 +315,8 @@
           (install "<" (binary int//<))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary id))
-          (install "to-frac" (unary runtimeT.int//to-float)))))
+          (install "to-frac" (unary runtimeT.int//to-float))
+          (install "char" (unary int//char)))))
 
 (def: deg-procs
   Bundle
@@ -544,7 +516,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/r/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/r/runtime.jvm.lux
index 88b40bcca..70a9f62df 100644
--- a/new-luxc/source/luxc/lang/translation/r/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/r/runtime.jvm.lux
@@ -664,83 +664,6 @@
       @@bit//logical-right-shift
       ))
 
-(runtime: (nat//< param subject)
-  (with-vars [pH sH]
-    ($_ r.then
-        (r.set! pH (..int64-high (@@ param)))
-        (r.set! sH (..int64-high (@@ subject)))
-        (let [lesser-high? (|> (@@ sH) (r.< (@@ pH)))
-              equal-high? (|> (@@ sH) (r.= (@@ pH)))
-              lesser-low? (|> (..int64-low (@@ subject)) (r.< (..int64-low (@@ param))))]
-          (|> lesser-high?
-              (r.or (|> equal-high?
-                        (r.and lesser-low?))))))))
-
-(runtime: (nat/// parameter subject)
-  (let [negative? (int//< int//zero)
-        valid-division-check [(|> (@@ parameter) (int//= int//zero))
-                              (r.stop (r.string "Cannot divide by zero!"))]
-        short-circuit-check [(|> (@@ subject) (nat//< (@@ parameter)))
-                             int//zero]]
-    (r.cond (list valid-division-check
-                  short-circuit-check
-
-                  [(|> (@@ parameter)
-                       (nat//< (|> (@@ subject) (bit//logical-right-shift (r.int 1)))))
-                   int//one])
-            (with-vars [result remainder approximate log2 approximate-result approximate-remainder delta]
-              ($_ r.then
-                  (r.set! result int//zero)
-                  (r.set! remainder (@@ subject))
-                  (r.while (|> (|> (@@ remainder) (nat//< (@@ parameter)))
-                               (r.or (|> (@@ remainder) (int//= (@@ parameter)))))
-                           (let [rough-estimate (r.apply (list (|> (int//to-float (@@ parameter)) (r./ (int//to-float (@@ remainder)))))
-                                                         (r.global "floor"))
-                                 calculate-approximate-result (int//from-float (@@ approximate))
-                                 calculate-approximate-remainder (int//* (@@ parameter) (@@ approximate-result))
-                                 delta (r.if (|> (r.float 48.0) (r.<= (@@ log2)))
-                                         (r.float 1.0)
-                                         (r.** (|> (r.float 48.0) (r.- (@@ log2)))
-                                               (r.float 2.0)))
-                                 update-approximates! ($_ r.then
-                                                          (r.set! approximate-result calculate-approximate-result)
-                                                          (r.set! approximate-remainder calculate-approximate-remainder))]
-                             ($_ r.then
-                                 (r.set! approximate (r.apply (list (r.float 1.0) rough-estimate)
-                                                              (r.global "max")))
-                                 (r.set! log2 (let [log (function (_ input)
-                                                          (r.apply (list input) (r.global "log")))]
-                                                (r.apply (list (|> (log (r.int 2))
-                                                                   (r./ (log (@@ approximate)))))
-                                                         (r.global "ceil"))))
-                                 update-approximates!
-                                 (r.while (|> (negative? (@@ approximate-remainder))
-                                              (r.or (|> (@@ approximate-remainder) (int//< (@@ remainder)))))
-                                          ($_ r.then
-                                              (r.set! approximate (|> delta (r.- (@@ approximate))))
-                                              update-approximates!))
-                                 ($_ r.then
-                                     (r.set! result (|> (@@ result)
-                                                        (int//+ (r.if (|> (@@ approximate-result) (int//= int//zero))
-                                                                  int//one
-                                                                  (@@ approximate-result)))))
-                                     (r.set! remainder (|> (@@ remainder) (int//- (@@ approximate-remainder))))))))
-                  (@@ result)))
-            )))
-
-(runtime: (nat//% param subject)
-  (let [flat (|> (@@ subject)
-                 (nat/// (@@ param))
-                 (int//* (@@ param)))]
-    (|> (@@ subject) (int//- flat))))
-
-(def: runtime//nat
-  Runtime
-  ($_ r.then
-      @@nat//<
-      @@nat///
-      @@nat//%))
-
 (runtime: (deg//* param subject)
   (with-vars [sL sH pL pH bottom middle top]
     ($_ r.then
@@ -1035,7 +958,6 @@
       runtime//bit
       runtime//int
       runtime//adt
-      runtime//nat
       runtime//deg
       runtime//frac
       runtime//text
diff --git a/new-luxc/source/luxc/lang/translation/ruby/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/ruby/procedure/common.jvm.lux
index a13dae50b..e38dfff28 100644
--- a/new-luxc/source/luxc/lang/translation/ruby/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/ruby/procedure/common.jvm.lux
@@ -233,9 +233,6 @@
      Nullary
      (<encode> <const>))]
 
