recursion.rkt

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0 0 17 3 26 #"; Recursion (general type)"
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#"; 1. We use recursion to work with recursively-defined data"
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0 0 17 3 41 #"; Think about recursive data definitions:"
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#"; A template for general recursion"
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#"; A template for number recursion"
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#"; A template for list recursion"
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0 0 24 3 1 #"("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 1 #")"
0 0 14 3 3 #"..."
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 19 #"recursive-list-<fn>"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 6 #"))))))"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 42 #"; recursive-sum : Listof-Numbers -> number"
0 0 24 29 1 #"\n"
0 0 17 3 49 #"; returns the sum of all the elements in the list"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 13 #"recursive-sum"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 21 3 1 #"0"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 17 3 16 #"; Recursive step"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 1 #"+"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 22 #")                     "
0 0 17 3 23 #"; (combiner (first lon)"
0 0 24 29 1 #"\n"
0 0 24 3 10 #"         ("
0 0 14 3 13 #"recursive-sum"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 8 #"))))))  "
0 0 17 3 30 #";   (recursive-fn (rest lon)))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 13 #"recursive-sum"
0 0 24 3 2 #" ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 21 3 1 #"1"
0 0 24 3 1 #" "
0 0 21 3 1 #"2"
0 0 24 3 1 #" "
0 0 21 3 1 #"3"
0 0 24 3 1 #" "
0 0 21 3 1 #"4"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 55 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 17 3 51 #"; Iterative Recursion (recursion with accumulators)"
0 0 24 29 1 #"\n"
0 0 17 3 2 #"; "
0 0 24 29 1 #"\n"
0 0 17 3 8 #"; IDEAS:"
0 0 24 29 1 #"\n"
0 0 17 3 61
#"; 1. Use accumulators to avoid leaving a long recursive trail"
0 0 24 29 1 #"\n"
0 0 17 3 67
#"; 2. Use local to package your iterative recursive functions nicely"
0 0 24 29 1 #"\n"
0 0 17 3 55 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7         391 17           0 0           0 64 0 17 3 70
(
 #"; Remember that the (recursive-sum) function above will look like th"
 #"is"
) 0 0 24 29 1 #"\n"
0 0 17 3 24 #"; before simplification:"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 1 #"+"
0 0 24 3 1 #" "
0 0 21 3 1 #"1"
0 0 24 3 2 #" ("
0 0 14 3 1 #"+"
0 0 24 3 1 #" "
0 0 21 3 1 #"2"
0 0 24 3 2 #" ("
0 0 14 3 1 #"+"
0 0 24 3 1 #" "
0 0 21 3 1 #"3"
0 0 24 3 2 #" ("
0 0 14 3 1 #"+"
0 0 24 3 1 #" "
0 0 21 3 1 #"4"
0 0 24 3 1 #" "
0 0 14 3 5 #"empty"
0 0 24 3 4 #"))))"
0 0 24 29 1 #"\n"
0 0 17 3 15 #";^^^^^^^^^^^^^^"
0 0 24 29 1 #"\n"
0 0 17 3 53 #"; we want to avoid this long chain of partial results"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 71
(
 #"; IDEA: Instead of having to remember the all previous recursive cal"
 #"ls,"
) 0 0 24 29 1 #"\n"
0 0 17 3 6 #"; keep"
0 0 17 3 1 #" "
0 0 17 3 2 #"an"
0 0 17 3 52 #" ACCUMULATOR to flatten all of those partial results"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 39 #"; the accumulator is the same idea from"
0 0 17 3 7 #" foldl:"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 5 #"foldl"
0 0 24 3 1 #" "
0 0 14 3 1 #"+"
0 0 24 3 1 #" "
0 0 21 3 1 #"0"
0 0 24 3 2 #" ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 21 3 1 #"1"
0 0 24 3 1 #" "
0 0 21 3 1 #"2"
0 0 24 3 1 #" "
0 0 21 3 1 #"3"
0 0 24 3 1 #" "
0 0 21 3 1 #"4"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"       "
0 0 17 3 3 #"; ^"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"       "
0 0 17 3 21 #"; initial accumulator"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 55 #"; iterative-sum-list : listof-numbers, number -> number"
0 0 24 29 1 #"\n"
0 0 17 3 57 #"; sums the list using iterative recursion (accumulators!)"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 1 #" "
0 0 14 3 1 #"l"
0 0 14 3 2 #"on"
0 0 24 3 1 #" "
0 0 14 3 11 #"partial-sum"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 17 3 16 #"; same base case"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 14 3 11 #"partial-sum"
