ListsofLists

CS5010ProgramDesignParadigms“Bootcamp”Lesson6.5

1©MitchellWand,2012-2015ThisworkislicensedunderaCreative Commons Attribution-NonCommercial 4.0 International License.

LearningOutcomes

• Attheendofthislesson,thestudentshouldbeableto– GiveexamplesofS-expressions– Give3reasonswhyS-expressionsareimportant–WritethedatadefinitionandtemplateforS-expressions

–WritefunctionsonS-expressionsusingthetemplate

2

S-expressions(informally)

• AnS-expressionissomethingthatiseitherastringoralistofS-expressions.

• Soifit'salist,itcouldcontainstrings,orlistsofstrings,orlistsoflistsofstrings,etc.

• Thinkofitasanestedlist,wherethere'snoboundonhowdeepthenestingcanget.

3

SomeHistory• AnS-expressionisakindofnestedlist,thatis,alistwhoseelementsmay

beotherlists.HereisaninformalhistoryofS-expressions.• S-expressionswereinventedbyJohnMcCarthy (1927-2011)forthe

programminglanguageLispin1958.McCarthyinventedLisptosolveproblemsinartificialintelligence.

• Lispintroducedlists,S-expressions,andparenthesizedsyntax.ThesyntaxofLispanditsdescendants,likeRacket,isbasedonS-expressions.

• TheuseofS-expressionsforsyntaxmakesiteasytoreadandwriteprograms:allyouhavetodoisbalanceparentheses.Thisismuchsimplerthanthesyntaxofotherprogramminglanguages,whichhavesemicolonsandotherrulesthatcanmakeprogramshardertoread.

• S-expressionsareoneofthegreatinventionsofmodernprogramming.TheyweretheoriginalideafromwhichthingslikeXMLandJSONgrew.

4

Examples"alice""bob""carole"(list "alice" "bob")(list (list "alice" "bob") "carole")(list "dave"

(list "alice" "bob") "carole")

(list (list "alice" "bob") (list (list "ted" "carole")))

5

HerearesomeexamplesofS-expressions, inlist notation

(SeeLesson4.1)

Examples

"alice""bob""carole"("alice" "bob")(("alice" "bob") "carole")("dave" ("alice" "bob") "carole")(("alice" "bob") (("ted" "carole")))

6

HerearethesameexamplesofS-expressions,inwrite notation(SeeLesson4.1).Weoftenusewritenotationbecauseitismore

compact.

DataDefinition

AnS-expressionofStrings(SoS)iseither-- aString-- aListofSoS's (LoSS)

AListofSoS's (LoSS)iseither-- empty-- (consSoS LoSS)

7

Let'swritedownaprecisedefinition:• AnS-expressioniseitherastring

oralistofS-expressions• AlistofS-expressions iseither

emptyortheconsofanS-expressionsandanother listofS-expressions.

• Notethatthedatadefinitionfor"listofS-expressions"followsthefamiliarpatternforlists.

• Thesetwodefinitionsaremutuallyrecursive,asyoucanseefromthetwoarrows

Thisismutualrecursion

SoS LoSS

8

definedintermsof

definedintermsof

DataStructures

"alice""bob""carole"("alice" "bob")

9

"alice" "bob"

AlistofS-expressionsisimplementedasasingly-linked list.Hereisanexample.

DataStructures

(("alice" "bob") "carole")

10

"carole"

"alice" "bob" Hereisaslightlymorecomplicatedexample.Observethatthefirst ofthislistisanother list.Thefirst ofthefirstisthestring"alice".

DataStructures(cont'd)

("alice" (("alice" "bob") "carole")"dave")

11

"carole"

"alice" "bob"

"alice" "dave"

Hereisastillmorecomplicatedexample.

ThetemplaterecipeQuestion Answer

Doesthedatadefinition distinguishamongdifferentsubclassesofdata?

Yourtemplateneedsasmanycondclausesassubclassesthatthedatadefinition distinguishes.

Howdothesubclassesdifferfromeachother?

Usethedifferences toformulateaconditionperclause.

Doanyoftheclausesdealwithstructuredvalues?

Ifso,addappropriateselectorexpressionstotheclause.

Doesthedatadefinition useself-references?

Formulate``naturalrecursions''forthetemplatetorepresenttheself-referencesofthedatadefinition.

Doanyofthefieldscontaincompound ormixeddata?

Ifthevalueofafieldisafoo, addacalltoafoo-fn touseit.

