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logic.clj
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logic.clj
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;----------------------------------------------------------
; Mini Kanren Examples
; Author: Carlos Rivero
;----------------------------------------------------------
(use '[clojure.test :rename {is test-is}])
(use '[clojure.core.logic :rename {== ===}])
(declare oddsizeo)
(declare reverseo)
(require '[clojure.core.logic.fd :as fd])
(defn removeo
[x lst result]
(fresh [head tail temp]
(conso head tail lst)
(conde [(=== x head)
(=== tail result)]
[(removeo x tail temp)
(appendo [head] temp result)])))
(defn rotateo
[lst result]
(fresh [head tail]
(conso head tail lst)
(appendo tail [head] result)))
(defn evensizeo
[lst]
(conde [(=== lst [])]
[(fresh [head tail]
(conso head tail lst)
(oddsizeo tail))]))
(defn oddsizeo
[lst]
(fresh [head tail]
(conso head tail lst)
(evensizeo tail)))
(defn reverseo
[lst result]
(conde
[(=== lst ())
(=== result ())]
[(fresh [head tail temp]
(conso head tail lst)
(reverseo tail temp)
(appendo temp [head] result))]))
(defn palindromeo
[lst]
(fresh [rev]
(reverseo lst rev)
(=== lst rev)))
(defn facto
"Logical function that succeeds if the factorial of
n is result."
[n result]
(conde [(=== n 0)
(=== result 1)]
[(fresh [temp1 temp2]
(fd/> n 0)
(fd/- n 1 temp1)
(facto temp1 temp2)
(fd/* temp2 n result))]))
(defn converto
[d k]
(conde
[(=== k :one)
(=== d 1)]
[(=== k :two)
(=== d 2)]
[(=== k :three)
(=== d 3)]
[(=== k :four)
(=== d 4)]
[(=== k :five)
(=== d 5)]
[(=== k :six)
(=== d 6)]
[(=== k :seven)
(=== d 7)]
[(=== k :eight)
(=== d 8)]
[(=== k :nine)
(=== d 9)]
[(=== k :zero)
(=== d 0)]))
(defn translateo
[lst result]
(conde [(=== lst [])
(=== result [])]
[(fresh [head tail key temp]
(conso head tail lst)
(translateo tail temp)
(converto head key)
(appendo [key] temp result))]))
(defn splito
[lst a b]
(conde [(=== lst [])
(=== a [])
(=== b [])]
[(fresh [temp element]
(=== lst [element])
(splito [] temp b)
(appendo [element] temp a))]
[(fresh [head second tail temp1 temp2 res]
(conso head tail lst)
(firsto tail second)
(resto tail res)
(splito res temp1 temp2)
(appendo [head] temp1 a)
(appendo [second] temp2 b))]))
(defn equalo
[lst]
(conde [(=== lst [])]
[(fresh [head tail]
(conso head tail lst)
(=== tail [])
(equalo []))]
[(fresh [head second tail]
(conso head tail lst)
(firsto tail second)
(=== head second)
(equalo tail))]))
(defn counto
[lst result]
(conde [(=== lst [])
(=== result 0)]
[(fresh [head tail temp]
(conso head tail lst)
(fd/- result 1 temp)
(counto tail temp))]))
(defn rangeo
[start end result]
(conde [(fd/> start end)
(=== result [])]
[(=== start end)
(=== result [start])]
[(fresh [temp res]
(fd/< start end)
(fd/+ 1 start temp)
(rangeo temp end res)
(appendo [start] res result))]))
(deftest test-removeo
(test-is (= [[:b :c :d :e]]
(run 1 [q] (removeo :a [:a :b :c :d :e] q))))
(test-is (= [[:a :b :d :e]]
(run 1 [q] (removeo :c [:a :b :c :d :e] q))))
(test-is (= [:d]
(run 1 [q]
(removeo q [:a :b :c :d :e] [:a :b :c :e]))))
(test-is (= []
(run 1 [q] (removeo :x [:a :b :c :d :e] q))))
(test-is (= [[:x :a :b :c :d :e]
[:a :x :b :c :d :e]
[:a :b :x :c :d :e]
[:a :b :c :x :d :e]
[:a :b :c :d :x :e]
[:a :b :c :d :e :x]]
(run 6 [q] (removeo :x q [:a :b :c :d :e]))))
