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͂ƕ֗Ȋ֐`ŏЉ܂Bl^ P-99: Ninety-Nine Prolog Problems łBٍ͐̃y[W Prolog Programming Yet Anotehr Prolog Problems ƓłA炸܂B

P

Xg̗vfЂƂ‚ׂq single? `ĂB

  gosh> (single? '(a))  #t  gosh> (single? '(a b))  #f  gosh> (single? '())  #f  

Q

Xg̗vf‚邩ׂq double? `ĂB

  gosh> (double? '(a b))  #t  gosh> (double? '(a b c))  #f  gosh> (double? '(a))  #f  

R

Xg xs ̓Xg ys ׂq longer? xs ys `ĂB

  gosh> (longer? '(a b c) '(a b))  #t  gosh> (longer? '(a b) '(a b))  #f  gosh> (longer? '(a) '(a b))  #f  

S

Xg xs ̍Ō߂֐ last ƁAŌ̗vf菜֐ butlast `ĂB

  gosh> (last '(a b c))  (c)  gosh> (last '(a))  (a)  gosh> (butlast '(a b c))  (a b)  gosh> (butlast '(a))  ()  

T

Xg xs ̐擪 n ‚̗vfo֐ take xs n `ĂB

  gosh> (take '(a b c d e) 3)  (a b c)  gosh> (take '(a b c d e) 0)  ()  gosh> (take '(a b c d e) 6)  (a b c d e)  

U

Xg xs ̐擪 n ‚̗vf菜֐ drop xs n `ĂB

  gosh> (drop '(a b c d e) 3)  (d e)  gosh> (drop '(a b c d e) 0)  (a b c d e)  gosh> (drop '(a b c d e) 6)  ()  

V

Xg xs n Ԗڂ m - 1 Ԗڂ܂ł̗vf𕔕XgƂĎo֐ subseq xs n m `ĂBȂAXg̗vf 0 琔n߂̂Ƃ܂B

  gosh> (subseq '(a b c d e) 2 4)  (c d)  gosh> (subseq '(a b c d e) 0 5)  (a b c d e)  gosh> (subseq '(a b c d e) 0 0)  ()  

W

Xg xs ̖ n ‚̗vf菜֐ butlastn xs n `ĂB

  gosh> (butlastn '(a b c d e) 3)  (a b)  gosh> (butlastn '(a b c d e) 0)  (a b c d e)  gosh> (butlastn '(a b c d e) 5)  ()  

X

Xg xs 𒷂 n ̕Xgɕ֐ group xs n `ĂB

  gosh> (group '(a b c d e f) 2)  ((a b) (c d) (e f))  gosh> (group '(a b c d e f) 3)  ((a b c) (d e f))  gosh> (group '(a b c d e f) 4)  ((a b c d) (e f))  

10

Xg ls ̒ x Ɠvf̈ʒu n ߂֐ position x ls `ĂBȂAXg̗vf 0 琔n߂̂Ƃ܂B

  gosh> (position 'a '(a b c d e))  0  gosh> (position 'c '(a b c d e))  2  gosh> (position 'e '(a b c d e))  4  gosh> (position 'f '(a b c d e))  #f  

11

Xg ls x Ɠvf̌ n ߂֐ count x ls `ĂB

  gosh> (count 'a '(a b a b c a b c d))  3  gosh> (count 'c '(a b a b c a b c d))  2  gosh> (count 'd '(a b a b c a b c d))  1  gosh> (count 'e '(a b a b c a b c d))  0  

12

Xg̗vf̍vl߂֐ sum-list `ĂB

  gosh> (sum-list '(1 2 3 4 5))  15  

13

Xg̒ől߂֐ max-list ƍŏl߂֐ min-list `ĂB

  gosh> (max-list '(5 6 4 7 3 8 2 9 1))  9  gosh> (min-list '(5 6 4 7 3 8 2 9 1))  1  

14

Xg ls ̒ŗvf x ̉Eׂɗvf y 邩`FbNq adjacent? x y ls `ĂB

  gosh> (adjacent? 'a 'b '(a b c d e f))  #t  gosh> (adjacent? 'e 'f '(a b c d e f))  #t  gosh> (adjacent? 'f 'e '(a b c d e f))  #f  

