From 06246a89bb33b58a6e03183f59a2fea88179a861 Mon Sep 17 00:00:00 2001
From: Eduardo Julian
Date: Sat, 28 Jan 2017 22:22:30 -0400
Subject: - Added support for fuzzy logic.

---
 stdlib/source/lux/math/logic/fuzzy.lux    | 150 +++++++++++++++++++++++++
 stdlib/test/test/lux/math/logic/fuzzy.lux | 175 ++++++++++++++++++++++++++++++
 stdlib/test/tests.lux                     |   3 +-
 3 files changed, 327 insertions(+), 1 deletion(-)
 create mode 100644 stdlib/source/lux/math/logic/fuzzy.lux
 create mode 100644 stdlib/test/test/lux/math/logic/fuzzy.lux

diff --git a/stdlib/source/lux/math/logic/fuzzy.lux b/stdlib/source/lux/math/logic/fuzzy.lux
new file mode 100644
index 000000000..12d8b9dc3
--- /dev/null
+++ b/stdlib/source/lux/math/logic/fuzzy.lux
@@ -0,0 +1,150 @@
+(;module:
+  lux
+  (lux (data [number "Deg/" Interval<Deg>]
+             (coll [list]
+                   [set])
+             text/format)
+       [math])
+  (.. ["&" continuous]))
+
+(type: #export (Fuzzy a)
+  (-> a Deg))
+
+(def: #export (membership elem set)
+  (All [a] (-> a (Fuzzy a) Deg))
+  (set elem))
+
+(def: #export (union left right)
+  (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
+  (lambda [elem]
+    (&;~or (membership elem left)
+           (membership elem right))))
+
+(def: #export (intersection left right)
+  (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
+  (lambda [elem]
+    (&;~and (membership elem left)
+            (membership elem right))))
+
+(def: #export (complement set)
+  (All [a] (-> (Fuzzy a) (Fuzzy a)))
+  (lambda [elem]
+    (&;~not (membership elem set))))
+
+(def: #export (difference sub base)
+  (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
+  (lambda [elem]
+    (&;~and (membership elem base)
+            (&;~not (membership elem sub)))))
+
+(def: #export (from-predicate predicate)
+  (All [a] (-> (-> a Bool) (Fuzzy a)))
+  (lambda [elem]
+    (if (predicate elem)
+      &;~true
+      &;~false)))
+
+(def: #export (from-set set)
+  (All [a] (-> (set;Set a) (Fuzzy a)))
+  (from-predicate (set;member? set)))
+
+(do-template [<ascending> <descending> <gradient> <type> <lt> <gt> <lte> <gte> <sub> <div> <post>]
+  [(def: (<ascending> from to)
+     (-> <type> <type> (Fuzzy <type>))
+     (lambda [elem]
+       (cond (<lte> from elem)
+             &;~false
+
+             (<gte> to elem)
+             &;~true
+
+             ## in the middle...
+             (<post> (<div> (<sub> from to)
+                            (<sub> from elem))))))
+
+   (def: (<descending> from to)
+     (-> <type> <type> (Fuzzy <type>))
+     (lambda [elem]
+       (cond (<lte> from elem)
+             &;~true
+
+             (<gte> to elem)
+             &;~false
+
+             ## in the middle...