0 0 24 3 2 #"  "
0 0 17 3 45 #"; was 0 before, now we return the partial-sum"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 17 3 60
#"; notice how the recursive call wraps the entire \"else\" case"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 17 3 44 #"; there's no (+ 1 ...) trail to leave behind"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 27 #"                          ("
0 0 14 3 1 #"+"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 14 3 11 #"partial-sum"
0 0 24 3 4 #"))))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 2 #" ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 21 3 1 #"1"
0 0 24 3 1 #" "
0 0 21 3 1 #"2"
0 0 24 3 1 #" "
0 0 21 3 1 #"3"
0 0 24 3 1 #" "
0 0 21 3 1 #"4"
0 0 24 3 1 #" "
0 0 21 3 1 #"5"
0 0 24 3 1 #" "
0 0 21 3 1 #"6"
0 0 24 3 1 #" "
0 0 21 3 1 #"7"
0 0 24 3 1 #" "
0 0 21 3 1 #"8"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 17 #"                 "
0 0 21 3 1 #"0"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 15 #"               "
0 0 17 3 3 #"; ^"
0 0 24 29 1 #"\n"
0 0 24 3 15 #"               "
0 0 17 3 49 #"; remember, we need to specify the start value of"
0 0 24 29 1 #"\n"
0 0 24 3 15 #"               "
0 0 17 3 39 #"; the accumulator, just like with foldl"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 34 #"; but that's kind of annoying....."
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 51 #"; IDEA: Use local to write a wrapper around our new"
0 0 24 29 1 #"\n"
0 0 17 3 53 #"; iterative recursive function, in order to eliminate"
0 0 24 29 1 #"\n"
0 0 17 3 50 #"; the need for the user to specify the start value"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 44 #"; better-sum-list : listof-numbers -> number"
0 0 24 29 1 #"\n"
0 0 17 3 65
#"; sums the list using iterative recursion, and NO extra '0' input"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 15 #"better-sum-list"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 15 3 5 #"local"
0 0 24 3 2 #" ["
0 0 17 3 47 #"; I just copy-pasted iterative-sum-list here..."
0 0 24 29 1 #"\n"
0 0 24 3 11 #"          ("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #" "
0 0 14 3 11 #"partial-sum"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 13 #"            ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 17 3 16 #"; same base case"
0 0 24 29 1 #"\n"
0 0 24 3 16 #"                "
0 0 14 3 11 #"partial-sum"
0 0 24 3 2 #"  "
0 0 17 3 45 #"; was 0 before, now we return the partial-sum"
0 0 24 29 1 #"\n"
0 0 24 3 17 #"                ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 37 #"                                    ("
0 0 14 3 1 #"+"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 14 3 11 #"partial-sum"
0 0 24 3 5 #"))))]"
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 17 3 69
(
 #"; In the body of the local, make the \"starting call\" with the 0 va"
 #"lue"
) 0 0 24 29 1 #"\n"
0 0 24 3 5 #"    ("
0 0 14 3 15 #"sum-list-helper"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #" "
0 0 21 3 1 #"0"
0 0 24 3 3 #")))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 73
(
 #"; GENERAL PROCESS: writing a wrapper over an iterative recursive fun"
 #"ction"
) 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 66
#"; Step 1 - write the wrapper's signature and stub out the function"
0 0 24 29 1 #"\n"
0 0 17 3 55 #"; typically you want to eliminate the accumulator input"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7          85 4           0 0           0 13 0 17 3 44
#"; better-sum-list : listof-numbers -> number"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 15 #"better-sum-list"
0 0 24 3 1 #" "
0 0 14 3 10 #"better-lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 2 #"  "
0 0 14 3 3 #"..."
0 0 24 3 1 #")"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 22 #"; Step 2 - add a local"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7         265 4           0 0           0 43 0 17 3 44
#"; better-sum-list : listof-numbers -> number"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 15 #"better-sum-list"
0 0 24 3 1 #" "
0 0 14 3 10 #"better-lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 15 3 5 #"local"
0 0 24 3 2 #" ["
0 0 14 3 7 #"...your"
0 0 24 3 1 #" "
0 0 14 3 3 #"old"
0 0 24 3 1 #" "
0 0 14 3 8 #"function"
0 0 24 3 1 #" "
0 0 14 3 4 #"will"
0 0 24 3 1 #" "
0 0 14 3 2 #"go"
0 0 24 3 1 #" "
0 0 14 3 7 #"here..."
