kef laio 7 logikìc programmatismìc: h gl¸ssa prologcgi.di.uoa.gr/~prondo/languages/ch6.pdf ·...

Kef�laio 7

Logikìc Programmatismìc:

H Gl¸ssa Prolog

P. Rontogi�nnhc

Ejnikì kai Kapodistriakì Panepist mio Ajhn¸n

Tm ma Plhroforik c kai Thlepikoiwni¸n

P. Rontogi�nnhc Logikìc Programmatismìc

Basik� StoiqeÐa Gl¸ssac Prolog

OrismoÐ (statements): EpiteloÔn to rìlo entol¸nstic klassikèc gl¸ssec programmatismoÔ

Gegonìta

Kanìnec

Erwt seic

'Oroi (terms): Monadik dom dedomènwn Prolog


Gegonìc

EÐnai to aploÔstero eÐdoc orismoÔ, pou uposthrÐzei hProlog.

Parèqei trìpo èkfrashc thc sqèshc pou isqÔeian�mesa se ontìthtec.


Par�deigma Gegonìtoc

Gegonìc

father (john, mary).

Ekfr�zei ìti o john eÐnai patèrac thc mary ìti h sqèshfather isqÔei an�mesa sta �toma john kai mary.


OrismoÐ

Sqèseic ìpwc to father onom�zontaikathgor mata.

Oi ontìthtec mary kai john onom�zontai orÐsmatatou kathgor matoc.

'Ena kathgìrhma mazÐ me ta orÐsmata pouperilamb�nei onom�zetai atomikìc tÔpoc.


Sqèsh Plus

SÔnolo gegonìtwn

plus(0,0,0).

plus(0,1,1).

plus(1,0,1).

plus(2,0,2).

plus(0,2,2).


Sqèsh Plus

OrÐzei thn prìsjesh fusik¸n arijm¸n

Den mporeÐ na oristeÐ apokleistik� me th qr shgegonìtwn

ApaiteÐtai �peiroc arijmìc gegonìtwn, (ìpwc

parap�nw)


Metablhtèc

H Prolog epitrèpei th qr sh metablht¸n se

Gegonìta, kanìnec kai erwt seic

Oi metablhtèc arqÐzoun p�nta me kefalaÐo gr�mma

H qr sh metablht¸n epitrèpei thn èkfrash sunìlougegonìtwn

Par�deigma

plus(0,X,X).

Ekfr�zei thn idiìthta tou oudèterou stoiqeÐou thcprìsjeshc.


Erwt seic

Parèqoun th dunatìthta exagwg c plhroforÐac apìèna logikì prìgramma.

DiereunoÔn thn isqÔ miac sqèshc an�mesa seorismènec ontìthtec.


Par�deigma

Er¸thsh

?-father(john, mary).

Diereun� an h sqèsh father isqÔei an�mesa sta �tomajohn kai mary.


Par�deigma

Er¸thsh

An èqei dojeÐ sthn Prolog to gegonìc:

father(john, mary).

Tìte h ap�nthsh sthn er¸thsh ?-father(john, mary).

ja eÐnai YES.


Metablhtèc kai Erwt seic (1)

Er¸thsh

?-father(X,mary).

Diab�zetai wc: {Up�rqei k�poio prìswpo X to opoÐo eÐnaipatèrac thc mary?}


Metablhtèc kai Erwt seic (2)

MÐa er¸thsh mporeÐ na epistrèyei perissìterec apìmÐa apant seic.

Par�deigma

An èqoume d¸sei sthn Prolog dÔo gegonìta

father(john, mary).

father(john, ann).

Tìte h er¸thsh: ?-father(john, X).

Ja epistrèyei dÔo lÔseic X=mary kai X=ann


SÔnjetec Erwt seic

Er¸thsh

?-father(X,mary), father(X,ann)

Anazht� to prìswpo pou eÐnai patèrac thc mary kai thcann.

H sÔnjeth er¸thsh apoteleÐtai apì upoerwt seic(kl seic). Oi kl seic se mÐa sÔnjeth er¸thshqwrÐzontai metaxÔ touc me kìmma, pou èqei thn ènnoialogikoÔ {kai}.

Gia na alhjeÔei mÐa sÔnjeth er¸thsh prèpei naalhjeÔoun ìlec oi aploÔsterec erwt seic, pou thnapoteloÔn.


