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PPL Unit 5

Principles of programming languages

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PPL Unit 5

Principles of programming languages

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balamurugan532005
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Functional and Logic Programming Languages Syllabus Introduction to lambda calculus ing language i fundamentals of functional programm Programing with Scheme - Programming with ML.- Introduction ta logic and loge prog Programming with Prolog - multiparadigm languages Contents 5.1 Introduction to Lambda Calculus 5.2 Fundamentals of Functional Programming Languages 53 Programming with Scheme 5.4 Programming with ML 5.5 Introduction to Logie and Logic Programming 5.6 Programming with Prolog 5.7 Comparison between Functional Programming and Logical Programming ‘and Object Oriented Programming Languages 58 Multi-paradigm Languages 5.9 Two Marks Questions with Answers Functional an ogi PAM Laren ning Languay El introduction to Lambda Calculus © The lambda calculus is a formal system for ‘computations based on functions. i ‘Any function which is expressible in the mathematical form 18 als e*Pressibie ww lambda calculus. 5 © The lambda calculus is first formulated by Alonozo Church to expr 1 expressing the matherna computations with functions ‘The name lambda is derived from the Greek letter 2. which is used to denote the binding of variable in function. The letter is arbitrary and basically has ‘¢ Many functional languages like ML, LISP, Haskell are based on lambda calculus, no meaning ‘Syntax of Lambda Calculus The syntax of lambda calculus is very simple. It can be denoted in BNF form as expr 0 ( -) | ( ) | | ‘+ The first rule is called lambda abstraction. It is used for building new functions Parentheses can be used to indicate that some part of an expression belongs together. The second rule represents the function application. The function application ‘means evaluating the function by substituting the values. The expression can be in any form, It can be there in prefix, postix or infix form. As LISP makes use of prefix expression form, many times the lambda calculus is expressed with prefix notation But one can make use of infix form of expression for convenience. ‘The third rule represents the variables. The variables can be any like a, b, ¢ 4, x.y and so on. ‘The forth rule represents the constant. The constant can be some value such as 0, 1, 2 or predefined functions such as +, * and so on. For example ¥ Head Body notner wih varable or Expratsion ®¢pression used 1 forfuncion es a Derivation of (Ax -( + 1 1) 8)is called lambda term. 4697 9S vatlabe > eape sy sy substituting let most symibg Sx-< ‘expr >) 20x always, we get (expr>) = Ox: (( )< er) = (x: ((< variable > < expr >) )) = (x: ((x) )) = (ox (x4) )) = (x: ((X +) )) =x a > 0x: +1) + The parenthesis are needed for function application to eliminate ambiguity + According to syntax description (2x: +1) should be written as @X- (4+ 1). + But in order to increase readability we omit parenthesis, if there is no ambiguity in the expression. EEE Lambda Abstraction The lambda abstraction is 2 wa cevariable> - Princes of Programming anguages__5-# metavariables ranging over lambda expression. The function application associate 1 £2 E3 means (E1 E299) 3. The Av ETE2ES means (x (EIEZE “Thus function application has ger 4. The series of abstraction can be interpreted a5 follows ~ yz means (Ay QE the lambda expression itself denotes the function For example wie function can be denoted as Twice = (if (AX (9) to the left and not ((x-E1E2)E9) precedence than the 2 jpstraction. Free and Bound Variable # In calculus, all the names are local to definitions. In the function Axx we say that xis bound since its occurrence in the body ofthe definition is preceded by 2x ‘A name not preceded by 1 is called free variable. + For example - xx) ‘The variable x is bound variable whereas y isa free variable. ‘The same variable can appear many times in the different context. Some instances of the variable may be bound whereas other are free. ‘+ For example -In the expression y+ y) Qooxy) The variable y in the body of first expression from the left is bound to the first A. Hence vis said to bound in first expression. Whereas variable x is bound to second lambda in the second expression but y is free. Hence in the second expression x is said to be bound variable while y is said to be free variable. Note that y in second expression is totally independent of the y in the first expression. Substitution While simplifying the lambda calculus, forthe expression (x-E) T the argument T will be substituted for x in an expression E. The substitution of a term T for a variable x in E is written as (T/x} E. It can be read as 4 occurrences of x in expression E by the term T. replace eset Propram ing There are ae eee iederstand them that a tone end Lape Programing Largueoes Te follow With the he} wed while s Ine%0N othe oloning SP of eames performing the substitution, Let case, 'S XPressior cxtipresnon F !ONE has no bound occurrences ml Prox Repiace’x in Eby, Replace x in E bye (txt (09) = (ety Similarly, we can obtain the values - 3.UsHexy)= ty) 4. (JdJ/NIx = Goo) Rule 1 : If the free variables of T has no bound occurrence in E then T replaces all occurrences of xin E to form {TIxIE. In the following cases, expression E has no free occurrences if x. 1. (tsly Here expression E contains y and no free occurrence of x. Hence the result will be E itself. Similarly - texy(* zy) = 29) 3. (uxlayy) = @yy) Rule 2: If E has no free