0 0 24 3 1 #"]"
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 14 3 6 #"...you"
0 0 21 3 1 #"'"
0 0 14 3 2 #"ll"
0 0 24 3 1 #" "
0 0 14 3 4 #"call"
0 0 24 3 1 #" "
0 0 14 3 4 #"your"
0 0 24 3 1 #" "
0 0 14 3 3 #"old"
0 0 24 3 1 #" "
0 0 14 3 8 #"function"
0 0 24 3 1 #" "
0 0 14 3 7 #"here..."
0 0 24 3 1 #")"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 62
#"; Step 2.5 - copy your old function inside the square brackets"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7         433 4           0 0           0 71 0 17 3 44
#"; better-sum-list : listof-numbers -> number"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 15 #"better-sum-list"
0 0 24 3 1 #" "
0 0 14 3 10 #"better-lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 15 3 5 #"local"
0 0 24 3 3 #" [("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #" "
0 0 14 3 11 #"partial-sum"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 13 #"            ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 17 3 16 #"; same base case"
0 0 24 29 1 #"\n"
0 0 24 3 16 #"                "
0 0 14 3 11 #"partial-sum"
0 0 24 3 2 #"  "
0 0 17 3 45 #"; was 0 before, now we return the partial-sum"
0 0 24 29 1 #"\n"
0 0 24 3 17 #"                ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 37 #"                                    ("
0 0 14 3 1 #"+"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 14 3 11 #"partial-sum"
0 0 24 3 5 #"))))]"
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 14 3 6 #"...you"
0 0 21 3 1 #"'"
0 0 14 3 2 #"ll"
0 0 24 3 1 #" "
0 0 14 3 4 #"call"
0 0 24 3 1 #" "
0 0 14 3 4 #"your"
0 0 24 3 1 #" "
0 0 14 3 3 #"old"
0 0 24 3 1 #" "
0 0 14 3 8 #"function"
0 0 24 3 1 #" "
0 0 14 3 7 #"here..."
0 0 24 3 1 #")"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 77
(
 #"; 3 - In the body of your local, add the \"kickoff\" call to your ol"
 #"d function,"
) 0 0 24 29 1 #"\n"
0 0 17 3 53 #"; which you've defined locally in the square brackets"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7         493 4           0 0           0 81 0 17 3 44
#"; better-sum-list : listof-numbers -> number"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 15 #"better-sum-list"
0 0 24 3 1 #" "
0 0 14 3 10 #"better-lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 15 3 5 #"local"
0 0 24 3 3 #" [("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #" "
0 0 14 3 11 #"partial-sum"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 13 #"            ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 17 3 16 #"; same base case"
0 0 24 29 1 #"\n"
0 0 24 3 16 #"                "
0 0 14 3 11 #"partial-sum"
0 0 24 3 2 #"  "
0 0 17 3 45 #"; was 0 before, now we return the partial-sum"
0 0 24 29 1 #"\n"
0 0 24 3 17 #"                ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 37 #"                                    ("
0 0 14 3 1 #"+"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lon"
0 0 24 3 2 #") "
0 0 14 3 11 #"partial-sum"
0 0 24 3 5 #"))))]"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 17 3 34 #"; notice we pass in two arguments:"
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 17 3 7 #"; - the"
0 0 17 3 1 #" "
0 0 17 3 4 #"list"
0 0 17 3 1 #" "
0 0 17 3 5 #"input"
0 0 17 3 1 #" "
0 0 17 3 8 #"provided"
0 0 17 3 1 #" "
0 0 17 3 2 #"to"
0 0 17 3 1 #" "
0 0 17 3 20 #"the wrapper function"
0 0 24 29 1 #"\n"
0 0 24 3 4 #"    "
0 0 17 3 55 #"; - the starting accumulator, which we know is always 0"
0 0 24 29 1 #"\n"
0 0 24 3 5 #"    ("
0 0 14 3 18 #"iterative-sum-list"
0 0 24 3 1 #" "
0 0 14 3 10 #"better-lon"
0 0 24 3 1 #" "
0 0 21 3 1 #"0"
0 0 24 3 3 #")))"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 44 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 17 3 54 #"; Using regular (non-iterative) recursion to implement"
0 0 24 29 1 #"\n"
0 0 17 3 16 #"; map and filter"
0 0 24 29 1 #"\n"