Kanìnec

Epitrèpoun ton orismì nèwn sqèsewn wc sun�rthsh�llwn sqèsewn.

Par�deigma

son(X,Y):-father(Y,X), male(X).

OrÐzei th sqèsh son wc sun�rthsh twn sqèsewn father

kai male.Diab�zetai wc: {O X eÐnai giìc tou Y an o Y eÐnai patèractou X kai o X eÐnai gènouc arsenikoÔ}.

To sÔmbolo {:-} diab�zetai san {e�n}, en¸ to {,}wc {kai}.


AnadromikoÐ Kanìnec

Par�deigma

ancestor(X,Y):-parent(X,Y).

ancestor(X,Y):-parent(X,Z), ancestror(Z,Y).

H sqèsh ancestor (prìgonoc) mporeÐ na orisjeÐ me qr shdÔo kanìnwn, ek twn opoÐwn o ènac eÐnai anadromikìc.

Genik�, ènac kanìnac èqei th morf

H:-B1,...,Bn.

ìpou to H lègetai kefal tou kanìna kai oi atomikoÐtÔpoi B1,...,Bn, apoteloÔn to s¸ma tou kanìna.


'Oroi

Basik dom ston logikì programmatismì

Stajer� (ìpwc john), metablht (ìpwc X) sÔnjetocìroc

O sÔnjetoc ìroc apoteleÐtai apì èna sunarthsiakì

sÔmbolo (functional symbol), pou efarmìzetai se

akoloujÐa apì ìrouc.

Par�deigma

list(a,nil)

ìpou list to sunarthsiakì sÔmbolo kai a,nil stajerèc


'Oroi

Qr sh gia kwdikopoÐhsh sÔnjetwn morf¸nplhroforÐac

Par�deigma

Orismìc kathgor matoc book, pou lamb�nei sanparamètrouc ìrouc gia perigraf twn qarakthristik¸nthc ènnoiac biblÐo. Me ton trìpo autì dhmiourgeÐtai mÐaapl b�sh dedomènwn:

book(author(surname(stoll), name(robert)),

subject(logic)).

book(author(surname(kleene), name(steven)),

subject(mathematics)).


'Oroi

Diafor� an�mesa sta

book (ìnoma kathgor matoc)

author, surname, name, subject (sunarthsiak�sÔmbola)


Par�deigma

Er¸thsh

Anaz thsh onomatepwnÔmwn, pou èqoun gr�yei biblÐa selogik

?-book(author(surname(X), name(Y)),

subject(logic)).

Er¸thsh

An den endiafèroun ta mikr� onom�twn suggrafèwn, her¸thsh mporeÐ na tejeÐ:

?-book(author(surname(X), ), subject(logic)).

'Opou me { } sumbolÐzontai oi ìroi twn opoÐwn h tim denmac endiafèrei.


'Oroi

Graf programm�twn ìqi mìno me qr sh kanìnwn kaigegonìtwn

Par�deigma

Orismìc thc sqèshc nat(X), h opoÐa alhjeÔei ìtan Qfusikìc arijmìc.

'Enac trìpoc eÐnai na sumfwnhjeÐ h anapar�stashtwn fusik¸n arijm¸n antÐ gia 0, 1, 2, . . . me0, s(0), s(s(0)), . . .

To sunarthsiakì sÔmbolo s ekfr�zei thn ènnoia tou{epìmenou arijmoÔ}.


Par�deigma

To prìgramma gia to nat gr�fetai:

Prìgramma

nat(0).

nat(s(X)):-nat(X).

Parìmoia orÐzontai kai �llec sqèseic p�nw se fusikoÔcarijmoÔc.


Par�deigma

To plus(X,Y,Z) eÐnai alhjèc an to Z eÐnai to �jroismatwn X kai Y.

Prìgramma

plus(0,X,X).

plus(s(X),Y,s(Z)):-plus(X,Y,Z).

Jètontac thn er¸thsh: ?-plus(s(0), s(0),K).

PaÐrnoume thn ap�nthsh K = s(s(0)).


OrÐsmata

Sthn Prolog den gÐnetai kajorismìc poia apì taorÐsmata enìc kathgor matoc eÐnai eÐsodoi kai poiaèxodoi.