-  [nat//min                 0                           ruby.int]
-  [nat//max                -1                           ruby.int]
-
   [frac//smallest          Double::MIN_VALUE            ruby.float]
   [frac//min               (f/* -1.0 Double::MAX_VALUE) ruby.float]
   [frac//max               Double::MAX_VALUE            ruby.float]
@@ -282,12 +279,6 @@
   [int//div        ruby./]
   [int//rem        ruby.%]
   
-  [nat//add        ruby.+]
-  [nat//sub        ruby.-]
-  [nat//mul        ruby.*]
-  [nat//div        runtimeT.nat///]
-  [nat//rem        runtimeT.nat//%]
-
   [deg//add        ruby.+]
   [deg//sub        ruby.-]
   [deg//mul        runtimeT.deg//*]
@@ -319,21 +310,10 @@
      Binary
      (<cmp> paramO subjectO))]
 
-  [nat//= ruby.=]
-  [nat//< runtimeT.nat//<]
   [int//= ruby.=]
   [int//< ruby.<]
   [deg//= ruby.=]
-  [deg//< runtimeT.nat//<])
-
-(do-template [<name>]
-  [(def: (<name> inputO)
-     Unary
-     inputO)]
-
-  [nat//to-int]
-  [int//to-nat]
-  )
+  [deg//< ruby.<])
 
 (def: frac//encode
   Unary
@@ -370,26 +350,6 @@
   [frac//to-deg runtimeT.deg//from-frac]
   )
 
-(def: nat//char
-  Unary
-  (ruby.send "chr" (list)))
-
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//=))
-          (install "<" (binary nat//<))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary nat//to-int))
-          (install "char" (unary nat//char)))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -403,8 +363,8 @@
           (install "<" (binary int//<))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary int//to-nat))
-          (install "to-frac" (unary int//to-frac)))))
+          (install "to-frac" (unary int//to-frac))
+          (install "char" (unary (ruby.send "chr" (list)))))))
 
 (def: deg-procs
   Bundle
@@ -647,7 +607,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/ruby/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/ruby/runtime.jvm.lux
index c3f2981e1..7f66b0cd5 100644
--- a/new-luxc/source/luxc/lang/translation/ruby/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/ruby/runtime.jvm.lux
@@ -181,40 +181,6 @@
 (def: high (-> Expression Expression) (bit//logical-right-shift (ruby.int 32)))
 (def: low  (-> Expression Expression) (ruby.bit-and "0xFFFFFFFF"))
 
-(runtime: (nat//< param subject)
-  (ruby.block! (list (ruby.set! (list "ph") (high param))
-                     (ruby.set! (list "sh") (high subject))
-                     (ruby.return! (ruby.or (ruby.< "ph" "sh")
-                                            (ruby.and (ruby.= "ph" "sh")
-                                                      (ruby.< (low param) (low subject))))))))
-
-(runtime: (nat/// param subject)
-  (ruby.if! (ruby.< (ruby.int 0) param)
-            (ruby.if! (nat//< param subject)
-                      (ruby.return! (ruby.int 0))
-                      (ruby.return! (ruby.int 1)))
-            (ruby.block! (list (ruby.set! (list "quotient") (|> subject
-                                                                (ruby.bit-shr (ruby.int 1))
-                                                                (ruby./ param)
-                                                                (ruby.bit-shl (ruby.int 1))))
-                               (ruby.set! (list "remainder") (ruby.- (ruby.* param "quotient")
-                                                                     subject))
-                               (ruby.if! (ruby.not (nat//< param "remainder"))
-                                         (ruby.return! (ruby.+ (ruby.int 1) "quotient"))
-                                         (ruby.return! "quotient"))))))
-
-(runtime: (nat//% param subject)
-  (let [flat (|> subject
-                 (nat/// param)
-                 (ruby.* param))]
-    (ruby.return! (ruby.- flat subject))))
-
-(def: runtime//nat
-  Runtime
-  (format @@nat//<
-          @@nat///
-          @@nat//%))
-
 (runtime: (deg//* param subject)
   (ruby.block! (list (ruby.set! (list "sL") (low subject))
                      (ruby.set! (list "sH") (high subject))
@@ -366,7 +332,6 @@
   (format runtime//lux "\n"
           runtime//adt "\n"
           runtime//bit "\n"
-          runtime//nat "\n"
           runtime//deg "\n"
           runtime//text "\n"
           runtime//array "\n"
diff --git a/new-luxc/source/luxc/lang/translation/scheme/procedure/common.jvm.lux b/new-luxc/source/luxc/lang/translation/scheme/procedure/common.jvm.lux
index cd828e082..67ec0e95c 100644
--- a/new-luxc/source/luxc/lang/translation/scheme/procedure/common.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/scheme/procedure/common.jvm.lux
@@ -235,9 +235,6 @@
      Nullary
      (_.int <expression>))]
 
-  [nat//min 0]
-  [nat//max -1]
-
   [int//min ("lux int min")]
   [int//max ("lux int max")]
 
