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UNTVERSITI SAINS MALAYSIAPeperiksaan Semester KeduaSidang Akademik 1993194APril 1994CSI502 - Functional ProgrammingMasa: t3jarnlARAHAN KEPADA CALON:. Sila pastikan bahawa kertas peperiksaan ini mengandungi EMPAT muka surat yangberc6tak sebelum anda memulakan peperilaaan ini.I, trxI (.....21-- 2 _ tcsr502lAnswer ALL questions.1. (a) (i) Define briefly the notions of:- Cartesian product of A and B sets,- relations and functions,- graph of function,- domain and range of function,- functional term, value of term.(ii) Let z=fl(x,y), x=f2( z,xl) be total functions and x,y,z,xl bevariables. Given the following words:fl(x,y)f2(xl,z)f 1 (f2(x I ,f 1 (x,y))fL f2(xl,z)f2(x1,z,x)Indicate which of these words are tenns ( YeVNo)(2sl100)(b) (i) Define an operator of primitive recursion f=R(g,h).(ii) Give an example of a primitive recursive function.(iii) Is the function z=xv a primitive recursive function (Yes/f.{o).(zst[w)(c) Define an operator of unbounded minimization M(0(15/100)(d) (l) Define the class of primitive recursive functions.(ii) State and discuss the nneaning of Church-Kleene thesis.(iii) Prove that x+y is a primitive rccursive function.(iv) V/hat are the functions f5 and f6 given by the schema of recursivederivation? The answer must be written as elementary function, forexampleo z=f(x,y)=x*y. Will you compute, piease, the value f(2) realizingthe schema of recursive derivation.88...31-[cs1502]-3-Recursive schernafl=i, x[x]f2=hxlx+11f3=),xlx2x3 [x2 ]f4=f2f3f5 to satisfvf5(0,x2)=fl(x2)f5 (Y+ 1,x2)=f4(Y, f5 (Y, x2)'x2\f=f6=f5(fl,fl)END of recursive schema(3sl100)2. (a) Givethedefinition of thefollowing objects and notions:(i) variables, operations, algorithm representation ,(ii) direct and data flow controle,(iii) mapping of an algorithm,(iv) realization of an algorithm.(v) comparative nonprocedurality of an algorithm representations (2sl100)(b) (i) Give a {efinition of an asynchronous block, trigger and control functions.(ii) Define an asynchronous program(iii) Give an example of asynchronous program (251100)(c) Define the rules of asynchronous program execution, including the following:(i) rulesofasynchronousblockexecution,(ii) condition of asynchronous program completion,(iii) rules of asynchronous program execution.(zsl100)...4t_i' ,sg,'.tlcsr502l-4-(d) Develope an asynchronous progrirm of pipe-line execution of the algorithm (Fig.1) Procedures input(v,n) and output(v,n) can be used to take or to put a valuefrom/in n-values box v If you want, instead of trigger and control functions youcan use Petri nets to define a control.y-5valuesboxz-3valuesboxf-3vaiuesbox(25l100)3. (a) Define a formal model of computations including:(i) computational model, tenns and their attributes,(ii) non-interpreted computations ( notion of (V,W)-plan),(iii) algorithm of (V,W)-plan building with minimum number of terms,(iv) notion of interpretation. (40/100)x,t-unlimitedboxesFig. 1.(b) Describe the derivation algorithm, including:(D the formulation of problem of program synthesis,(ii) a bottom-up part of algorithm,(iii) an up-down part of algorithm,(iv) feasible modifications of problem of program synthesis(c) Describe an algorithm to buid an application problem solutionincluding:(i) an algorithm of choice,(ii) list basic strategies of operation choice.- oooOooo -(3sl100)algorithm,(251100)90

CSI 502 - FUNCTIONAL PROGRAMMING - APR. 1994

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CSI 502 - FUNCTIONAL PROGRAMMING - APR. 1994

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