Poll� progr�mmata èqoun diaforetikèc qr seic

Par�deigma: An tejeÐ h er¸thsh:?-plus(X,s(0), s(s(s(0)))).

DÐnetai h ap�nthsh X=s(s(0)), pou antistoiqeÐ stonarijmì, pou lamb�netai an afairèsoume apì to trÐtoìrisma to deÔtero.


Ektèlesh Programm�twn Prolog

'Estw to prìgramma

Prìgramma

grandparent(X,Y):-parent(X,Z), parent(Z,Y).

parent(tom,jim).

parent(jim,george).

'Otan tejeÐ h er¸thsh:?-grandparent(A,B). o mhqanismìcektèleshc thc Prolog ekteleÐ anaz thsh lÔsewn thc morf ctou dèntrou, pou akoloujeÐ.


Dèntro ektèleshc thc er¸thshc

grandparent(A,B)

parent(A,Z),parent(Z,B)

parent(jim,B)

�

{A=tom,Z=jim}

parent(george,B)

fail

{A=jim,Z=george}


Ektèlesh Programm�twn Prolog

Arqik� o mhqanismìc thc Prolog anazht� stoprìgramma kathgìrhma me to ìnoma grandparent

¸ste na tairi�zei me th dedomènh er¸thsh.

Mìlic brejeÐ prìtash, pou afor� autì tokathgìrhma, antikajist� thn dedomènh er¸thsh me tos¸ma thc prìtashc kai dhmiourgeÐtai nèa (sÔnjeth)er¸thsh parent(A,Z), parent(Z,B).


Mhqanismìc Ektèleshc Prolog

'Estw ìti èqoume èna prìgramma kai mÐa er¸thsh thcmorf c ?− A1, . . . , An. Tìte:

H Prolog exet�zei e�n ikanopoioÔntai ìloi oi stìqoiA1, . . . , An xekin¸ntac apì to A1 kai phgaÐnontac procto An.

Gia na ikanopoi sei èna apì ta Ai h Prolog,

dialègei thn pr¸th prìtash sto prìgramma thc

opoÐac h kefal tairi�zei me to Ai,

kai antikajist� to Ai me to s¸ma thc prìtashc

aut c (afoÔ pr¸ta to tropopoi sei kat�llhla).

H diadikasÐa suneqÐzetai mèqri na mhn up�rqei plèon�llh kl sh, pou na prèpei na ikanopoihjeÐ.


Apl� Anadromik� Progr�mmata se Prolog

Me th qr sh ìrwn gr�fontai apl� kai ekfrastik�progr�mmata, ìpwc to

Prìgramma

plus(0,X,X).

plus(s(X),Y,s(Z)):-plus(X,Y,Z).

'Omoia orÐzetai gia ton pollaplasiasmì fusik¸narijm¸n

Prìgramma

times(0,X,0).

times(s(X),Y,Z):-times(X,Y,W), plus(W,Y,Z).


Sqìlia

H parap�nw sqèsh qrhsimopoieÐ dÔo basik�axi¸mata tou pollaplasiasmoÔ:

0 · X = 0(X + 1) · Y = X · Y + Y

O orismìc tou pollaplasiasmoÔ qrhsimopoieÐ autìnthc prìsjeshc


Majhmatikèc Sqèseic Fusik¸n Arijm¸n

Me qr sh tou orismoÔ tou pollaplasiasmoÔ dÐnetai hsqèsh gia to paragontikì enìc fusikoÔ arijmoÔ

Prìgramma

factorial(0,s(0)).

factorial(s(N),F):-factorial(N,F1),times(s(N),F1,F).


Majhmatikèc Sqèseic Fusik¸n Arijm¸n

Sqèsh between(X,Y,Z): alhjeÔei ìtan X eÐnai ènacfusikìc arijmìc mikrìteroc Ðsoc apì ton Y kai o Y eÐnaimikrìteroc Ðsoc apì ton Z.

Prìgramma

between(0,0,Z).

between(0,s(Y),s(Z)):-between(0,Y,Z).

between(s(X),s(Y),s(Z)):-between(X,Y,Z).


Sqìlia

Oi fusikoÐ arijmoÐ anaparÐstantai me polÔ pio bolikìtrìpo sthn Prolog (ìpwc kai stic upìloipec gl¸ssecprogrammatismoÔ).