occurrence of variable x. then (T/x} = Eis E itself. In following case Rale 3, The fre variable ts in T has a bound occurrence in , Then expression Eis * onmed by renaming bound occurrence of tin E For example 1 uaiaesy=? Functonal and Loge rex ———rssmeerpuiges 5-6 Funatone/ end Ln ae We will introduce a new variable for it as 12. Then replace the by t. Then the expression becomes, Dtini(tx) = [atixen)= zt) Similarly, 2. [Walee) = (tx@zz) = 0x2) CERES tie towing using substitution VOxx 2 i) xy) 2 i) (Axyx) 20 io) xa) (yy) v)(axtayy) Solution: DOxxdz Here is a bind variable and body of & expression is x. The statement for evaluation can be read as replace x by z and throw-away Ax. Oxxz =z i Oxyd z Here x is bind variable binding of x with o OfyS)2) = aye : Oxyx)z = ayz iif) Oxyd zu Binding variable is, substitute xby 2 Oy2)u As the binding v. substitution takes pla and y is free, We will substitute x by 2. Then we will eliminate ‘riable is y and there is no ce and we get expression itself Qy2yu 2 Bow) yy) ¥ im expression (body), Hence no Clearly \ is a binding variable, Place Ay-y tor each x =O ayy) Now visa binding variable. We replace yby ayy = ayy) prope or Homan Lanpuaey 0x09) 2) Oy 22 netent na toe Programming yor the binding Variable y we prown away, ¥ We have substituted variable 2. Due to which Ay will Be Now the term become: romes (Ax. 2 pethe term (x2) iteepy on™” 2) Bu asin this erm binding variable is x- the result will BE Peta conversion ‘The basic operation in la ‘mbda calculus isthe application of expression. For example (x +1))) is equal to alto. +1 variable x anton the labs TNE ME ae singh val 3 forte vas aaa called beta conversion. ersion is lambdas. 'on i a process of simplifying the expression and this removing the ‘There are two approaches for applying beta conversion __1.Pass by value 2. Passby name Let us discuss them with the help of examples - 4.8 by value Consider following expression in which evaluate an expression with arguments (° 3 first and the result of evaluation is substituted, Cae Note : Number of opening brackets are equal to number of closing brackets. ‘The B is used to show evaluation steps So, oxen) an oxi a> wide 2. Pass by name ig method we does not evaluate the expression in early stage. The argument fated directly and at the end when the situation arises such that we ther then evaluation is done. Int expression is substi can not substitute furl sree gna aso called a8 delayed evaluation or outermost evaluation or normal order Prneples of Progamming Lanpunges 5-8 xis ay) Wxeede The call by value reach a normal form faster than call by name. That means fewer bts reductions take place in call by value Verity the flowing equalities ASIN =] where Sis Axyz(xz) (yz) and Lis 2x i twice vice) £ =p ((F (6), where vice is At ffs) Solution: i)Let, SUil=s Gexyz(xzy(yzlM), This isthe value of S (Given) SI is root ran nl an (exyz-xz(y2)) (xx) Boe) (ie) Now we will apply f reductions. But before that we will rename bound variables. xyr2{y2) (docx (boc) xn) mp (anya x2(92)) (230 0) (XII) = Now rename underlined tuple (axyzxalyz))(huuy(avv)Q%x) =p Rename underlined tuple Gaxyzxztyz))uuyavvy(e (a) Now we will solve equation (1) any xaly2)) (a wyv-vytt) =p Place Jur for x as xis bind variable Then eliminate x from hxy2. ¥)\ ayz-(ausn)z{yz (Av vit) = Gayzztyz avs) ve tA) for binding variable» \ezz beomes Bene ate trwe rename ty then, At davst Sllls3 Lis proved ii) The twice function is defined as twice = Af Qi) twvice (tice) £ = twice twice = hice f (twice f) = twice ff (E00) = Hie) FEMI co vtiotvie atowing BAX Ax + XD) DS fi) (Ax Ay -4N(Ax Solution : i) x Grt(enD) DS Gotan? Ges De 52) r bev i Govdy-an(Qx-r978 10 acyl “5 (away -¥5)7 8) 18) ante oxi) 28) eevee L 0 = Support these rule Explain the syntax of lamba ccs in te form of BNF ral a deriving some lamiada expression. Explain the concept ambea abstraction. Explin wth suitable istration in oda coc the concept of Explain th rules used or substitution inl alee 0th stations Write a short note on beta conversion in lambda calculus ee and bound variables, EJ Fundamentals of Functional Programming Languages ; / © Functional languages are those languages in which the basic building block fanctions, awid she ‘* In functional programming the programmer is conce! and not memory related variable storage and assignment sequence. .med only with functionality Features of functional programming language 1. The functional programming languages are modelled on the concept of mathematical functions and make use of only conditional expressions and recursion for the computational purpose. 2. The programs are constructed by building functional applications. That means, the values produced by one or more functions become the parameters to another functions. 3. The purest form of functional programming languages use neither variables nor assignment statements, although this is relaxed somewhat in most applied functional languages. 