34 lines
1.3 KiB
Plaintext
34 lines
1.3 KiB
Plaintext
; use { } to read a set
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(define A { 1 2 3 4 3 5 5}) → { 1 2 3 4 5 } ; duplicates are removed from a set
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; or use make-set to make a set from a list
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(define B (make-set ' ( 3 4 5 6 7 8 8))) → { 3 4 5 6 7 8 }
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(set-intersect A B) → { 3 4 5 }
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(set-intersect? A B) → #t ; predicate
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(set-union A B) → { 1 2 3 4 5 6 7 8 }
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(set-substract A B) → { 1 2 }
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(set-sym-diff A B) → { 1 2 6 7 8 } ; ∆ symmetric difference
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(set-equal? A B) → #f
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(set-equal? { a b c} { c b a}) → #t ; order is unimportant
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(set-subset? A B) → #f ; B in A or B = A
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(set-subset? A { 3 4 }) → #t
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(member 4 A) → (4 5) ; same as #t : true
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(member 9 A) → #f
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; check basic equalities
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(set-equal? A (set-union (set-intersect A B) (set-substract A B))) → #t
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(set-equal? (set-union A B) (set-union (set-sym-diff A B) (set-intersect A B))) → #t
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; × : cartesian product of two sets : all pairs (a . b) , a in A, b in B
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; returns a list (not a set)
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(define A { albert simon})
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(define B { antoinette ornella marylin})
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(set-product A B)
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→ ((albert . antoinette) (albert . marylin) (albert . ornella) (simon . antoinette) (simon . marylin) (simon . ornella))
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; sets elements may be sets
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{ { a b c} {c b a } { a b d}} → { { a b c } { a b d } } ; duplicate removed
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; A few functions return sets :
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(primes 10) → { 2 3 5 7 11 13 17 19 23 29 }
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