12

Rememberthetemplaterecipe

Template:functionscomeinpairs;; sos-fn : SoS -> ??(define (sos-fn s)(cond[(string? s) ...][else (loss-fn s)]))

;; loss-fn : LoSS -> ??(define (loss-fn los)(cond[(empty? los) ...][else (... (sos-fn (first los))

(loss-fn (rest los)))]))

13

(firstlos)isaSoS.Thisismixeddata,sothelastruleinthetemplaterecipetellsusweneedtowrapitina(sos-fn ...).

Thisismutualrecursion

sos-fn loss-fn

14

definedintermsof

definedintermsof

Onefunction,onetask

• Eachfunctiondealswithexactlyonedatadefinition.

• Sofunctionswillcomeinpairs• Writecontractsandpurposestatementstogether,or

• Writeone,andtheotheronewillappearasawishlist function

15

occurs-in?;; occurs-in? : SoS String -> Boolean;; returns true iff the given string occurs somewhere in

the given sos.;; occurs-in-loss? : LoSS String -> Boolean;; returns true iff the given string occurs somewhere in

the given loss.

16

Here'sanexampleofapairofrelatedfunctions:occurs-in? ,whichworksonaSoS,andoccurs-in-loss? ,whichworksonaLoSS.

Examples/Tests(check-equal?

(occurs-in? "alice" "alice")true)

(check-equal? (occurs-in? "bob" "alice")false)

(check-equal?(occurs-in? (list "alice" "bob")"cathy")

false)

(check-equal?(occurs-in? (list (list "alice" "bob")

"carole") "bob")

true)

(check-equal? (occurs-in? (list "alice"

(list (list "alice" "bob") "dave")

"eve")"bob")

true)17

sos-and-loss.rkt

18

sos-and-loss.rkt

19

Theinspiration forthislivecoding exercisecomesfromhere orhere. Backgroundinformation

Livecoding:sos-and-loss.rkt

• occurs-in?:http://youtu.be/w_URqq2LrQU• number-of-strings:http://youtu.be/9z-jdukgRx4

20

Theinspiration forthislivecoding exercisecomesfromhere andhere (ignorethesappymusic).Backgroundinformation

TheS-expressionpattern

Candothisforthingsotherthanstrings:An SexpOfX is either-- an X-- a ListOfSexpOfX

A ListOfSexpOfX is either-- empty-- (cons SexpOfX ListOfSexpOfX)

21

TheTemplateforSexpX;; sexp-fn : SexpOfX-> ??(define (sexp-fn s)(cond[(X? s) ...][else (losexp-fn s)]))

;; losexp-fn : ListOfSexpOfX -> ??(define (losexp-fn los)(cond[(empty? los) ...][else (... (sexp-fn (first los))

(losexp-fn (rest los)))]))

22

(firstlos)isaSexpOfX.Thisismixeddata,sothelastruleinthetemplaterecipetellsusweneedtowrapitina(sexp-fn ...).

Sexp ofSardines

An SoSardines is either-- a Sardine-- a LoSSardines

A LoSSardines is either-- empty-- (cons SoSardines

LoSSardines)

23

AnExampleoftheSexpOfX pattern.

TheTemplateforSoSardines;; sosard-fn : SoSardines -> ??(define (sosard-fn s)(cond[(sardine? s) ...][else (lossard-fn s)]))

;; lossard-fn : LoSSardines -> ??(define (lossard-fn los)(cond[(empty? los) ...][else (... (sosard-fn (first los))

(lossard-fn (rest los)))]))

24

Summary

• NestedListsoccurallthetime• Mutuallyrecursivedatadefinitions• Mutualrecursioninthedatadefinitionleadstomutualrecursioninthetemplate

• Mutualrecursioninthetemplateleadstomutualrecursioninthecode

25

MoreExamples;; number-of-strings : SoS -> Number;; number-of-strings-in-loss : LoSS -> Number;; returns the number of strings in the given sos or

loss.

;; characters-in : SoS -> Number;; characters-in-loss : LoSS -> Number;; returns the total number of characters in the strings

in the given sos or loss.

;; number-of-sardines : SoSardines -> Number;; returns the total number of sardines in the given

SoSardines.

26

Summary

• Youshouldnowbeableto:– GiveexamplesofS-expressions– Give3reasonswhyS-expressionsareimportant–WritethedatadefinitionandtemplateforS-expressions

–WritefunctionsonS-expressionsusingthetemplate

27

NextSteps

• Studythefile06-5-sos-and-loss.rktintheExamplesfolder

• Ifyouhavequestionsaboutthislesson,askthemontheDiscussionBoard

• DoGuidedPractice6.5• Goontothenextlesson

28