15

Xg ls ̒ŗvf x vf y OɏoĂ邩ׂq before? x y ls `ĂB

  gosh> (before? 'a 'b '(a b c d e f))  (b c d e f)  gosh> (before? 'c 'b '(a b c d e f))  #f  

16

n m ܂łi[Xg֐ iota n m `ĂB

  gosh> (iota 1 5)  (1 2 3 4 5)  

17

Xgdvf菜ďW𐶐֐ set-of-list `ĂB

  gosh> (set-of-list '(a b c d e f a b c))  (d e f a b c)  

18

2 ‚̏W̘a߂֐ union `ĂB

  gosh> (union '(a b c d) '(c d e f))  (a b c d e f)  

19

2 ‚̏W̐ς߂֐ intersection `ĂB

  gosh> (intersection '(a b c d) '(c d e f))  (c d)  

20

2 ‚̏W̍߂֐ difference `ĂB

警察航空ユニットは、それをworhtされ

  gosh> (difference '(a b c d) '(c d e f))  (a b)  

21

2 ‚̃¥[gς݂̃XgЂƂ‚̃¥[gς݂̃Xgɂ܂Ƃ߂֐ merge-list `ĂB

  gosh> (merge-list < '(1 3 5 7) '(2 4 6 8))  (1 2 3 4 5 6 7 8)  

22

֐ merge-list găXg¥[g merge-sort `ĂB

  gosh> (merge-sort < 9 '(5 6 4 7 8 3 2 9 1 10))  (1 2 3 4 5 6 7 8 9)  gosh> (merge-sort < 10 '(5 6 4 7 8 3 2 9 1 10))  (1 2 3 4 5 6 7 8 9 10)  gosh> (merge-sort < 11 '(5 6 4 7 8 3 2 9 1 10 0))  (0 1 2 3 4 5 6 7 8 9 10)  

23

Xg ps Xg ls ́uړ (prefix) v肷֐ prefix ls ps `ĂBړƂ́A̐擪炠ʒu܂ł̂̕ƂłBXg [a, b, c, d] ̐ړ [ ], [a], [a, b], [a, b, c], [a, b, c, d] 5 ‚ɂȂ܂B

  gosh> (prefix '(a b c d e f) '(a b c))  #t  gosh> (prefix '(a b c d e f) '(a b c e))  #f  gosh> (prefix '(a b c d e f) '())  #t  

24

Xg ss Xg ls ́uڔ (suffix) v肷֐ suffix ls ss `ĂBڔƂ́Âʒu疖܂ł̂̕ƂłBXg [a, b, c, d] ̐ڔ [a, b, c, d], [b, c, d], [c, d], [d], [ ] 5 ‚ɂȂ܂B

  gosh> (suffix '(a b c d e f) '(d e f))  #t  gosh> (suffix '(a b c d e f) '())  #t  gosh> (suffix '(a b c d e f) '(f g))  #f  

25

Xg xs Xg ls ̕Xg肷֐ sublist xs ls `ĂB

  gosh> (sublist '(c d e) '(a b c d e f))  #t  gosh> (sublist '(d e) '(a b c d e f))  #t  gosh> (sublist '(d e g) '(a b c d e f))  #f  gosh> (sublist '() '(a b c d e f))  #t  

---

𓚂P

  Xg : vfЂƂ‚    (define (single? ls)     (and (pair? ls) (null? (cdr ls))))  

Scheme ̏ꍇA ls XgŁA (cdr ls) 󃊃Xgł΁ÃXg̗vf͈‚ȂƂ킩܂Blength ŃXg̒߂Kv͂܂B

𓚂Q

  Xg : vf‚邩    (define (double? ls)    (and (pair? ls) (single? (cdr ls))))  

Scheme ̏ꍇAq pair? ^ł΃XgɈˆȏ̗vf邱Ƃ킩܂BƂ (cdr ls) ‚vfȂƂq single? ŊmF܂Blength ŃXg̒߂Kv͂܂B

𓚂R

  Xg : Xg xs  ys     (define (longer? xs ys)    (cond ((null? xs) #f)          ((null? ys) #t)          (else           (longer? (cdr xs) (cdr ys)))))    ; ʉ  (define (longer? xs ys)    (and (pair? xs)         (or (null? ys)             (longer? (cdr xs) (cdr ys)))))  