4, The functional languages can be categorized in two types - Pure functional languages and impure functional languages. a. The pure functional language support only functional paradigm. Example of pure functional language is ML, Haskell. b. The impure functional language can be used to write imperative style programs(For example C is a imperative style programming language). Example of impure functional programming language is LISP, ommonly used functional programming languages: LISP, S sal, Haskell, ML, APL, scheme are some commonly used functional languages. The main domain of pene nm an guagE is used na ental Programmin machine leami, for building 3g language is artificial intelligence 1 Natural lang a8 NPEM sYstems, knowledge representation, ‘Sage processing, modeling speech and vision. > Functional languageis aac for bu ding mathematical software. ‘ame the commonly used te the applications of finctond ye tonal prog B)Programming with Scheme _senetsa dle ip among ge Sees ass rare at the MIT Al Lab and released by its developers, Guy L. Stesle and Gerald Jay Sussman. Features of scheme 1) Tthas ability to evaluate its own code natively 2) It contains a full set of numerical data. 5) Tt has shared namespaces for variables and procedures, That means, SAN" primitives used to operate on variables can operate On ‘procedures and functions as well. |4) The bindings of all variables in scheme are determined by the unit of code that the variable appears. Thisis known as lexical scope sg) The scheme has 2 macro system that owe the programmer to extend the functionality of the language ‘without interfering with the language's native inetionalit syntax. Pere re nity 0a standard procedures and functions eter 5 scheme InterPr ; ExT Tre jnnerpreter is. 2 read-evaluate-write infinite loop, That means the +The scheme lyre on exresson cemtered by user, interprets it and interpreter" displays Ine interpreted by the function EVAL «Expression Prmcpes of Programming Languages __s-12_Furctonel end LOE . » evaluated 35 - firstly, each of the Expressions that call the primitive functions are evaluated hi Parameter expressions are evaluated. Then primitive Parameter values and result is displayed on the interpreter. function is applied to Primitive Numeric Functions Expressions can be created with the help of operators. There are ‘operators such as +, -, * and used for manipulating the scheme, Following ill use of operators >(+23) 5 (23) 6 >¢53) ‘ > (423-53), 10 farious arithmetic ustrates the Note that the evaluation of expression is based on prefix notation. Prefix notation is a notation in which operator comes first and then two operands appear. For instance +23 will be converted to 2 +3 and result of operation will be 5. Defining Fuinctions In scheme we can define a nameless function called lambda function. For example - [enon > (Clambda (x) (* x x)) 12) 144 Here variable x is called bound variable. Similarly, we can define user defined function using define. The syntax is (define function_name parameters) (expression) ones of Programming Ly oeample weean define ne the function na, get edd num sug) CM add as om) rum2) follows - Languages ) Now, We can call the somumbers ‘Bove fancton with two parameters fr performing ation of {084 10 20) Pa rs for perf 8 2 Write a fun, solution = > (define cubs(a) Output (REESE Write procetie to cisplay su of squares. Solution : > (define square(x) x0) > (defun sum-of-square(stat end) (i> start end) ° (4 (equate stan) (sum-of-aquara(+ 1 tat) end) ) I output > (eumof-equare 1 6) 5s ‘Output Functions function 15 Use ction i usin . 4 to display some message or result of expression on the ences g the keyword display. The syntax for output Ninerpreter, The output ae a Principles of Programming Languages 5-14 __Furetonel and PETES Yay For example > (display (+ 23) 5 Similarly we can display the text message using display. For example - > (dlsplay “Weicorne') Welcome ‘The newline can be entered with the help of display functio > (newline) Jn as follows - Numeric Predicate Functions ‘A predicate function is a function that returns boolean value either true(= Operator Purpose Example < Less than, Itreturns true if first operand is (< 1020 less than second argument. > Greater than, Ie returns true if first operand is greater than second argument = It first operand is equal to second operand then it returns true . Less than equal to, >= Greater than equal to Is even number odd oxkd number ote? Ist revo? ¢ ring SPemrme rae: 5.15 peu ma ige Pager ea EE contro! Flow = There are two fwo important control flow stat low statements - 4, IF Statement The if is a two-way ai) Then expression and ii The syntax is (ifptedicate then expression else expression) For example - > (f(> 1020) (display “10 is greater than 20°) (display "10 is lesser than 20) ) 1018 lesser than 20 selector function. It has three parts — i) Predicate exp} i) Else expression. 2, COND Statement ‘The cond is a multiple selector which is based on mathematical expression. Ths of cond statement is as follows - (cond (predicate_1 expression) (predicate_2 expression) (predicate _n exp (else expressicn!] Here, else is optional clause For example ~ Sent {C10 10) play "1018 roar an 1 {(< 10 10) (aispiay “10 Ls Re ie (else (display "30 # ‘equal to 1¢ ) The output willbe Oia equal 10 roche otPepanmngagieges 5.18 ___—_—Furtnsa os AESLay List Functions ‘| The car returns first element of a non empty list For example - > (ear 234) 1 ‘© The cdr returns rest of the lst after the first element is removed. It is pronounced as couldcer. > (oie (12349 as) * We can combine two lists using cons. The cons fur returns a new cons cell containing the two values > (eon 1020 3040) (1020 0 40) Write sequences of CAR’ following sexpresion : 1) (apple orange pear grapes) it) (apple orange) (pear grapes) itt) (apple orange) (pear) (grapes))) Solution : 4) (car(cdr(cdr'(apple orange pear grapes)))) ii) (car(car(ede'((apple orange) (peat grapes))))) ily (can(car(car(cdr(cdr(apple (orange) (peat))((grapes))))))) mnction takes two arguments and, sand CDR’s that wil pick the atom pear out ofthe Predicate Functions for Symbolic Atoms and Lists (1) Equal (eq?) : It takes two arguments and if two arguments are equal then it returns Ht otherwise it returns #f > (oq? gh) “ > (ea? 