Given the definition
f([]) = []
f(h::t) = (h*h)::f(t) when h > 10
f(h::t) = f(t) when h <= 10
show an inside-out evaluation of expression f([4,12,15,6,11]).
Show the entire expression at each step.
Assume that arithmetic is done as soon as possible.
Write an equational definition of a function prefix so that prefix(x,y) is true just when list x is a prefix of list y. For example, prefix([1,2], [1,2,4,6]) is true, but prefix([1,2], [1,5,2,6]) is false. The empty list is a prefix of every list.
Show an inside-out evaluation of prefix([1,2], [1,2,3,4]) using your definition of prefix from the preceding question. Show the entire expression at each step.
Write an equational definition of a function called smallest so that smallest(n,x) is the smallest member of list n::x. For example, smallest(3, [6,4,7]) = 3 and smallest(8, [2,5]) = 2. You may presume that you have a function called min that takes the minimum of two numbers. For example, min(7,4) = 4.
In a purely functional language, is it ever possible to compute the same expression twice in the same context and get different values? For example, if E is an expression, and you compute E two times, one right after another, could the first computation yield a different result from the second computation? Why or why not? (Note: Astarte is not a purely functional language. Think about the functional subset of Astarte. What is functional programming?)
Answer the preceding question, but instead of for a purely functional language, for an imperative language such as C++.
By choosing among the operations foldLtoR, foldRtoL and map write a definition for each of the following that does not use recursion or loops.
Write a function called doubleAll that takes a list x of numbers as its parameter and produces a list of the doubles numbers in list x as its result. For example, doubleAll([5,2,19,3]) = [10,4,38,6].
Write a function called maxlist(m,L) that computes the largest value in list m::L. That is, it computes the maximum of m and the largest value in list L. Assume that function max is available where max(x,y) is the larger of x and y.
Function select is written so that (select p x) returns a the first member m of list x such that p(m) is true. Notice that p is a predicate, a function that produces a boolean result. (For the purposes of this question, it will not matter what select does when there is no such m.) Predicate odd? returns true on an odd number and false on an even number.
What is the value of Astarte expression map(select odd?)[[2,3,4,5],[1,2,3,4],[2,4,6,7,8]]?
You are given the following function definition in Astarte.
Define f ?x ?y ?z = y x (x::z).