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Write the double negation (Involution)law:

*Computer Science (lambda calculus)* Reduce each of the lambda terms shown below and explain the technique used for reduction as well as the final result. 1) ((λx.(x y))(λz.z)) 2) (λg.((λf.((λx.(f (x x)))(λx.(f (x x))))) g)) 3) ((λx.(x x))(λx.(x x)))

Explain differences between recursive and non recursive functions.

(Ex.1 in Ch9 of the book KRR) In this chapter, we considered the semanticsof a description logic language that includes concept-forming operators such as FILLS andEXISTS but no role-forming operators. In this question, we extend the language with newconcept-forming operators and role-forming operators. (a) Present a formal semantics in the style of Section 9.3.1 for the following concept-formingoperators:ˆ [SOME r] Role existence. Something with at least 1 r.ˆ [AT-MOST n r] Maximum role cardinality. Something with at most n r’s. (b) Do the same for the following role-forming operators:ˆ [INVERSE r] Role inverse. So the :Child role could be defined as[INVERSE :Parent].ˆ [COMPOSE r1 ... rn−1 rn ] Role composition. The rn’s of the rn−1’s . . . of ther1’s. So[ALL[COMPOSE :Parent:BrotherInLaw]Rich]would mean something all of whose uncles are rich (where an uncle is a brother-in-lawof a parent). (c) Use this semantic specification to show that for any roles r, s, and t, the…

(Ex.1 in Ch9 of the book KRR) In this chapter, we considered the semanticsof a description logic language that includes concept-forming operators such as FILLS andEXISTS but no role-forming operators. In this question, we extend the language with newconcept-forming operators and role-forming operators. (a) Present a formal semantics in the style of Section 9.3.1 for the following concept-formingoperators:ˆ [SOME r] Role existence. Something with at least 1 r.ˆ [AT-MOST n r] Maximum role cardinality. Something with at most n r’s. (b) Do the same for the following role-forming operators:ˆ [INVERSE r] Role inverse. So the :Child role could be defined as[INVERSE :Parent].ˆ [COMPOSE r1 ... rn−1 rn ] Role composition. The rn’s of the rn−1’s . . . of ther1’s. So[ALL[COMPOSE :Parent:BrotherInLaw]Rich]would mean something all of whose uncles are rich (where an uncle is a brother-in-lawof a parent). (c) Use this semantic specification to show that for any roles r, s, and t, the…

. avoid plagiarism Write a rule in Prolog called hailstone(x) that, given a positive integer x, returns the number of elements in the hailstone sequence starting with that x. So, for example, for n=35, the function would return 14.

What are the performance considerations when using function objects in a recursive manner?

What do you understand by function overloading explain with code?(IN C++)