(test-is (= [[:a [:b :c :d :e]]
[:b [:a :c :d :e]]
[:c [:a :b :d :e]]
[:d [:a :b :c :e]]
[:e [:a :b :c :d]]]
(run* [q1 q2]
(removeo q1 [:a :b :c :d :e] q2)))))
(deftest test-rotateo
(test-is (= [:yes]
(run 1 [q]
(rotateo [:a :b :c :d :e]
[:b :c :d :e :a])
(=== q :yes))))
(test-is (= []
(run 1 [q]
(rotateo [:a :b :c :d :e]
[:a :b :c :d :e])
(=== q :yes))))
(test-is (= []
(run 1 [q] (rotateo [] q))))
(test-is (= [[:a]]
(run 1 [q] (rotateo [:a] q))))
(test-is (= [[:b :c :d :e :a]]
(run 1 [q] (rotateo [:a :b :c :d :e] q))))
(test-is (= [[:e :a :b :c :d]]
(run 1 [q] (rotateo q [:a :b :c :d :e]))))
(test-is (= '[[[_0] [_0]]
[[_0 _1] [_1 _0]]
[[_0 _1 _2] [_1 _2 _0]]
[[_0 _1 _2 _3] [_1 _2 _3 _0]]
[[_0 _1 _2 _3 _4] [_1 _2 _3 _4 _0]]
[[_0 _1 _2 _3 _4 _5] [_1 _2 _3 _4 _5 _0]]
[[_0 _1 _2 _3 _4 _5 _6] [_1 _2 _3 _4 _5 _6 _0]]]
(run 7 [q1 q2] (rotateo q1 q2)))))
(deftest test-evensizeo-oddsizeo
(test-is (= [:yes]
(run 1 [q] (evensizeo []) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q] (oddsizeo [:x]) (=== q :yes))))
(test-is (= []
(run 1 [q] (evensizeo [:x]) (=== q :yes))))
(test-is (= []
(run 1 [q] (oddsizeo []) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(evensizeo [:a :b :c :d :e :f]) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(oddsizeo [:a :b :c :d :e]) (=== q :yes))))
(test-is (= '[[]
[_0 _1]
[_0 _1 _2 _3]
[_0 _1 _2 _3 _4 _5]
[_0 _1 _2 _3 _4 _5 _6 _7]]
(run 5 [q] (evensizeo q))))
(test-is (= '[[_0]
[_0 _1 _2]
[_0 _1 _2 _3 _4]
[_0 _1 _2 _3 _4 _5 _6]
[_0 _1 _2 _3 _4 _5 _6 _7 _8]]
(run 5 [q] (oddsizeo q)))))
(deftest test-palindromeo
(test-is (= [:yes]
(run 1 [q] (palindromeo []) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q] (palindromeo [:a]) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(palindromeo [:a :b :c :b :a]) (=== q :yes))))
(test-is (= []
(run 1 [q]
(palindromeo [:a :b :c :d]) (=== q :yes))))
(test-is (= '[[]
[_0]
[_0 _0]
[_0 _1 _0]
[_0 _1 _1 _0]
[_0 _1 _2 _1 _0]
[_0 _1 _2 _2 _1 _0]]
(run 7 [q] (palindromeo q)))))
(deftest test-converto
(test-is (= [:yes]
(run 1 [q] (converto 0 :zero) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(converto 0 :zero)
(converto 1 :one)
(converto 2 :two)
(converto 3 :three)
(converto 4 :four)
(converto 5 :five)
(converto 6 :six)
(converto 7 :seven)
(converto 8 :eight)
(converto 9 :nine)
(=== q :yes))))
(test-is (= []
(run 1 [q] (converto 12 :twelve) (=== q :yes))))
(test-is (= [7]
(run 1 [q] (converto q :seven))))
(test-is (= [:seven]
(run 1 [q] (converto 7 q))))
(test-is (= [[1 :two 3]]
(run 1 [q1 q2 q3]
(converto q1 :one)
(converto 2 q2)
(converto q3 :three)))))
(deftest test-translateo
(test-is (= [:yes]
(run 1 [q]
(translateo [1 2 3] [:one :two :three])
(=== q :yes))))
(test-is (= []
(run 1 [q]
(translateo [1 2 3] [:one :two :four])
(=== q :yes))))
(test-is (= [:three]
(run 1 [q] (translateo [1 2 3] [:one :two q]))))
(test-is (= [[:four :five :six :seven :eight :nine]]
(run 1 [q] (translateo [4 5 6 7 8 9] q))))
(test-is (= [[1 2 0]]
(run 1 [q] (translateo q [:one :two :zero]))))
(test-is (= [[[] []]]
(run 1 [q1 q2] (translateo q1 q2)))))
(deftest test-splito
(test-is (= [:yes]
(run 1 [q] (splito [] [] []) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q] (splito [:a] [:a] []) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(splito [:a :b] [:a] [:b]) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(splito [:a :b :c :d :e :f]