+             (<post> (<div> (<sub> from to)
+                            (<sub> elem to))))))
+
+   (def: #export (<gradient> from to)
+     (-> <type> <type> (Fuzzy <type>))
+     (if (<lt> to from)
+       (<ascending> from to)
+       (<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]
+  )
+
+(do-template [<triangle> <trapezoid> <type> <ascending> <descending> <lt>]
+  [(def: #export (<triangle> bottom middle top)
+     (-> <type> <type> <type> (Fuzzy <type>))
+     (case (list;sort <lt> (list bottom middle top))
+       (^ (list bottom middle top))
+       (intersection (<ascending> bottom middle)
+                     (<descending> middle top))
+
+       _
+       (undefined)))
+
+   (def: #export (<trapezoid> bottom middle-bottom middle-top top)
+     (-> <type> <type> <type> <type> (Fuzzy <type>))
+     (case (list;sort <lt> (list bottom middle-bottom middle-top top))
+       (^ (list bottom middle-bottom middle-top top))
+       (intersection (<ascending> bottom middle-bottom)
+                     (<descending> middle-top top))
+
+       _
+       (undefined)))]
+
+  [d.triangle d.trapezoid Deg  d.ascending d.descending d.<]
+  [r.triangle r.trapezoid Real r.ascending r.descending r.<]
+  )
+
+(def: #export (gaussian deviation center)
+  (-> Real Real (Fuzzy Real))
+  (lambda [elem]
+    (let [scale (|> deviation math;square (r.* 2.0))
+          membership (|> elem
+                         (r.- center)
+                         math;square
+                         (r.* -1.0)
+                         (r./ scale)
+                         math;exp)]
+      (if (r.= 1.0 membership)
+        &;~true
+        (real-to-deg membership)))))
+
+(def: #export (cut treshold set)
+  (All [a] (-> Deg (Fuzzy a) (Fuzzy a)))
+  (lambda [elem]
+    (let [membership (set elem)]
+      (if (d.> treshold membership)
+        (|> membership (d.- treshold) (d.* &;~true))
+        &;~false))))
+
+(def: #export (to-predicate treshold set)
+  (All [a] (-> Deg (Fuzzy a) (-> a Bool)))
+  (lambda [elem]
+    (d.> treshold (set elem))))
+
+(type: #export (Fuzzy2 a)
+  (-> a [Deg Deg]))
+
+(def: #export (type-2 lower upper)
+  (All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy2 a)))
+  (lambda [elem]
+    (let [l-deg (lower elem)
+          u-deg (upper elem)]
+      [(d.min l-deg
+              u-deg)
+       u-deg])))
diff --git a/stdlib/test/test/lux/math/logic/fuzzy.lux b/stdlib/test/test/lux/math/logic/fuzzy.lux
new file mode 100644
index 000000000..5b25ecf44
--- /dev/null
+++ b/stdlib/test/test/lux/math/logic/fuzzy.lux
@@ -0,0 +1,175 @@
+(;module:
+  lux
+  (lux [io]
+       (control monad)
+       (codata function)
+       (data (coll [list]
+                   [set])
+             [bool "B/" Eq<Bool>]
+             [number]
+             text/format)
+       ["R" random]
+       pipe
+       (math/logic ["&" fuzzy]
+                   continuous))
+  lux/test)
+
+(do-template [<desc> <gen> <triangle> <lt> <lte> <gt> <gte>]
+  [(test: (format "[" <desc> "] " "Triangles")
+     [x <gen>
+      y <gen>
+      z <gen>
+      sample <gen>
+      #let [[bottom middle top] (case (list;sort <lt> (list x y z))
+                                  (^ (list bottom middle top))
+                                  [bottom middle top]
+
+                                  _
+                                  (undefined))
+            triangle (<triangle> x y z)]]
+     ($_ seq
+         (assert "The middle value will always have maximum membership."
+                 (d.= ~true (&;membership middle triangle)))
+         
+         (assert "Boundary values will always have 0 membership."
+                 (and (d.= ~false (&;membership bottom triangle))
+                      (d.= ~false (&;membership top triangle))))
+
+         (assert "Values within range, will have membership > 0."
+                 (B/= (d.> ~false (&;membership sample triangle))
+                      (and (<gt> bottom sample)
+                           (<lt> top sample))))
+
+         (assert "Values outside of range, will have membership = 0."
+                 (B/= (d.= ~false (&;membership sample triangle))
+                      (or (<lte> bottom sample)
+                          (<gte> top sample))))
+         ))]
+
+  ["Real" R;real &;r.triangle r.< r.<= r.> r.>=]
+  ["Deg"  R;deg  &;d.triangle d.< d.<= d.> d.>=]
+  )
+
+(do-template [<desc> <gen> <trapezoid> <lt> <lte> <gt> <gte>]
+  [(test: (format "[" <desc> "] " "Trapezoids")
+     [w <gen>
+      x <gen>
+      y <gen>
+      z <gen>
+      sample <gen>
+      #let [[bottom middle-bottom middle-top top] (case (list;sort <lt> (list w x y z))
+                                                    (^ (list bottom middle-bottom middle-top top))
+                                                    [bottom middle-bottom middle-top top]
+
+                                                    _
+                                                    (undefined))
+            trapezoid (<trapezoid> w x y z)]]
+     ($_ seq
+         (assert "The middle values will always have maximum membership."
+                 (and (d.= ~true (&;membership middle-bottom trapezoid))
+                      (d.= ~true (&;membership middle-top trapezoid))))
+         
+         (assert "Boundary values will always have 0 membership."
