63 lines
3.1 KiB
Racket
63 lines
3.1 KiB
Racket
(module intermediate-funs scheme/base
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(require "teachprims.ss" "and-or-map.ss"
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mzlib/etc
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scheme/list
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syntax/docprovide
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(for-syntax scheme/base))
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(provide-and-document
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procedures
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(all-from-except beginner: lang/private/beginner-funs procedures
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+ * - / append)
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("Numbers (relaxed conditions)"
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(+ (number ... -> number) "to add all given numbers")
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(* (number ... -> number) "to multiply all given numbers")
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(- (number ... -> number) "to subtract from the first all remaining numbers")
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(/ (number ... -> number) "to divide the first by all remaining numbers")
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)
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("Lists"
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((intermediate-append append) ((listof any) ... -> (listof any))
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"to create a single list from several, by juxtaposition of the items"))
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("Higher-Order Functions"
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(map ((X ... -> Z) (listof X) ... -> (listof Z))
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"to construct a new list by applying a function to each item on one or more existing lists")
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(for-each ((any ... -> any) (listof any) ... -> void)
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"to apply a function to each item on one or more lists for effect only")
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(filter ((X -> boolean) (listof X) -> (listof X))
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"to construct a list from all those items on a list for which the predicate holds")
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((intermediate-foldr foldr) ((X Y -> Y) Y (listof X) -> Y)
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"(foldr f base (list x-1 ... x-n)) = (f x-1 ... (f x-n base))")
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((intermediate-foldl foldl) ((X Y -> Y) Y (listof X) -> Y)
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"(foldl f base (list x-1 ... x-n)) = (f x-n ... (f x-1 base))")
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(build-list (nat (nat -> X) -> (listof X))
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"(build-list n f) = (list (f 0) ... (f (- n 1)))")
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((intermediate-build-string build-string) (nat (nat -> char) -> string)
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"(build-string n f) = (string (f 0) ... (f (- n 1)))")
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((intermediate-quicksort quicksort) ((listof X) (X X -> boolean) -> (listof X))
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"to construct a list from all items on a list in an order according to a predicate")
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((intermediate-sort sort) ((listof X) (X X -> boolean) -> (listof X))
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"to construct a list from all items on a list in an order according to a predicate")
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((intermediate-andmap andmap) ((X -> boolean) (listof X) -> boolean)
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"(andmap p (list x-1 ... x-n)) = (and (p x-1) ... (p x-n))")
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((intermediate-ormap ormap) ((X -> boolean) (listof X) -> boolean)
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"(ormap p (list x-1 ... x-n)) = (or (p x-1) ... (p x-n))")
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(argmin ((X -> real) (listof X) -> X)
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"to find the (first) element of the list that minimizes the output of the function")
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(argmax ((X -> real) (listof X) -> X)
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"to find the (first) element of the list that maximizes the output of the function")
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(memf ((X -> boolean) (listof X) -> (union false (listof X)))
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"to determine whether the first argument produces true for some value in the second argument")
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(apply ((X-1 ... X-N -> Y) X-1 ... X-i (list X-i+1 ... X-N) -> Y)
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"to apply a function using items from a list as the arguments")
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(compose ((Y-1 -> Z) ... (Y-N -> Y-N-1) (X-1 ... X-N -> Y-N) -> (X-1 ... X-N -> Z))
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"to compose a sequence of procedures into a single procedure")
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(procedure? (any -> boolean)
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"to determine if a value is a procedure"))))
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