55) * (2) List(list?) : This predicate is used to test if the argument is list or not. If it is list then it returns #t otherwise it returns #f For example - > (it? (10 20 309) * > fist? 10) ©) Nulinutir, tt (102 a, functors na tage Programming Languages. ee “to check itis empty list oF not. Hf the arg otherwise it retums #f Explain with With the help Explain mum PP I uital example how to meric predicay torte a function in scheme ? What are the types of functions used in scheme control flow st fatements used in scheme ? Explain ind CONS ? EB} Programming with ML What is CAR COR a © ML is also known a ‘own as SML. The long form is Standard Meta Language. Itis a type-safe Programming, functional programming language The difference betw ‘een ML and scheme is that ML is strongly typed language whereas scheme is a typeless, aannanianer acamnncan alae Features of ML. * ML isa static scoped functional progeamming language. © The syntax of ML programming language is more like imperative programming, language. Everything is built from expressions. It provides for structured values such as ists, tuples and so on. ‘Simple Declarations We can evaluate simple expressions using ML for example - @@@ Standard ML ofNew) = 10+20; , val it = 30: int Se —t Similarly, WE Standard ML of New) ~ val x = 2434u; val x = 1d: int For example on declaring the ated as follows = We can get the name of the data types as follows - integer, string data we get the name of data type. Its illust. WH Standard ML of New) - 10; val it = 10: int = "hello val it = "hello" : string - 10.56; val it = 10.56 : real jinding Expressions Binding allows us to refer to an item as a/symbolic name, Here variable ais assigned with the value 20. This variable a can be adde we get the value 35, ed to 15 and eee BB runction, For example fan cubetnine) Following sere. We can also specify the return type to this function. For example fun cubstcint)ine REIDSISREEE ite o Mprgra to find factorial of given numer Solution : The function definition is as follow fun fact(nsint)int = if = Orbea ise n*tact(n-th ‘The function call is as follows - fact(S); //ourput:120 [REMIT cee ML prose nt Solution cme ign = Other ‘tan fb(nint): pp(e-1) +822 ‘The call to the function |= f(3), /outper? complexities ot F wat without usin; set [] with the elements separated Principle 9 Lan, tonal and Loge Prog St Fregramming Languoges 5-20 ___—Functonal and Logic Progr “ot Frepremming Languages 5-20 ‘There are two constructors in st = (1) Empty ist (2) Cons operator represented y “The nil constructor is the ist containing nothing. The operator: takes an item, m the left and a list on the right. F ‘or example - @ Standard ML of News > lirnil; val it = [1] : int list 2nd val it = [2,1] : int list > 3::Q2::Ctinily); val it = [32,1] : int list ‘There are some built in functions associated with the list. The hd returns the head of the list and tl returns the tall ofthe list. That means the hd returns the first element of the list and €l returns all bu the first element of the lis. @ Standard ML of News - hd[1e, 20, 30]; val it = 10): int ~ tl{10, 20, 30,49]; val it = [20,30,u0]': int List Writes ML rose ippena st tw eiting tn The nome rrenrc om Functional and Loge Programmang Languages Function Definition tstepenta) Toa = sete nenataan vansnaano Function Definition fun reverse(man) = if null) thon n se reverse(t(m) hoa), Funetion call reverse({10,20,30,401,0; (40,20,20,10) //ourput Write a MEL program to find the length of st. Sotution : Function Call ‘un nl) = 0 = [en(a:x Hens); Function Definition len({10,20,90,40,501) eae ist the features of ML- ee er defined function in ML ? Explain it with the help of example. duction to Logic and Logic Programming — ming is a programming paradigm in which the set of sentences are problem domain. aah PURI IEATIONS® a Progranring Larges Princip rine of Programming Languages 0-22 Functions nd bn sntrolled deduction. separation of programs + Logie prog be viewed ing * An important concept in logie programming, is the to their logic component and their control component. + Kowalski illustrates the logic programming by following equation, Algorithm = Logie + Control represents a logic program in the form of facts implemented by applying the rules where "Li and rules. The “Control” represents how the algorithm can be in particular order. * The concept of logic programming is linked up Prolog is acronym of PROgramming inLOGIC. « rogramming with Prolog st") toc An this section we will get introduced with some basic features of logic programming using prolog. The programs in prolog can be implemented and tested using SWI-Prolog systems. We can get the interpreter for the prolog from _www.s prolog.org/download/stable. Choose the appropriate binaries depending upon your with a language called prolog. wo FFE operating system version, ‘The interpreter window appears on which-? is a prompt. We can type and test various simple prolog statements on this prompt window. Here are some sample examples of execution and testing of SWI-Prolog ST Sibmereere Menu eee [ecsmentreesioa . | | Forhet, use? hep Topi) a? aprozos(Wons) } rio | ne bonzmn frauds - Ap } | tose | 3.2. wate(Envoy Protogt’) - | | borrow" Note that every statement in prolog must be terminated by dot. Prolog is used in arti Problems. "ficial intelligence and expert system to solve com 2) Wis used ©” pattern mat 3) Itis used to develop hatching algorithm. 