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(.module:
lux
(lux (data [number "Rev/" Interval<Rev>]
(coll [list]
[set #+ Set])
text/format)
[math])
(// ["&" continuous]))
(type: #export (Fuzzy a)
(-> a Rev))
(def: #export (membership elem set)
(All [a] (-> a (Fuzzy a) Rev))
(set elem))
(def: #export (union left right)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.~or (membership elem left)
(membership elem right))))
(def: #export (intersection left right)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.~and (membership elem left)
(membership elem right))))
(def: #export (complement set)
(All [a] (-> (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.~not (membership elem set))))
(def: #export (difference sub base)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(&.~and (membership elem base)
(&.~not (membership elem sub)))))
(def: #export (from-predicate predicate)
(All [a] (-> (-> a Bool) (Fuzzy a)))
(function (_ elem)
(if (predicate elem)
&.~true
&.~false)))
(def: #export (from-set set)
(All [a] (-> (Set a) (Fuzzy a)))
(from-predicate (set.member? set)))
(def: (ascending from to)
(-> Rev Rev (Fuzzy Rev))
(function (_ elem)
(cond (r/<= from elem)
&.~false
(r/>= to elem)
&.~true
## in the middle...
(r// (r/- from to)
(r/- from elem)))))
(def: (descending from to)
(-> Rev Rev (Fuzzy Rev))
(function (_ elem)
(cond (r/<= from elem)
&.~true
(r/>= to elem)
&.~false
## in the middle...
(r// (r/- from to)
(r/- elem to)))))
(def: #export (gradient from to)
(-> Rev Rev (Fuzzy Rev))
(if (r/< to from)
(ascending from to)
(descending from to)))
(def: #export (triangle bottom middle top)
(-> Rev Rev Rev (Fuzzy Rev))
(case (list.sort r/< (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)
(-> Rev Rev Rev Rev (Fuzzy Rev))
(case (list.sort r/< (list bottom middle-bottom middle-top top))
(^ (list bottom middle-bottom middle-top top))
(intersection (ascending bottom middle-bottom)
(descending middle-top top))
_
(undefined)))
(def: #export (cut treshold set)
(All [a] (-> Rev (Fuzzy a) (Fuzzy a)))
(function (_ elem)
(let [membership (set elem)]
(if (r/> treshold membership)
(|> membership (r/- treshold) (r/* &.~true))
&.~false))))
(def: #export (to-predicate treshold set)
(All [a] (-> Rev (Fuzzy a) (-> a Bool)))
(function (_ elem)
(r/> treshold (set elem))))
(type: #export (Fuzzy2 a)
(-> a [Rev Rev]))
(def: #export (type-2 lower upper)
(All [a] (-> (Fuzzy a) (Fuzzy a) (Fuzzy2 a)))
(function (_ elem)
(let [l-rev (lower elem)
u-rev (upper elem)]
[(r/min l-rev
u-rev)
u-rev])))
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