[:a :c :e]
[:b :d :f])
(=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(splito [:a :b :c :d :e :f :g]
[:a :c :e :g]
[:b :d :f])
(=== q :yes))))
(test-is (= [[[:a :c :e] [:b :d :f]]]
(run 1 [q1 q2]
(splito [:a :b :c :d :e :f] q1 q2))))
(test-is (= [[:a :b :c :d :e :f :g]]
(run 1 [q] (splito q [:a :c :e :g] [:b :d :f]))))
(test-is (= '[[[] [] []]
[[_0] [_0] []]
[[_0 _1] [_0] [_1]]
[[_0 _1 _2] [_0 _2] [_1]]
[[_0 _1 _2 _3] [_0 _2] [_1 _3]]
[[_0 _1 _2 _3 _4] [_0 _2 _4] [_1 _3]]
[[_0 _1 _2 _3 _4 _5] [_0 _2 _4] [_1 _3 _5]]]
(run 7 [q1 q2 q3] (splito q1 q2 q3)))))
(deftest test-equalo
(test-is (= [:yes]
(run 1 [q] (equalo []) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q] (equalo [:x]) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q] (equalo [:x :x]) (=== q :yes))))
(test-is (= [:yes]
(run 1 [q]
(equalo [:x :x :x :x :x]) (=== q :yes))))
(test-is (= [:x]
(run 1 [q] (equalo [:x :x q :x]))))
(test-is (= '[_0]
(run 1 [q] (equalo [q q q q q q]))))
(test-is (= '([_0 _0 _0 _0 _0])
(run 1 [q1 q2 q3 q4 q5]
(equalo [q1 q2 q3 q4 q5]))))
(test-is (= []
(run 1 [q] (equalo [:x :y]) (=== q :yes))))
(test-is (= []
(run 1 [q1 q2]
(equalo [q1 q1 q2 q1 q1]) (!= q1 q2))))
(test-is (= '([]
[_0]
[_0 _0]
[_0 _0 _0]
[_0 _0 _0 _0]
[_0 _0 _0 _0 _0]
[_0 _0 _0 _0 _0 _0])
(run 7 [q] (equalo q)))))
(deftest test-counto
(test-is (= [0]
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto [] q))))
(test-is (= [1]
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto [:a] q))))
(test-is (= [2]
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto [:a :b] q))))
(test-is (= [3]
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto [:a :b :c] q))))
(test-is (= [10]
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto (repeat 10 :x) q))))
(test-is (= '([_0])
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto q 1))))
(test-is (= '([_0 _1 _2 _3 _4])
(run 1 [q]
(fd/in q (fd/interval 0 10))
(counto q 5))))
(test-is (= '([[] 0]
[(_0) 1]
[(_0 _1) 2]
[(_0 _1 _2) 3]
[(_0 _1 _2 _3) 4]
[(_0 _1 _2 _3 _4) 5]
[(_0 _1 _2 _3 _4 _5) 6])
(run 7 [q1 q2]
(fd/in q1 q2 (fd/interval 0 10))
(counto q1 q2)))))
(deftest test-rangeo
(test-is (= [[3 4 5 6 7 8 9 10]]
(run 1 [q]
(rangeo 3 10 q))))
(test-is (= [[7]]
(run 1 [q]
(rangeo 7 7 q))))
(test-is (= [[]]
(run 1 [q]
(rangeo 10 1 q))))
(test-is (= [6]
(run 1 [q]
(fd/in q (fd/interval 1 10))
(rangeo 2 q [2 3 4 5 6]))))
(test-is (= [[2 6]]
(run 1 [q1 q2]
(fd/in q1 q2 (fd/interval 1 10))
(rangeo q1 q2 [2 3 4 5 6])))))
(test-is (= #{[]
[1] [1 2] [1 2 3] [1 2 3 4]
[2] [2 3] [2 3 4]
[3] [3 4]
[4]}
(set
(run* [q]
(fresh [start end]
(fd/in start end (fd/interval 1 4))
(rangeo start end q))))))
(deftest test-facto
(test-is (= [1]
(run 1 [q] (facto 0 q))))
(test-is (= [1]
(run 1 [q] (facto 1 q))))
(test-is (= [720]
(run 1 [q] (facto 6 q))))
(test-is (= [2432902008176640000]
(run 1 [q] (facto 20 q))))
(test-is (= [0 1]
(run 2 [q] (facto q 1))))
(test-is (= [5]
(run 1 [q] (facto q 120))))
(test-is (= [10]
(run 1 [q] (facto q 3628800))))
(test-is (= [:yes]
(run 1 [q] (facto 4 24)
(=== q :yes))))
(test-is (= [:yes]
(run 1 [q] (facto 15 1307674368000)
(=== q :yes))))
(test-is (= [[0 1]
[1 1]
[2 2]
[3 6]
[4 24]
[5 120]
[6 720]
[7 5040]
[8 40320]
[9 362880]]
(run 10 [n r] (facto n r)))))
(run-tests)