4) Prolog is vag ets son object vented concepts dese © build decison sport systems that at organizations 9 'N8: For example - Decision systems for medical diagnoses. EBD Basic Building Blocks Relations + Prolog makes u Prolog makes use of elation instead of using fumeios. elton ate more Hexible ‘teats the arguments and results uniformly. +. For example - Consider following list label * As we know that the list can be considered as (HIT]. That means in the list H Le head occurs first and then comes Ti. tail. Hence prolog will teat [a,b,c] 25, {a.b.e]= [a| [bee] Queries ‘In prolog, the simple queries can be created to check whether particular tuple belongs to a relation «In below given execution, the first two queries represent the simple Hand T relation between the members of the ist. Hence the answer fur out to be true or yes. © smrrows han ovsnaanon 2) aoe fe eat Seting Run Crug Hee 32-pnd bib a2 -pne Atos sr-ped=tancital 4s But in the third query since d isnot the member of the lis [ab] the answer tum out to be false, sm Funcuonal end Lope Programming Langues * A prolog program consists of a mumber of clauses. Each clause is either a factor a rule. After a prolog program is loaded (or consulted) in a prolog interPreter, users can submit goals or queries and the prolog intepreter will give results (answers) according to the facts and rules. (1) Terms : + Prolog term is a constant, a variable, ora structure. A constant is either an atom or an integer. Atoms are the symbolic values of prolog ‘+ A variable is any string of letters, digits and underscores that begins with an uppercase letter or an underscore (_ ). Variables are not bound to types by declarations. The binding of a value and thus a type, to a variable is called an instantiation. (2) Goals: «A goal is a statement starting with a predicate and probably followed by its arguments. In a valid goal, the predicate must have appeared in at least one fact or rule in the consulted program and the number of arguments in the goal must be the ‘same as that appears in the consulted program. Also, all the arguments (if any) are constants. «The purpose of submitting a goal isto find out whether the statement represented by the goal is true according to the knowledge database (ie. the facts and rules in the consulted program). This is similar to proving a hypothesis - The goal being the hypothesis, the facts being the axioms and the rules being the theorems. (3) Fact, «A fact must start with a predicate (which is an atom) and end with a fullstop. The predicate may be followed by one or more arguments which are enclosed by parentheses. The arguments can be constants, numbers, variables or lists Arguments are separated by commas «The syntax of fact is, pred(arg!, ar92, .. arg) Where pred is the name ofthe predicate and argi, ..argN are the arguments For example - sman(anand), ‘manarun). omnanianuredha) Troman\jayashres) arenttanand perth), 5 ‘means Mecs(eniradta.pany) SMO! parent of pant jtlanm snuradha} psent avashree,enuradna, ‘The result as either true or false lepending upon the facts. It is as follows 2s -Proog (Mulvnreaded version 72 version 7.22) File Eat Seting Run Debug Her 12 - parentiana Tee amen pec, 2.2 -parentiarun.am 22 -paren{arunanuradha} 37 - par False tarun,anan), 42 (4) Rule: «A rule can be viewed as an extension ofa fact with added conditions that also have te beatified for it to be true It consists of two parts, A rule is no more than a stored query. Its syntax is tnead :- body. where head is a predicate definition (ust ikea fact) sis the neck symbol, sometimes read a5 body is one or more goals (@ 469) For example - facen(#c)-mnancF parent C) Example using Fact and Rule 1p Pacts */ manianana) j man(arst) eet eee ‘woman(anuradha), ‘woman(jayashree) Parent(anand parth). % means anand is parent of parth Parentianuradha path). arent(arun anuradha) arent{jayashree.anuradha) ("A general rule */ fatner(F.C)-man(F) parent(F.C), ‘mother(M.C):-woman(h0) parent(M.C). ewe query +? father(X part The above query can be read who is father of parth ? The answer is X = anand is 3 father of parth. Response to Query Control represents how a language computes a response to-a query. The control execution is based on two rules - 1. Goal order : That means choose the leftmost subgoal 2. Rule order: That means select the first applicable rule |A goal is a statement starting with a predicate and probably followed by its arguments. In a valid goal, the predicate must have appeared in at least one fact or rule in the consulted program and the number of arguments in the goal must be the same as that appears in the consulted program. Also, all the arguments (if any) are constants. The purpose of submitting a goal is to find out whether the statement represented by the goal is true according to the knowledge database (ie. the facts and rules in the consulted program). Let us understand how control in prolog works with the help of simple example. Following is a family.pl file in which the rules and facts are written. ‘-Rules*/ ofather(X.Y) father(X-2),parent(2,¥). parentiXY): father(XY), Facts") {ther(dashrath,cam), Xmeans dashrath i father of ram father(raghu.aja). father(aja.dashrath). father(ram,luv). fesmeriraen inveh). ‘The goals can ‘be executed on the prompt window as follows ~ 12. gfameriaa ram Uz vara 2 paremx yy X= daswan, {2am 3 7-tarerxy) tater amy x ct ¥ 2 asmath Now consider the goal gfather(aja,ram). ‘As we know there are two rues for execution of contol - 1. Goal order : That means choose the leftmost subgoal 2. Rule order : That means selec the fist applicable rule Here the mules are, y= tater XZ) parent(2.¥), parent(X.¥)= fatberOX%) step 1: For gfather(aiaram) W inter X19 jaxbertXZ)porent2.1) ssabgoal ie father (XZ) is chosen firs.