+                 (and (d.= ~false (&;membership bottom trapezoid))
+                      (d.= ~false (&;membership top trapezoid))))
+
+         (assert "Values within inner range will have membership = 1"
+                 (B/= (d.= ~true (&;membership sample trapezoid))
+                      (and (<gte> middle-bottom sample)
+                           (<lte> middle-top sample))))
+
+         (assert "Values within range, will have membership > 0."
+                 (B/= (d.> ~false (&;membership sample trapezoid))
+                      (and (<gt> bottom sample)
+                           (<lt> top sample))))
+
+         (assert "Values outside of range, will have membership = 0."
+                 (B/= (d.= ~false (&;membership sample trapezoid))
+                      (or (<lte> bottom sample)
+                          (<gte> top sample))))
+         ))]
+
+  ["Real" R;real &;r.trapezoid r.< r.<= r.> r.>=]
+  ["Deg"  R;deg  &;d.trapezoid d.< d.<= d.> d.>=]
+  )
+
+(test: "Gaussian"
+  #seed +1485654865687
+  [deviation R;real
+   center R;real
+   #let [gaussian (&;gaussian deviation center)]]
+  ($_ seq
+      (assert "The center value will always have maximum membership."
+              (d.= ~true (&;membership center gaussian)))
+      ))
+
+(def: gen-triangle
+  (R;Random (&;Fuzzy Real))
+  (do R;Monad<Random>
+    [x R;real
+     y R;real
+     z R;real]
+    (wrap (&;r.triangle x y z))))
+
+(test: "Combinators"
+  [left gen-triangle
+   right gen-triangle
+   sample R;real]
+  ($_ seq
+      (assert "Union membership as as high as membership in any of its members."
+              (let [combined (&;union left right)
+                    combined-membership (&;membership sample combined)]
+                (and (d.>= (&;membership sample left)
+                           combined-membership)
+                     (d.>= (&;membership sample right)
+                           combined-membership))))
+      
+      (assert "Intersection membership as as low as membership in any of its members."
+              (let [combined (&;intersection left right)
+                    combined-membership (&;membership sample combined)]
+                (and (d.<= (&;membership sample left)
+                           combined-membership)
+                     (d.<= (&;membership sample right)
+                           combined-membership))))
+      
+      (assert "Complement membership is the opposite of normal membership."
+              (d.= (&;membership sample left)
+                   (~not (&;membership sample (&;complement left)))))
+
+      (assert "Membership in the difference will never be higher than in the set being subtracted."
+              (B/= (d.> (&;membership sample right)
+                        (&;membership sample left))
+                   (d.< (&;membership sample left)
+                        (&;membership sample (&;difference left right)))))
+      ))
+
+(test: "From predicates and sets"
+  [#let [set-10 (set;from-list number;Hash<Nat> (list;n.range +0 +10))]
+   sample (|> R;nat (:: @ map (n.% +20)))]
+  ($_ seq
+      (assert "Values that satisfy a predicate have membership = 1.
+               Values that don't have membership = 0."
+              (B/= (d.= ~true (&;membership sample (&;from-predicate n.even?)))
+                   (n.even? sample)))
+
+      (assert "Values that belong to a set have membership = 1.
+               Values that don't have membership = 0."
+              (B/= (d.= ~true (&;membership sample (&;from-set set-10)))
+                   (set;member? set-10 sample)))
+      ))
+
+(test: "Thresholds"
+  [fuzzy gen-triangle
+   sample R;real
+   threshold R;deg
+   #let [vip-fuzzy (&;cut threshold fuzzy)
+         member? (&;to-predicate threshold fuzzy)]]
+  ($_ seq
+      (assert "Can increase the threshold of membership of a fuzzy set."
+              (B/= (d.> ~false (&;membership sample vip-fuzzy))
+                   (d.> threshold (&;membership sample fuzzy))))
+
+      (assert "Can turn fuzzy sets into predicates through a threshold."
+              (B/= (member? sample)
+                   (d.> threshold (&;membership sample fuzzy))))
+      ))
diff --git a/stdlib/test/tests.lux b/stdlib/test/tests.lux
index 12601f75b..e3d0e15c3 100644
--- a/stdlib/test/tests.lux
+++ b/stdlib/test/tests.lux
@@ -53,7 +53,8 @@
                    ["_;" complex]
                    ## ["_;" random]
                    ["_;" simple]
-                   (logic ["_;" continuous]))
+                   (logic ["_;" continuous]
+                          ["_;" fuzzy]))
              ## ["_;" macro]
              (macro ["_;" ast]
                     ["_;" syntax]
-- 
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