Xg̐擪珇ԂɂǂAr ys 󃊃XgɂȂ ys ̕Ƃ킩܂Blength ŃXg̒߂ĔrÃvO̕IƎv܂B

𓚂S

  Xg :  Xg̍Ō߂    (define (last ls)    (if (null? (cdr ls))        ls      (last (cdr ls))))  

֐ last ͒PȍċA`ŃXg̍Ō߂Ă܂BGauche ɂ͓֐ last-pair ܂B

  Xg : Ō̗vf菜    (define (butlast ls)    (if (single? ls)        '()      (cons (car ls) (butlast (cdr ls)))))    ; ʉ  (define (butlast ls)    (let loop ((ls ls) (a '()))      (if (single? ls)          (reverse! a)        (loop (cdr ls) (cons (car ls) a)))))  

butlast ͈̃Xg ls ̗vf‚ɂȂ܂ōċAĂяo܂Bvf‚ɂȂ󃊃XgԂ܂BƂ́AċAĂяo̕Ԃl cons ŗvfljĂłB

ʉ named let ɂ閖ċAo[WłBݐϕϐ a ɗvfi[A ls ̗vfЂƂ‚ɂȂȂ΁Areverse! ŃXg a jIɔ]ĕԂ܂Breverse gIłB

𓚂T

  Xg : Xg̐擪 n ‚̗vfo    (define (take ls n)    (if (or (<= n 0) (null? ls))        '()      (cons (car ls) (take (cdr ls) (- n 1)))))    ; ʉ  (define (take ls n)    (let loop ((ls ls) (n n) (a '()))      (if (or (<= n 0) (null? ls))          (reverse! a)        (loop (cdr ls) (- n 1) (cons (car ls) a)))))  

n 0 ȉ܂͈ ls 󃊃Xg̏ꍇ͋󃊃XgԂ܂BłȂ take ċAĂяoāA̕ԂlɃXg̐擪vf (car ls) lj܂Bʉ named let ɂ閖ċAo[WłBݐϕϐ a ɗvfi[āAn 0 ȉ܂ ls 󃊃XgɂȂAreverse! ŃXg a jIɔ]ĕԂ܂B

ȂAtake Scheme ̃Cu SRFI-1 ɗpӂĂ܂B

2トラップは、RDを下回る。

𓚂U

  Xg : Xg̐擪 n ‚̗vf폜    (define (drop ls n)    (if (or (<= n 0) (null? ls))        ls      (drop (cdr ls) (- n 1))))  

drop ͊ȒPłB n 0 ȉ܂͈ ls 󃊃XgɂȂ܂ drop ċAĂяo邾łBȂAdrop Scheme ̃Cu SRFI-1 ɗpӂĂ܂B

𓚂V

  Xg : Xgo    (define (subseq ls s e)    (take (drop ls s) (- e s)))  

subseq drop take gƊȒPłBdrop ls s ‚̗vf菜ÃXg e - s ‚̗vf take ŎołB

𓚂W

  Xg : Xg̖ n ‚̗vf菜    (define (butlastn ls n)    (take ls (- (length ls) n)))  

Xg ls ̒ m ƂƁAXg̖ n ‚̗vf菜Ƃ́AXg̐擪 m - n ‚̗vfoƂƓɂȂ܂Bovf̌ (- (length ls) n)) ŋ߂ take ŗvfo܂B

𓚂X

  Xg : Xg̕    (define (group ls n)    (if (null? ls)        '()      (cons (take ls n) (group (drop ls n) n))))    ; ʉ  (define (group ls n)    (let loop ((ls ls) (a '()))      (if (null? ls)          (reverse! a)        (loop (drop ls n) (cons (take ls n) a)))))  

֐ group take drop gƊȒPɒ`ł܂Bls 󃊃Xg̏ꍇ͕łȂ̂ŋ󃊃XgԂ܂BꂪċA̒‾ɂȂ܂Bls 󃊃XgłȂꍇA܂ take n ‚̗vfi[Xg߂܂BɁAn ‚̗vf菜Xg drop ŋ߂ group ċAĂяo܂B̕Ԃl take ŎoXg cons Œlj΂킯łB