0 0 17 3 1 #";"
0 0 24 29 1 #"\n"
0 0 17 3 8 #"; IDEAS:"
0 0 24 29 1 #"\n"
0 0 17 3 24 #"; 1. pick a sample input"
0 0 24 29 1 #"\n"
0 0 17 3 42 #"; 2. figure out what the output looks like"
0 0 24 29 1 #"\n"
0 0 17 3 65
#"; 3. figure out what the output looks like before it's simplified"
0 0 24 29 1 #"\n"
0 0 17 3 40 #"; 4. try to notice the recursive pattern"
0 0 24 29 1 #"\n"
0 0 17 3 61
#"; 5. Now write a function to build up that thing, recursively"
0 0 24 29 1 #"\n"
0 0 17 3 45 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 33 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 17 3 19 #"; HOW A MAP IS BORN"
0 0 24 29 1 #"\n"
0 0 17 3 33 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 36 #"; map : proc        lst       -> lst"
0 0 24 29 1 #"\n"
0 0 17 3 43 #";       (A -> B)    (listof A)   (listof B)"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 33 #"; thanks-obama : string -> string"
0 0 24 29 1 #"\n"
0 0 17 3 11 #"; demo proc"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 12 #"thanks-obama"
0 0 24 3 1 #" "
0 0 14 3 1 #"s"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 14 3 13 #"string-append"
0 0 24 3 1 #" "
0 0 19 3 19 #"\"Thanks Obama for \""
0 0 24 3 1 #" "
0 0 14 3 1 #"s"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 10 #"; demo lst"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 1 #" "
0 0 14 3 20 #"list-of-great-things"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 19 3 13 #"\"hoverboards\""
0 0 24 3 1 #" "
0 0 19 3 14 #"\"Fall Out Boy\""
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7         289 4           0 0           0 47 0 17 3 7 #"; IDEA:"
0 0 17 3 1 #" "
0 0 17 3 5 #"Using"
0 0 17 3 1 #" "
0 0 17 3 3 #"the"
0 0 17 3 1 #" "
0 0 17 3 5 #"above"
0 0 17 3 1 #" "
0 0 17 3 4 #"proc"
0 0 17 3 1 #" "
0 0 17 3 3 #"and"
0 0 17 3 1 #" "
0 0 17 3 4 #"lst,"
0 0 24 29 1 #"\n"
0 0 17 3 7 #"; write"
0 0 17 3 1 #" "
0 0 17 3 1 #"a"
0 0 17 3 1 #" "
0 0 17 3 8 #"function"
0 0 17 3 1 #" "
0 0 17 3 4 #"that"
0 0 17 3 1 #" "
0 0 17 3 29 #"produces something like this:"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 4 #"cons"
0 0 24 3 2 #" ("
0 0 14 3 12 #"thanks-obama"
0 0 24 3 1 #" "
0 0 19 3 13 #"\"hoverboards\""
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 4 #"cons"
0 0 24 3 2 #" ("
0 0 14 3 12 #"thanks-obama"
0 0 24 3 1 #" "
0 0 19 3 14 #"\"Fall Out Boy\""
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 12 #"            "
0 0 14 3 5 #"empty"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 50 #"; since that's what the resulting list looks like."
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 45 #"; my-map : (A -> B), (listof A) -> (listof B)"
0 0 24 29 1 #"\n"
0 0 17 3 43 #"; NOT with iterative recursion/accumulators"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 6 #"my-map"
0 0 24 3 1 #" "
0 0 14 3 4 #"proc"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 14 3 5 #"empty"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 17 3 16 #"; Recursive step"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 4 #"cons"
0 0 24 3 2 #" ("
0 0 14 3 4 #"proc"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 3 13 #"            ("
0 0 14 3 6 #"my-map"
0 0 24 3 1 #" "
0 0 14 3 4 #"proc"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 5 #")))))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 7         391 4           0 0           0 64 0 24 3 1 #"("
0 0 14 3 6 #"my-map"
0 0 24 3 1 #" "
0 0 14 3 12 #"thanks-obama"
0 0 24 3 1 #" "
0 0 14 3 20 #"list-of-great-things"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 29 #"; expand list-of-great-things"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 6 #"my-map"
0 0 24 3 1 #" "
0 0 14 3 12 #"thanks-obama"
0 0 24 29 1 #"\n"
0 0 24 3 9 #"        ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 19 3 13 #"\"hoverboards\""
0 0 24 3 1 #" "