(Goal ordering) apply the first applicable rule(Rule ordering) ap 2: The match for father\2) 15 searched in the fact lst with X = aja. We wall find the ed veijadashrath), Hence value of Z= dashrath, match with fathe eS Pie Popwmnny pages 5.25 Pst as RSI en Hence the first rule now becomes tats) tari 2 pare. wit z=daabentn and YF Step 3: For the subgoal parent(Z.¥) select the rule Parent XY): father CY), with X = Z = dashrath and Y= ram, The parent will retur™ “ihe father(X. Y)efather(dashrath ram) which comes out tobe true. Hence we Bet the answer gy true While executing the control the prolog choose a rule PY» i) Searching sequentially in the program from top to bottom whose Read matche, with the goal with possible uniter. fi) Remember the position of the matched rule. i) Join the rule body in front of the sequence of sub goals to be solved, iv) Repeat until either goal is satisfied or is failed. Another example Consider another example for goal ordering and rule ordering. Consider following prolog database Rule order affects tl h for solutions Step 1 familyl.pl /rRules*/ descend Y)- child), descend XY): cild(X.2) descend). ponciles of Progra peneiples SA Rrogemmning Languages 5 Now try out following queries step 2: Now just change the ordering of the rules as follows family2.pl pRuies"/ sdeacond (X.Y): child(X.Z}.descendi2.¥). deacend(X.Y):- child(%.¥). Facts"! cenuld(tuv ram). child(ram,dashrath). chid(dasbrath. aja). child(aje rag) We will get following result on execution of descend query ‘Thus due to change in ordering of the ules we get different results dar changes the solutions Goal or change the ordering ofthe goals by keeping the ordering of the rules as jon of the above program by changing the order of gos! step 3: Now just itis. W family3Pl fe will create another Versi Functional and Logie Programming Langu, ves of Programming Languages _§- 30 _Funeton [Facts childtuv ram) chuldtram dasheat). childidashrath,sia) chliaja.rapbu, ‘We will get following result on execution of descend query ‘ip cine pocutr: escant? OHM os 9 You will get an error message (‘out of local stack’, or something similar). Prolog is Iooping. Why? Well, in order to satisfy the query descend(uv/X) Prolog uses the frst rule This means that its next goal will be to satisfy the query, descend(luvX1) For some new variable X1 . But to satisfy this new goal, Prolog again has to use the first rule, and this means that its next goal is going to be, descend (Iuv.X2) For some new variable X2. And to be descend(juv,X3) and then descend(Iuv,X4) and so on. Thus change in the goal order has resulted in procedtural disaster. of course, this in turn means that its next goal is going Standard Terminology ‘The standard terminology is that in a rule the leftmost item of the body must be identical with the rule's head. Step 4: To overcome the above error causing situation just change the rule ordering follows - /Rules*/ descend(X¥)~ child), easend(XY)~ descend(2,¥)chilA(X2), /rFects*/ chalga ran) sbuidram.dasbrath) Frneiles of Programming child dashrath =, —S=31__Funetona and Logie Programming Languages. chlltaia agi). a Now the output will be Lists, Operators and Arithmetic ists * A list is an ordered sequence of objects and lists. In Prolog, a list is written as ts elements separated by commas and enclosed in brackets. For example 11 & represents empty ist label. ‘* In Prolog list elements are enclosed by brackets and separated by commas 234) [Operator Predicate calculus is a fundamental notation for representing and reasoning with logical statements. t extends propositional calculus by introducing the quantifiers and Py allowing predicates and functions of any number of variables. 4) Propositional symbols :P, QR, 5, T, .. denote propositions, or statements about the world that maybe either true or false, such as “Sun is bright” or “India is a country”. 2) Truth symbols : true, false. 3) Connectives : A (and), V (08), ~ (not), =.= 4) Propositional calculus sentences : Every propositional symbol and truth symbol isa sentence. For example The negation of a sentence is a sentence. Denoted as ~ P are a sentence. Any tsvo sentences connected by ane of [A V.= For instance PV-Q=R, cf a Lgl Pree Lara, Pins of Pepramming Languages 5.32 S a) ory ere ie or conjuncts InP VQ, P and Q are called disjunct 6) Symbols : The symbols ( ) and { ] are and so control thir order of evaluation and meanin Pv(-Q=R)are different, nto sub-expressin used to group symbols i ae (Py ~Q)= Rand ‘Arithmetic “The operator «is used for unification in Prolog, Following example iustrates the ure of = for binding with the corresponding valve In above code, variable A is bound to 10 + 20 ‘The infix operator is evaluates the expression hence we get A = 30 for the second query statement. In the third query statement, 10 + 20 does not unify with 30. Hence we get false as 2 result of third query. List Structure A list is an ordered sequence of objects and lists. In prolog, a list is written as is ‘elements separated by commas and enclosed in brackets. For example 1] + represents empty et lane ll The list contains Head and Tail part. For example -If we type following query 2 Hm) = 110,20,30-401 We will get H=10, T = (20, 30,40). fe fe tn 3-labebixy 3rlabervziy Now if we execute Pe laibiol = faltolietnn. ‘Then we will get - true EEE consite town hed(CH | TI, HD. cee tnil(CH | TI, 7). ist(QH | TI, H, D. ‘What will be D hendd), X). ii) list), X, 0. iti) head{({a, b,c, dl, X). in) tail fal, 0. ) Hist(a, bl, X.Y. Solution i) No ‘The fact for head returns ‘the ‘The empty list has neither hea¢ head of the list and we have passed an empty list. .d, nor tail hence we get the answer as no or false. ii) No ‘The fact for list returns head in X and til in Y. With the empey list we will get no head and no tail: Hence isthe answer. iii) X=a “The fact for head returns h get the answer a. TECHNICAL PUBLICATIONS® - an up-trust for knowledge ead of the list. As ais the head for the listfab.cd], we Seal ordering and rule on Givw the exampte explaining hove Explain the basic e Explain list manipulation in protog tering coal tering changes the solution i proieg. Comparison between Functional Programming and Logical Programming and Object Oriented Programming Languages 1. Funetional Programming Vs. Logical Programming Logical programming Logical programming uses predicates, Predicate cannot return a value. The predicate In logic programming, a variable does not Sr.No. Functional programming 1. Functional programming uses functions. 