H anapar�stash, pou qrhsimopoi jhke staparap�nw progr�mmata den eÐnai genik� bolik kaiapotelesmatik . Uiojet jhke gia na deiqjoÔn oiarqikèc dunatìthtec thc Prolog.


Anadromikìc Programmatismìc me LÐstec

LÐsta

PolÔ qr simh dom dedomènwn gia programmatismì seProlog

Ken - sumbolÐzetai me []

Perièqei stoiqeÐa, p.q. h [a,b,c] eÐnai mh ken lÐsta

To pr¸to stoiqeÐo lÐstac onom�zetai kefal (head)H lÐsta pou prokÔptei an afairèsoume thn kefal ,

onom�zetai our� (tail)O telest c | apoteleÐ eidik anapar�stash, pou

deÐqnei �mesa thn kefal kai thn our� miac lÐstac. H

lÐsta [a,b,c] gr�fetai wc [ a|[b,c] ] kai h [a] wc

[a|[ ]].


Par�deigma 7.1

Oi lÐstec Prolog mporoÔn na perièqoun sa stoiqeÐatouc kai �llec lÐstec, all� kai polÔplokouc ìrouc,ìpwc

[[ ]] epitrept lÐsta

[[1,X], s(s(X))]

Oi [ a| [ 1|[2] ] ] kai [X,Y|[a]] eÐnai isodÔnamec metic lÐstec [a,1,2] kai [X,Y,a] antÐstoiqa.


Par�deigma 7.2

H sqèsh member(X,Y) eÐnai alhj c, ìtan to X eÐnaistoiqeÐo thc lÐstac Y.

Prìgramma

member(X,[X|Y]).

member(X,[Y|Z]):-member(X,Z).

To nìhma tou progr�mmatoc eÐnai: {To X eÐnai mèloc miaclÐstac an eÐnai h kefal thc lÐstac an eÐnai mèloc thcour�c thc lÐstac}.


Par�deigma 7.3

H sqèsh append(X,Y,Z) eÐnai alhj c, ìtan to Z eÐnai hlÐsta, pou prokÔptei apì thn sunènwsh twn list¸n X kaiY.

Prìgramma

append([ ],Y,Y).

append([X|Xs],Ys,[X|Zs]):-append(Xs,Ys,Zs).

H dom tou parap�nw progr�mmatoc eÐnai parìmoia meaut tou progr�mmatoc gia ton orismì thc sqèshc plus.


Par�deigma 7.4

Suqn� ston programmatismì se PrologqrhsimopoioÔntai aplèc sqèseic, dh orismènec gia nagrafoÔn pio polÔploka progr�mmata.

Sqèseic ìpwc h member kai h append

qrhsimopoioÔntai sqedìn se opoiod pote meg�loprìgramma grafteÐ se Prolog.


Par�deigma 7.4

Sqèsh reverse(X,Y) orÐzetai sa sun�rthsh thc append.EÐnai alhj c, ìtan h lÐsta Y eÐnai h antÐstrofh thclÐstac X:

Prìgramma

reverse([ ],[ ]).

reverse([X|Xs],Ys):-reverse(Xs,Rs),

append(Rs,[X],Ys).

To nìhma tou parap�nw progr�mmatoc eÐnai: {HantÐstrofh thc ken c lÐstac eÐnai h ken lÐsta.H antÐstrofh mh-ken c lÐstac mporeÐ na paraqjeÐantistrèfontac thn our� thc kai proskoll¸ntac stotèloc thc antestrammènhc our�c thn kefal thc arqik clÐstac.}


Par�deigma 7.4

To prohgoÔmeno par�deigma mporeÐ na grafeÐ kai qwrÐcth qr sh thc append, all� me prosj kh enìc bohjhtikoÔkathgor matoc tou reverse1, pou diajètei èna epiplèonìrisma:

Prìgramma

reverse(Xs, Ys):-reverse1(Xs,[ ],Ys).

reverse1([ ],Ys, Ys).

reverse1([X|Xs],A,Ys):-reverse1(Xs,[X|A],Ys).

To ìrisma A onom�zetai susswreut c (accumulator)diìti susswreÔei b ma-b ma to telikì apotèlesma (dhlad thn antÐstrofh lÐsta).


