You intend to execute two expressions inside the consequent part of the if, but if only allows one expression in the consequent and one in the alternative. Surrounding both expressions between parenthesis (as you did) won’t work: the resulting expression will be evaluated as a function application of the first expression with the second expression … Read more
This is an interesting way to represent data: as functions. Notice that this definition of cons returns a lambda which closes over the parameters x and y, capturing their values inside. Also notice that the returned lambda receives a function m as a parameter: ;creates a closure that “remembers’ 2 values (define (cons x y) … Read more
Great question. For the benefit of those without a functioning DrRacket installation (myself included) I’ll try to answer it. First, let’s use some sane (short) variable names, easily trackable by a human eye/mind: ((lambda (h) ; A. (h h)) ; apply h to h (lambda (g) (lambda (lst) (if (null? lst) 0 (add1 ((g g) … Read more
A list in Scheme is either the empty list () (also known as nil in some Lisps), or a cons cell whose car (also known as first) is an element of the list and whose cdr (also known as rest) is either the rest of the list (i.e., another list), or an atom that terminates … Read more
The following is an implementation of tail recursion modulo cons optimization, resulting in a fully tail recursive code. It copies the input structure and then appends the new element to it, by mutation, in the top-down manner. Since this mutation is done to its internal freshly-created data, it is still functional on the outside (does … Read more
What’s in a powerset? A set’s subsets! An empty set is any set’s subset, so powerset of empty set’s not empty. Its (only) element it is an empty set: (define (powerset aL) (cond [(empty? aL) (list empty)] [else As for non-empty sets, there is a choice, for each set’s element, whether to be or not … Read more
Let is parallel, (kind of; see below) let* is sequential. Let translates as ((lambda(a b c) … body …) a-value b-value c-value) but let* as ((lambda(a) ((lambda(b) ((lambda(c) … body …) c-value)) b-value)) a-value) and is thus creating nested scope blocks where b-value expression can refer to a, and c-value expression can refer to both … Read more
In Prolog’s terms, condA is “soft cut” a.k.a. *->, where A *-> B ; C is like (A, B ; not(A), C), only better ; whereas condU is “committed choice”, a combination of once and a soft cut so that (once(A) *-> B ; false) expresses (A, !, B) (with the cut inside): condA: A *-> … Read more
“number (N) of ways … using N kinds” these two Ns are clearly not the same. so let’s say K kinds of coins. We have many coins, but each coin is either 1, 5, 10, 25 or 50 cents, in total 5 kinds of coins. We need to buy something for a dollar, 100 cents. … Read more
I’ll answer this question incrementally. Let’s start with the = equivalence predicate. The = predicate is used to check whether two numbers are equal. If you supply it anything else but a number then it will raise an error: (= 2 3) => #f (= 2.5 2.5) => #t (= ‘() ‘()) => error The … Read more