2 The functions can return a value can be true or fase, 3. In functional programming, the variable denotes the concrete value. need to refer to concrete value 4 Functional programming is normally used for modelling reasoning % Examples - ML, HASKELL are fu Programming languages Logical programming is normally used for ‘modelling knowledge. unctional Example - PROLOG isa logical programming language. 2. OOP Vs. Logical Programming Vs. Functional Programming sr. No. Object oriented programming Its based on objects and classes, It is mainly used for enterprise level applications, cecution is by means. Program of exchange of message between abject Logical programming tis based on predicates Itis used for modelling knowledge. Program execution is by ‘means of proving the logic. Functional programming Itis based on evaluation of functions. Itis mainly used for mathematical computations Program execution is by means of evaluation of functions MOOS of Frogran ‘i ZAIN Langapes wl result is ——Firconat and Lope Programming Lanquopes denoted by state . Final results denoted by Fi result i denoted Examples -jova, Co ale of the main mucin SI 2 eet diffrence tesa Ftonal eg 7 ce eee orang and ogc programming lang el programming with logic and fnctional programing lang EB uti Definition ; an : Popaming paradigm can be defined as a method of problem solving © programming language design, __} Various types of programming paradigm are 1. Imperative or procedural programming 2. Object oriented programming 3. Functional programming Examples Prolog ples - Prog Example LISP, ML. Haskell aradigm Languages 4, Logic programming. Examples of various programming languages based on the above mentioned paradigm is as shown by following table Imperative Object. «Functional Logie piamnming —ofinted programming programming ALGOL smaliaik USP Prolog coBot Simla Haskell ADA oo art c jaa PAScat FORTRAN et us discuss them in bret Programming impetrate means to comman jented language. also called as procedural programming lans¥28* ERD imperative The Latin word ferent ori 1d, Hence this language is command stat driven _ myperativ® PCB! Then mming is Friehles rPranming Languages _5-a¢ Funan Le PET Lap jon of each statement ‘A Program consists of sequence of statements. After executi f teMENt the ‘alae arestore inthe meme The central features of this language are a aS Fortan an soo Examples of imperative programming are -C, Pascal, Ada, Merit 1, Simple to implement. 2. These languages have low memory wtilibzation. Demerits : 1. Large complex problems can not be implemented using this category of language 2. Parallel programming is not possible in this language. 3. This language is less productive and at low level compared to other programming languages. F] Object Oriental Programming In this language everything is modeled as object. Hence is the name. This language has a modular programming approach in which data and functions are bound in one entity called class. This programming paradigm has gained a great popularity in recent years because of its characteristic features such as data abstraction, encapsulation, inheritance, polymorphism and so on. Examples of object oriented programming languages are - Smalltalk, C+, Java. Merits : 1. It provides a modular programming approach, 2. It provides abstract data type in which some of the implementation details can be hidden and protected. Modifying the code for maintenance become easy, due to modules in the program Modification in one module can not disturb the rest of the code. 4. Finding bugs become easy. Object oriented programming provides good framework for code library fro which the software components can be easily used and modified by the programmer oS _ 218 of Programmi 2 Coen n eamautees 5-27 santana Loi orang Languages. 1 Sometimes reat w, implement. y. Hence it is complex to ‘orld objects can not be realized easi Some of the mem Not be ace bers(data or methods) of the class are hidden. Hence they can Ie oben aan PY Beat oF ther cas object orient modules jean Prostamming everything ig arranged in the form of classes and For the lower level applications i is not desirable feature. EEE Functional Programming In this parac Fane adism the computations are expressed inthe frm of anions a ‘onal programming paradigms treat values as single entities. Unlike variables, es are never modified. Instead, values are transforme¢ fang Pistons of functional languages are performed largely through applying tions to values ie, (+ 1020), This expression is interpreted as 10 + 20, The result 30 will be returned. For building more complex functions the previously developed functions are used. Thus program development proceeds by developing simple function development to complex function development, Examples of function programming are LISP, Haskell, ML to new values. Merits : 1. Due to use of functions the programs are easy to understand. 