Anadromikìc Programmatismìc me Dèntra

Dèntra

PolÔ qr simoc tÔpoc dedomènwn

AnaparÐstantai me qr sh ìrwn (monadik dom dedomènwn Prolog)

Qr sh tou sunarthsiakoÔ sumbìlou tree me treic

paramètrouc:

tree(Element, Left, Right)

To stoiqeÐo Element eÐnai h rÐza tou sugkekrimènou

dèntrou, to Left to aristerì upìdentro kai to Right

to dexÐ upodèntro.To kenì dèntro anaparÐstatai me th stajer� void.


Par�deigma

Par�deigma

Dèntro me koruf a, aristerì paidÐ b kai dexÐ paidÐ cgr�fetai wc:

tree(a, tree(b,void,void), tree(c,void, void))


Par�deigma

Prìgramma gia èlegqo tou an ènac dedomènoc ìroc eÐnaipr�gmati duadikì dèntro (an�logo tou kathgor matocnat)

Prìgramma

binary tree(void).

binary tree(tree(E,L,R)):-binary tree(L),

binary tree(R).


Par�deigma

Prìgramma gia èlegqo tou an èna dedomèno stoiqeÐoan kei se èna dèntro ìqi. To prìgramma eÐnai an�logome to member , pou orÐsjhke gia tic lÐstec:

Prìgramma

tree member(X, tree(X, , )).

tree member(X, tree(Y,L,R)):-tree member(X,L).

tree member(X, tree(Y,L,R)):-tree member(X,R).


Par�deigma

To parap�nw prìgramma elègqei an èna dedomènostoiqeÐo eÐnai tautìshmo me thn koruf tou dedomènoudèntrou.

An nai, to prìgramma stamat� me epituqÐa.

An ìqi, to prìgramma suneqÐzei anadromik� thdiereÔnhsh sto aristerì kai to dexÐ upodèntro.


Kathgor mata

Ousiastik� {diasqÐzoun} èna dedomèno dèntro me mÐaprokajorismènh seir�.

To apotèlesma thc di�sqishc epistrèfetai se mÐalÐsta.


Par�deigma

H preorder di�sqish enìc duadikoÔ dèntrou orÐzetai apì toakìloujo kathgìrhma:

Prìgramma

preorder(void,[ ]).

preorder(tree(X,L,R),Xs):-preorder(L,Ls),

preorder(R,Rs),

append([X|Ls],Rs,Xs).

Kat� thn preorder di�sqish enìc dèntrou katagr�fetaiarqik� h rÐza tou dèntrou kai katìpin episkeptìmasteanadromik� pr¸ta to aristerì upodèntro kai met� to dexÐ.


Par�deigma

Me an�logo trìpo gr�fetai prìgramma, pou ulopoieÐ thndi�sqish inorder:

Prìgramma

inorder(void,[ ]).

inorder(tree(X,L,R),Xs):-inorder(L,Ls),

inorder(R,Rs),

append(Ls,[X|Rs],Xs).


Par�deigma

Prìgramma gia thn postorder di�sqish:

Prìgramma

postorder(void,[ ]).

postorder(tree(X,L,R),Xs):-postorder(L,Ls),

postorder(R,Rs),

append(Ls,Rs,Ms),

append(Ms,[X],Xs).

Ta parap�nw progr�mmata diafèroun mìno wc proc tontrìpo, pou gÐnetai h sunènwsh twn epimèroucapotelesm�twn (append).


Telestèc

Sunarthsiak� sÔmbola

Qr sh se epexergasÐa pio polÔplokwn dom¸n apì ìtioi lÐstec kai ta dèntra

Sthn èkfrash 1+3, to + eÐnai telest c

IsodÔnamh èkfrash +(1,3) kai ìqi o arijmìc 4, ìpwc

sumbaÐnei se �llec gl¸ssec programmatismoÔ

H prìsjesh ja pragmatopoioÔtan an o ìroc 1+3

tan ìrisma sto eidikì kathgìrhma is thc Prolog gia

upologismì arijmhtik¸n ekfr�sewn


Telestèc (2)

Oi telestèc +,-,*,/,... den lamb�noun sugkekrimènonìhma apì thn Prolog

QrhsimopoioÔntai gia na grafoÔn efarmogèc mekomyì kai sunoptikì trìpo

Sto epìmeno par�deigma oi telestècqrhsimopoioÔntai, gia th diatÔpwsh thc diadikasÐacparag¸gishc sunart sewn


Parag¸gish

Prìgramma

derivative(N,X,0):-nat(N).

derivative(X,X,s(0)).

derivative(X^s(N),X,s(N)*(X^N)).

derivative(sin(X),X,cos(X)).

derivative(cos(X),X,-sin(X)).

derivative(e^X,X,e^X).

derivative(log(X),X,1/X).