0 0 19 3 14 #"\"Fall Out Boy\""
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 15 #"; expand my-map"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 4 #"cons"
0 0 24 3 2 #" ("
0 0 14 3 12 #"thanks-obama"
0 0 24 3 1 #" "
0 0 19 3 13 #"\"hoverboards\""
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 6 #"my-map"
0 0 24 3 1 #" "
0 0 14 3 12 #"thanks-obama"
0 0 24 3 2 #" ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 19 3 1 #"\""
0 0 19 3 4 #"Fall"
0 0 19 3 1 #" "
0 0 19 3 8 #"Out Boy\""
0 0 24 3 3 #")))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 23 #"; expand recursive call"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 4 #"cons"
0 0 24 3 1 #" "
0 0 19 3 30 #"\"Thanks Obama for hoverboards\""
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 4 #"cons"
0 0 24 3 1 #" "
0 0 19 3 31 #"\"Thanks Obama for Fall Out Boy\""
0 0 24 29 1 #"\n"
0 0 24 3 12 #"            "
0 0 14 3 5 #"empty"
0 0 24 3 2 #"))"
0           0 0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 33 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 17 3 22 #"; HOW A FILTER IS BORN"
0 0 24 29 1 #"\n"
0 0 17 3 33 #";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 39 #"; filter : pred        lst       -> lst"
0 0 24 29 1 #"\n"
0 0 17 3 46 #";          (A -> bool) (listof A)   (listof A)"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 54 #"; my-filter : (A -> boolean), (listof A) -> (listof A)"
0 0 24 29 1 #"\n"
0 0 17 3 43 #"; NOT with iterative recursion/accumulators"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 15 3 6 #"define"
0 0 24 3 2 #" ("
0 0 14 3 9 #"my-filter"
0 0 24 3 1 #" "
0 0 14 3 4 #"pred"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 3 #"  ("
0 0 14 3 2 #"if"
0 0 24 3 2 #" ("
0 0 14 3 6 #"empty?"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 14 3 5 #"empty"
0 0 24 29 1 #"\n"
0 0 24 3 6 #"      "
0 0 24 29 1 #"\n"
0 0 24 3 7 #"      ("
0 0 14 3 2 #"if"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"       "
0 0 17 3 33 #"; test the first item in the list"
0 0 24 29 1 #"\n"
0 0 24 3 8 #"       ("
0 0 14 3 4 #"pred"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"       "
0 0 17 3 36 #"; if it passes, then cons first item"
0 0 24 29 1 #"\n"
0 0 24 3 8 #"       ("
0 0 14 3 4 #"cons"
0 0 24 3 2 #" ("
0 0 14 3 5 #"first"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 1 #")"
0 0 24 29 1 #"\n"
0 0 24 3 14 #"             ("
0 0 14 3 9 #"my-filter"
0 0 24 3 1 #" "
0 0 14 3 4 #"pred"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 3 #")))"
0 0 24 29 1 #"\n"
0 0 24 3 7 #"       "
0 0 17 3 27 #"; else just skip first item"
0 0 24 29 1 #"\n"
0 0 24 3 8 #"       ("
0 0 14 3 9 #"my-filter"
0 0 24 3 1 #" "
0 0 14 3 4 #"pred"
0 0 24 3 2 #" ("
0 0 14 3 4 #"rest"
0 0 24 3 1 #" "
0 0 14 3 3 #"lst"
0 0 24 3 5 #")))))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 64
#"; EXAMPLE: Calling my-filter with an inline lambda, which checks"
0 0 24 29 1 #"\n"
0 0 17 3 4 #"; if"
0 0 17 3 1 #" "
0 0 17 3 1 #"a"
0 0 17 3 1 #" "
0 0 17 3 6 #"number"
0 0 17 3 1 #" "
0 0 17 3 2 #"is"
0 0 17 3 1 #" "
0 0 17 3 4 #"over"
0 0 17 3 5 #" 9000"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 24 3 1 #"("
0 0 14 3 9 #"my-filter"
0 0 24 29 1 #"\n"
0 0 24 3 1 #" "
0 0 17 3 18 #"; number -> number"
0 0 24 29 1 #"\n"
0 0 24 3 1 #" "
0 0 17 3 33 #"; checks if a number is over 9000"
0 0 24 29 1 #"\n"
0 0 24 3 2 #" ("
0 0 15 3 6 #"lambda"
0 0 24 3 2 #" ("
0 0 14 3 1 #"n"
0 0 24 3 3 #") ("
0 0 14 3 1 #">"
0 0 24 3 1 #" "
0 0 14 3 1 #"n"
0 0 24 3 1 #" "
0 0 21 3 4 #"9000"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 3 2 #" ("
0 0 14 3 4 #"list"
0 0 24 3 1 #" "
0 0 21 3 1 #"0"
0 0 24 3 1 #" "
0 0 21 3 1 #"1"
0 0 24 3 1 #" "
0 0 21 3 1 #"2"
0 0 24 3 1 #" "
0 0 21 3 4 #"9001"
0 0 24 3 2 #"))"
0 0 24 29 1 #"\n"
0 0 24 29 1 #"\n"
0 0 17 3 30 #"; this will return (list 9001)"
0           0