ʉ named let ɂ閖ċAo[WłBtake ŎoXgݐϕϐ a Ɋi[Als 󃊃XgɂȂ reverse! ŃXg a jIɔ]ĕԂ܂B

10

  Xg : vf̈ʒu߂    (define (position x ls)    (let loop ((ls ls) (n 0))      (cond ((null? ls) #f)            ((eqv? (car ls) x) n)            (else             (loop (cdr ls) (+ n 1))))))  

named let ̈ n vf̈ʒu¥܂Bls 󃊃Xg̏ꍇAx Ɠvf͌‚Ȃ̂ #f Ԃ܂BłȂ΁Aq eqv? ŃXg̐擪vf (car ls) x r܂Bꍇ n Ԃ܂BȂꍇ loop ċAĂяoĎ̗vf𒲂ׂ܂B

11

  Xg : vf̌߂    (define (count x ls)    (let loop ((ls ls) (n 0))      (cond ((null? ls) n)            ((eqv? (car ls) x) (loop (cdr ls) (+ n 1)))            (else (loop (cdr ls) n)))))    ; ʉ  (define (count x ls)    (fold (lambda (y n) (if (eqv? x y) (+ n 1) n)) 0 ls))  

named let ŃXg̗vfԂɒׁAx Ɠvf‚Ηݐϕϐ n ̒l +1 ܂Bʉ͏ݍ݂s֐ fold go[WłBfold Gauche Œ`Ă̂g܂B

12

  Xg : vf̍vl߂    (define (sum-list ls)    (let loop ((ls ls) (sum 0))      (if (null? ls)          sum        (loop (cdr ls) (+ (car ls) sum)))))    ; ʉ  (define (sum-list ls)    (fold (lambda (x sum) (+ x sum)) 0 ls))  

sum-list named let ŃXg̗vfݐϕϐ sum ɉZ邾łBʉ͏ݍ݂s֐ fold go[WłB

13

  Xg : Xgőlƍŏl߂    (define (max-list ls)    (let loop ((ls (cdr ls)) (a (car ls)))      (cond ((null? ls) a)            ((< a (car ls)) (loop (cdr ls) (car ls)))            (else (loop (cdr ls) a)))))    (define (min-list ls)    (let loop ((ls (cdr ls)) (a (car ls)))      (cond ((null? ls) a)            ((> a (car ls)) (loop (cdr ls) (car ls)))            (else (loop (cdr ls) a)))))    ; ʉ  (define (max-list ls)    (fold (lambda (x a) (if (< a x) x a)) (car ls) (cdr ls)))    (define (min-list ls)    (fold (lambda (x a) (if (> a x) x a)) (car ls) (cdr ls)))  

max_list min_list named let ŃvOĂ܂Bݐϕϐ a ɃXg ls ̐擪vfZbg܂BƂ́Ac̗vfԂɒׁAa 傫 () vf‚A̒l a ɃZbg܂Bʉ fold go[WłB

WAは、リストを呼び出すことはありません

14

  Xg : x  y ׂ͗荇Ă邩    (define (adjacent x y ls)    (if (and (pair? ls) (pair? (cdr ls)))        (if (and (eqv? (car ls) x) (eqv? (cadr ls) y))            #t          (adjacent x y (cdr ls)))      #f))    ; ʉ  (define (adjacent x y ls)    (let ((xs (memv x ls)))      (if xs          (if (eqv? (cadr xs) y)              #t            (adjacent x y (cdr xs)))        #f)))  

ŏɃXg̗vfˆȏ゠邱Ƃ`FbN܂BɁA擪̗vf x ƓāA̗vf y ƓƂ`FbN܂Bł #t ԂAłȂ adjacent ċAĂяoāA̗vf𒲂ׂ܂Bʉ͊֐ memv go[WłB

15

  Xg : x  y OɏoĂ邩    (define (before x y ls)    (let ((xs (memv x ls)))      (if xs          (memv y (cdr xs))        #f)))  