2. The functions are reusable. 3. It is possible to develop and maintain large programs consisting of large number of functions. Demerits : 1, Functional programming is less efficient than the other languages. 2, They consume large amount of time and memory for execution. Purely functional programming is not a good option for commercial software development. Logie Programming In this paradigm we express computation in terms of mathematical logic only. tis also i= ( - ) | ( ) || | 2 Explain the term Lambda abstraction | ans: The lambda abstractions away of defining a new functions. The / (a ) 2 SS (+ 1)) @) is a nameless abstra, fraction. The function is eval function in which x is a variable and (x+1) is lambda luated by substituting 3 for the variable x. ‘and bound variable? 23 What do you mean byte Ans. : In 2 cal - aleulus, a tec ll the names are local to definitions. In the function Ax - x we say und since ts accurence inthe body ofthe dito s preceded by 2. A ed by Ais called free variable. For example name not (xe xy) The vari ‘able x is bound variable whereas y is a free variable. The same variable can appear many time: wp ‘any times in the different context. Some instances of the variable may be ound whereas other are free. For example - In the expression yy) Ax xy) The variable y in the body of first expression from the left is bound to the frst 4, Hence ¥ is said to bound in first expression. Whereas variable x is bound to second lambda in the second expres ion but y is free. Hence in the second expression x is said to be bound variable while y is said to be free variable. Q.4 What is beta conversion? ‘Ans. : The basic operation in lambda calculus is the application of expression. For example (2(x + 1))@) is equal to (3 + 1). Thus we are substituting the value 3 for the variable x and throwing the lambda away. This is called beta conversion. ‘Thus beta conversion is a process of simplifying the expression and this removing the lambdas. 5. Enlist the features of functional programming? ‘Ans. 1. The functional programming languages are modelled on the concept of ‘mathematical functions and make use of only conditional expressions and recursion for the computational purpose. ‘The programs are constructed by building functional applications, That means the values produced by one or more functions become the parameters to another functions. 5, The purest form of functional programming languages use neither variables nor statements, although this is relaxed somewhat in most applied assignmen ing? ‘Applications of functional prograrnmna The main domain of functional programming IaNBUABS . ee — ain domain of functional prog owledge representa This Tanguage is used fr building exper SYNE ine speech and ae ™ ‘machine learning, natural language processing ™ i al software. Functional language is aso used for building mathematic he function deft mpl 7 Explain the function definition in Scheme with sultale examPl® ; . less function called lambda function. We de In scheme we can define a namel Ne user defined function using define. The syntax is |[Sene tunction_oame parameters) (expression) » For example We can define the function named add as follows - |>(detine (ade num’ mum2} (+ mumt num2) H Now, we can call the above function with two parameters for performing addition of two numbers > (add 19 20) 30 1.8 What Is car, edr and cons ? ‘Ans. : The car returns first element of a non empty list. For example - > (car(1234)) 1 + The cdr returns rest of the list after the first element is removed. Itis pronounced 2 could-er. > (edr'(1 234) (2.3.4) * We can combine two lists using cons. The cons function takes two arguments a returns a new cons cell containing the two values, > (cons 10 (20 30 40)) (10 20 30 40) Prneles of yore Programming Languages 5-41 umetonal end Logis PrOarMMund = Q.9 Wha Is Null predicate function in Scheme? Ans. : This Predicate is used > (au? 41020 Sa ie 30) > (nun?) le check if it is empty list oF not. If the isa li argument is a list then it returns #t otherwise it returns éf. 2.10 Give the features of ML programming langu Ans. * MLisa static scoped functional programming language. * The syntax of ML programming language is more like imperative programming language. * Everything is built from expressions. © It provides for structured values such as lists, tuples and so on. Q.11 How to use functions in ML? Ans. : The function can be defined in ML using following syntax ltun function name(formal parameters) = function body: For example leur cube(xint) = x" Q.12 Describe the logic programming language lke Prolog. % Ans. 1) Prolog is used in artificial intelligence and expert system ‘0 solve comple problems. 2) Ieis used on pattern matching algorithm. 3) Tris used to develop systems based on object oriented concepts. 1d to build decision support systems that aid organizations 4) Prolog is uset Je - Decision systems for medical diagnoses. decision-making, For examp! .13 State any four distinguishing features of functional and logical programming languages (Refer section 5.7) cers) Principles Functional and Logic Programing Language of Programming Languages ___5- 42 _Funct a 14 What is programming paradigm 7 | Ans. : Programming paradigm can be defined as a method of problem solving and an approach to programming language design. Various types of programming paradigm are - 1. Imperative or procedural programming 2. Object oriented programming 3. Functional programming 4. Logic programming. aqua

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