Parag¸gish

Prìgramma

derivative(F+G, X, DF+DG):-

derivative(F,X,DF),derivative(G,X,DG).

derivative(F-G, X, DF-DG):-


derivative(F*G, X, F*DG+G*DF):-


derivative(1/F, X, -DF/(F*F)):-

derivative(F,X,DF).

derivative(F/G, X, G*DF-F*DG/(G*G)):-

derivative(F,X,DF), derivative(G,X,DG).


Parag¸gish

To prìgramma upologÐzei thn par�gwgo mÐacmeg�lhc kathgorÐac sunart sewn.

Oi telestèc, pou qrhsimopoioÔntai ekfr�zoun pr�xeicmetaxÔ sunart sewn.

Thn èkfrash F*G, o programmatist c thnkatalabaÐnei san pollaplasiasmì sunart sewn kaiautì eÐnai dunatì kaj¸c h Prolog den dÐneiprokajorismèno nìhma se sÔmbola, ìpwc to *.


Parag¸gish

An sto parap�nw prìgramma dojeÐ h er¸thsh

?-derivative(cos(x)*(x^s(s(0))),x,D).

H opoÐa anazht� thn par�gwgo thc sun�rthshc cos x · x2

Ja l�boume thn ap�nthsh

D=cos(x)*(s(s(0))*x^s(0))+x^s(s(0))*(-sin(x))

H opoÐa antistoiqeÐ sth sun�rthsh cos x · 2x + x2 · (− sin x).


Arijmhtikèc pr�xeic kai Prolog

K�je gl¸ssa programmatismoÔ parèqei idiaÐtereceukolÐec sth qr sh kai epexergasÐa arijm¸n.

H Prolog diajètei

Eidik� kathgor mata, gnwst� wc kathgor matasust matoc (system predicates).


Kathgor mata Prolog

Basikì kathgìrhma to is, pou qrhsimopoieÐtai sthmorf V is E.

H Prolog upologÐzei thn tim tou E kai an aut h tim sumfwneÐ me to V, tìte epitugq�nei.

An V metablht , tìte lamb�nei thn tim tou E.

'Otan E perièqei metablhtèc me �gnwsth tim thstigm thc ektèleshc, o diermhnèac thc Prolog dÐneim numa l�jouc.


Par�deigma 7.5

H er¸thsh

?-8 is 5+3 epitugq�nei

H er¸thsh

?-5+3 is 8 apotugq�nei

diìti h Prolog blèpei to aristerì mèloc thc san tonìro +(5,3) kai den upologÐzei thn tim tou.


Par�deigma

H er¸thsh

?-X is 5+3

ja d¸sei thn ap�nthsh Q = 8

H er¸thsh

?-X is 2+Y

ja d¸sei m numa l�jouc,diìti h arijmhtik tim tou dexioÔ mèlouc den mporeÐna upologisjeÐ lìgw thc metablht c Y.


Kathgor mata thc Prolog gia arijmhtikèc

pr�xeic

X =:= Y Oi arijmhtikèc timèc twn X kai Y eÐnai ÐdiecX == Y Oi arijmhtikèc. timèc twn X kai Y eÐnai

diaforetikècX < Y H arijmhtik tim tou X eÐnai mikrìterh

apì aut tou Y

X =< Y H arijmhtik tim tou X eÐnai mikrìterh Ðsh apì aut tou Y

X > Y H arijmhtik tim tou X eÐnai megalÔterhapì aut tou Y

X >= Y H arijmhtik tim tou X eÐnai megalÔterh Ðsh apì aut tou Y


Kathgor mata

Me qr sh twn prohgoÔmenwn kathgorhm�twn mporoÔnna xanagrafoÔn kathgor mata pou orÐsjhkan meqr sh twn ìrwn

(p.q. 0, s(0), s(s(0)) . . .)