֐ before ͊֐ memv gƊȒPɃvO邱Ƃł܂Bls x memv ŒT܂Bx ‚ꍇAxs ̐擪vf x ɂȂ܂B菜Xg memv y T΂킯łB

16

  Xg : ̐    (define (iota n m)    (if (> n m)        '()      (cons n (iota (+ n 1) m))))    ; ʉ  (define (iota n m)    (let loop ((m m) (a '()))      (if (< m n)          a        (loop (- m 1) (cons m a)))))  

֐ iota ͊ȒPłBn m 傫ꍇ͋󃊃XgɂȂ܂Bn m ȉ̏ꍇAiota ċAĂяo n + 1 m ܂ł̃Xg𐶐A̐擪 n lj邾łBʉ named let go[WłB̏ꍇA납琔l𐶐Ă邱ƂɒӂĂBm n ȂȂ΃Xg a Ԃ܂B

17

  Xg : W̐    (define (set-of-list ls)    (cond ((null? ls) '())          ((memv (car ls) (cdr ls))           (set-of-list (cdr ls)))          (else           (cons (car ls) (set-of-list (cdr ls))))))    ; ʉ  (define (set-of-list ls)    (let loop ((ls ls) (a '()))      (cond ((null? ls) (reverse! a))            ((memv (car ls) (cdr ls))             (loop (cdr ls) a))            (else             (loop (cdr ls) (cons (car ls) a))))))  

q set-of-list ̓Xgdvf菜܂B󃊃Xg͏dvfȂ̂ŋ󃊃Xĝ܂܂łB̐߂ŁAXg̐擪vf (car ls) c̃Xg (cdr ls) ɂ邩 memv ŒׁAvfΏWɉ܂Belse ߂œvfȂꍇ͂Wɉ܂Bʉ named let gċAo[WłB

18

  Xg : W̘a    (define (union xs ys)    (cond ((null? xs) ys)          ((memv (car xs) ys)           (union (cdr xs) ys))          (else           (cons (car xs) (union (cdr xs) ys)))))    ; ʉ 1  (define (union xs ys)    (let loop ((xs xs) (a ys))      (cond ((null? xs) a)            ((memv (car xs) ys)             (loop (cdr xs) a))            (else             (loop (cdr xs) (cons (car xs) a))))))    ; ʉ 2  (define (union xs ys)    (fold (lambda (x a) (if (memv x ys) a (cons x a))) ys xs))  

ŏ̐߂͋W (󃊃Xg) ƏW ys ̘a ys ł邱Ƃ¥Ă܂B̐߂ŁAvf (car xs) W ys Ɋ܂܂Ă΁AVWɉ܂Belse ߂ (car xs) ys Ɋ܂܂ĂȂ΁AWɒlj܂Bʉ named let fold go[WłB

19

  Xg : W̐    (define (intersection xs ys)    (cond ((null? xs) '())          ((memv (car xs) ys)           (cons (car xs) (intersection (cdr xs) ys)))          (else           (intersection (cdr xs) ys))))    ; ʉ 1  (define (intersection xs ys)    (let loop ((xs xs) (a '()))      (cond ((null? xs) a)            ((memv (car xs) ys)             (loop (cdr xs) (cons (car xs) a)))            (else             (loop (cdr xs) a)))))    ; ʉ 2  (define (intersection xs ys)    (fold (lambda (x a) (if (memv x ys) (cons x a) a)) '() xs))  

ŏ̐߂͋W (󃊃Xg) ƏW ys ̐ς͋Wł邱Ƃ¥Ă܂B̐߂ŁAvf (car xs) W ys Ɋ܂܂Ă΁AVWɒlj܂BłȂ΁Aelse ߂ŗvf (car xs) Wɒlj܂Bʉ named let fold go[WłB

20

  Xg : W̍    (define (difference xs ys)    (cond ((null? xs) '())          ((memv (car xs) ys)           (difference (cdr xs) ys))          (else           (cons (car xs) (difference (cdr xs) ys)))))    ; ʉ 1  (define (difference xs ys)    (let loop ((xs xs) (a '()))      (cond ((null? xs) a)            ((memv (car xs) ys)             (loop (cdr xs) a))            (else             (loop (cdr xs) (cons (car xs) a))))))    ; ʉ 2  (define (difference xs ys)    (fold (lambda (x a) (if (memv x ys) a (cons x a))) '() xs))  