@@ -266,12 +263,6 @@
   [int//div        _.quotient]
   [int//rem        _.remainder]
 
-  [nat//add        _.+]
-  [nat//sub        _.-]
-  [nat//mul        _.*]
-  [nat//div        runtimeT.nat///]
-  [nat//rem        runtimeT.nat//%]
-
   [deg//add        _.+]
   [deg//sub        _.-]
   [deg//rem        _.-]
@@ -303,14 +294,11 @@
      Binary
      (<cmp> paramO subjectO))]
 
-  [nat//= _.=]
-  [nat//< runtimeT.nat//<]
-
   [int//= _.=]
   [int//< _.<]
 
   [deg//= _.=]
-  [deg//< runtimeT.nat//<]
+  [deg//< _.<]
   )
 
 (def: deg//to-frac
@@ -321,25 +309,9 @@
          (_./ f2^32)
          (_./ (_.float 1.0)))))
 
-(def: nat//char (|>> (_.apply1 (_.global "integer->char"))
+(def: int//char (|>> (_.apply1 (_.global "integer->char"))
                      (_.apply1 (_.global "string"))))
 
-(def: nat-procs
-  Bundle
-  (<| (prefix "nat")
-      (|> (dict.new text.Hash<Text>)
-          (install "+" (binary nat//add))
-          (install "-" (binary nat//sub))
-          (install "*" (binary nat//mul))
-          (install "/" (binary nat//div))
-          (install "%" (binary nat//rem))
-          (install "=" (binary nat//=))
-          (install "<" (binary nat//<))
-          (install "min" (nullary nat//min))
-          (install "max" (nullary nat//max))
-          (install "to-int" (unary id))
-          (install "char" (unary nat//char)))))
-
 (def: int-procs
   Bundle
   (<| (prefix "int")
@@ -353,8 +325,8 @@
           (install "<" (binary int//<))
           (install "min" (nullary int//min))
           (install "max" (nullary int//max))
-          (install "to-nat" (unary id))
-          (install "to-frac" (unary (|>> (_./ (_.float 1.0))))))))
+          (install "to-frac" (unary (|>> (_./ (_.float 1.0)))))
+          (install "char" (unary int//char)))))
 
 (def: deg-procs
   Bundle
@@ -519,7 +491,6 @@
   (<| (prefix "lux")
       (|> lux-procs
           (dict.merge bit-procs)
-          (dict.merge nat-procs)
           (dict.merge int-procs)
           (dict.merge deg-procs)
           (dict.merge frac-procs)
diff --git a/new-luxc/source/luxc/lang/translation/scheme/runtime.jvm.lux b/new-luxc/source/luxc/lang/translation/scheme/runtime.jvm.lux
index 09259c2b9..e8016eb0a 100644
--- a/new-luxc/source/luxc/lang/translation/scheme/runtime.jvm.lux
+++ b/new-luxc/source/luxc/lang/translation/scheme/runtime.jvm.lux
@@ -239,43 +239,6 @@
 (def: int-high (bit//logical-right-shift (_.int 32)))
 (def: int-low (_.bit-and (_.int (hex "FFFFFFFF"))))
 
-(runtime: (nat//< param subject)
-  (with-vars [pH sH]
-    (_.let (list [pH (int-high (@@ param))]
-                 [sH (int-high (@@ subject))])
-      (_.or (list (_.< (@@ pH) (@@ sH))
-                  (_.and (list (_.= (@@ pH) (@@ sH))
-                               (_.< (int-low (@@ param)) (int-low (@@ subject))))))))))
-
-(runtime: (nat/// param subject)
-  (_.if (_.< (_.int 0) (@@ param))
-    (_.if (nat//< (@@ param) (@@ subject))
-      (_.int 0)
-      (_.int 1))
-    (with-vars [quotient]
-      (_.let (list [quotient (|> (@@ subject)
-                                 (bit//logical-right-shift (_.int 1))
-                                 (_.quotient (@@ param))
-                                 (_.arithmetic-shift (_.int 1)))])
-        (let [remainder (_.- (_.* (@@ param) (@@ quotient))
-                             (@@ subject))]
-          (_.if (_.not (nat//< (@@ param) remainder))
-            (_.+ (_.int 1) (@@ quotient))
-            (@@ quotient)))))))
-
-(runtime: (nat//% param subject)
-  (let [flat (|> (@@ subject)
-                 (nat/// (@@ param))
-                 (_.* (@@ param)))]
-    (|> (@@ subject) (_.- flat))))
-
-(def: runtime//nat
-  Runtime
-  (_.begin
-   (list @@nat//<
-         @@nat///
-         @@nat//%)))
-
 (runtime: (frac//to-deg input)
   (with-vars [two32 shifted]
     (_.let* (list [two32 (|> (_.float 2.0) (_.expt (_.float 32.0)))]
@@ -405,7 +368,6 @@
                  runtime//lux
                  runtime//bit
                  runtime//adt
-                 runtime//nat
                  runtime//frac
                  ## runtime//text
                  runtime//array