Kathgor mata

To kathgìrhma plus mporeÐ na orisjeÐ wc:

Prìgramma

plus(X,Y,Z):-Z is X+Y

Meionèkthma: Q�netai h antistreyimìthta k�poiwnprogramm�twn


Kathgor mata

H er¸thsh

?-plus(A,B,8)

ja d¸sei m numa l�jouc (kai ìqi ìla ta zeÔghfusik¸n me �jroisma 8).

Autì sumbaÐnei giatÐ h parap�nw er¸thsh an�getaiapì to mhqanismì thc Prolog sthn er¸thsh

?-8 is A+B


Kathgor mata

Me qr sh kathgorhm�twn sust matoc mporoÔn nagrafoÔn progr�mmata, pou ekteloÔn arijmhtikèc pr�xeicme to sunhjismèno trìpo:

Prìgramma

sumlist([ ],0).

sumlist([I|L],Sum):-sumlist(L,S), Sum is S+I.


Apokop

Progr�mmata Prolog

Anapotelesmatik�, giatÐ to dèntro

anaz thshc eÐnai arket� meg�lo

Endiafèron

'Uparxh lÔshc probl matoc

'Oqi gia thn posìthta eÐdoc lÔsewn


Apokop

Den eÐnai aparaÐthto o mhqanismìc ektèleshc thcProlog na diasqÐsei olìklhro to dèntro anaz thshc,all� èna mèroc tou.

O programmatist c kajodhgeÐ to mhqanismìanaz thshc proc apofug peritt¸n anazht sewn meth bo jeia thc apokop c (cut) (sÔmbolo {!}).


Par�deigma 7.6

'Estw er¸thsh thc morf c

?- A, B, C.

Kai to akìloujo tm ma progr�mmatoc

Prìgramma

B : −A1, · · · , Ak, !, Ak+1, · · · , An.B : −D1, · · · , Dm.B : −F1, · · · , Fk.


Rìloc Apokop c

'Otan o mhqanismìc ektèleshc thc Prolog per�sei apìthn apokop , tìte

ta A1, · · · , Ak den prìkeitai na xanaexetastoÔn gia

epiplèon lÔseic

oi enallaktikèc prot�seic gia to B, pou up�rqoun

sto prìgramma met� thn prìtash, pou perièqei thn

apokop , den prìkeitai na exetastoÔn

K�poiec lÔseic apokìptontai apì th diadikasÐa


Par�deigma 7.7

'Estw to prìgramma:

Prìgramma

father(tom,jim).

male(jim).

son(X,Y):-father(Y,X), male(X).

son(george, jim).

son(john, nick).

Kai h er¸thsh

?-son(S,F).


Par�deigma 7.7

O mhqanismìc thc Prolog ja d¸sei treic lÔseic:

{ S=jim, F=tom }

{ S=george, F=jim }

{ S=john, F=nick }


Par�deigma 7.7

An to prìgramma antikatastajeÐ me to:

Prìgramma

father(tom,jim).

male(jim).

son(X,Y):-father(Y,X), !, male(X).

son(george, jim).

son(john, nick).


Par�deigma 7.7

O mhqanismìc ektèleshc thc Prolog dÐnei th lÔsh

{S=jim, F=tom}.

Oi �llec dÔo lÔseic apokìptontai lìgw tou sumbìlou !,pou den epitrèpei thn exètash twn enallaktik¸nprot�sewn gia to son(S,F).


Sqìlia

H apokop qrhsimopoieÐtai sun jwc ìtan gnwrÐzoumeìti to prìblhma èqei mÐa kai monadik lÔsh kaiepijumoÔme ton periorismì �skopou yaxÐmatoc. Taprogr�mmata eÐnai ètsi pio apotelesmatik�.

H apokop den an kei sto logikì tm ma thc Prologkai gi' autì endèqetai na dhmiourg sei dusnìhtaprogr�mmata. Lanjasmènh qr sh thc perikìpteilÔseic qr simec kai epijumhtèc.


kef laio 7 logikìc programmatismìc: h gl¸ssa prologcgi.di.uoa.gr/~prondo/languages/ch6.pdf ·...

Documents