ŏ̐߂́AWƏW ys ̍͋Wł邱Ƃ¥Ă܂B̐߂ŁAvf (car xs) ys Ɋ܂܂ꂢꍇ͏Wɂlj܂BłȂ΁Aelse ߂ŗvf (car xs) Wɒlj܂Bʉ named let fold go[WłB

21

  Xg : Xg̃}[W    (define (merge-list pred xs ys)    (cond ((null? xs) ys)          ((null? ys) xs)          ((pred (car xs) (car ys))           (cons (car xs) (merge-list pred (cdr xs) ys)))          (else           (cons (car ys) (merge-list pred xs (cdr ys))))))  

ŏ̐߂́A󃊃XgƃXg ys }[W ys ɂȂ邱Ƃ¥Ă܂B̐߂́AXg xs Ƌ󃊃Xg}[W xs ɂȂ邱Ƃ¥Ă܂B 2 ‚̐߂AċAĂяo̒‾ɂȂ܂B

3 Ԗڂ̐߂ŁAꂼ̃Xg̐擪vfq pred ŔrApred ^Ԃꍇ (car xs) }[WXg̐擪ɒljAłȂ΍Ō̐߂ (car ys) }[WXg̐擪ɒlj܂Bmerge-list ċAĂяoƂ́Axs ܂ ys ̐擪vf菜ČĂяoƂɒӂĂB

22

}[W¥[g̓Xg̒ 1, 2, 4, 8, ... Ƒ₵ĂAċAIɍlȒPłB܂A¥[g郊Xg 2 ‚ɕāAO¥[g܂BɁA㔼¥[gāǍʂ}[W΂킯łB

ċAĂяo邽тɃXg 2 ‚ɕ̂ŁAŌɃXg̗vf͂ЂƂ‚ƂȂ܂B̓¥[gς݂̃XgȂ̂ŁAōċAĂяoIă}[Ws΂킯łBvÔ͎悤ɂȂ܂B

  Xg : }[W¥[g    (define (merge-sort pred n ls)    (if (= n 1)        (list (car ls))      (let ((m (quotient n 2)))        (merge-list          pred          (merge-sort pred m ls)          (merge-sort pred (- n m) (drop ls m))))))  

֐ merge-sort ̈ pred vfrqA ls ¥[g郊XgA n Xg̒¥܂Bmerge-sort ̓Xg𕪊鏈ŁAVXgȂƂɒӂĂBmerge-sort ̓¥[g郊Xg͈̔͂Jnʒuƒŕ¥Ă܂BXg񕪊ꍇAO ls m (= n / 2) ŕ¥A㔼 (drop ls m) (- n m) ŕ¥܂B

Ƃ merge-sort ċAĂяoŃXg𕪊ĂAXg̒ 1 ɂȂȂΐVXgԂ܂BāAmerge-sort Ń¥[gXg merge-list Ń}[W΂킯łB

23

  Xg : ړ̔    (define (prefix ls ps)    (cond ((null? ps) #t)          ((eqv? (car ls) (car ps))           (prefix (cdr ls) (cdr ps)))          (else #f)))  

ړ̔͊ȒPłBŏ̐߂́A󃊃Xg͐ړł邱Ƃ¥Ă܂B̐߂ŁAXg̐擪vfꍇ́Ac̃Xg (cdr ps) (cdr ls) ̐ړł邱Ƃm߂܂B

24

  Xg : ڔ̔    (define (suffix ls ss)    (prefix (drop ls (- (length ls) (length ss))) ss))  

ڔ̔ȒPłBXg ls ss ̒̍߁Als ̐擪獷̌vf菜܂B ls ss ̒Ȃ̂ŁAƂ prefix Ŕr邾łB

25

  Xg : Xg̔    (define (sublist ks ls)    (cond ((null? ls) #f)          ((prefix ls ks) #t)          (else (sublist ks (cdr ls)))))  

sublist prefix gƊȒPłBŏ̐߂ ls 󃊃Xg̏ꍇAks ͕Xgł͂Ȃ̂ #f Ԃ܂B̐߂ŁAks ls ̐ړłΕXgȂ̂ #t Ԃ܂BȊȌꍇ ls ̐擪vf菜āAsublist ċAĂяo邾łB

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