Part 1: Association Lists¶

An association list is a list of pairs, where a pair is a 2-element list of the form (key value). For example:

    (define pets
       '((cat 1) (dog 1) (fish 1) (cat 2) (fish 2))
)

pets is an association list containing 5 pairs. Notice that both cat and fish appear twice as keys: association lists allow keys to occur more than once.

Implement and test the following functions:

• (is-pair? x) returns #t if x is a 2-element list, and #f otherwise. For example, (is-pair? '(fish 1)) and (is-pair? '(5 4)) return #t, but (is-pair? '(fish 1 2)) and (is-pair? 5) return #f.

  The input x could be any Scheme value, not necessarily a list.

• (is-alist? x) returns #t if, and only if, x is an association list, i.e. a list of pairs. The empty list is an association list. For example, (is-alist? pets) and (is-alist? '()) return #t, but (is-alist? '((cat 1) (dog 1)(hamster))) returns #f.

  The input x could be any Scheme value, not necessarily a list.

• (get-all-pairs key lst) returns the list of all pairs in lst that have key as their first element. If no pairs match, then the empty list is returned. For example, (get-all-pairs 'cat pets) returns ((cat 1) (cat 2)), and (get-all-pairs 'bird pets) returns '().

  If lst is not an association list, then use the error function to stop the program, e.g. by calling something like (error "lst is not an association list").

• (get-first-pair key lst) returns the first pair in lst that has key as its first element. If no pair matches, then '() is returned. For example, (get-all-pairs 'cat pets) returns (cat 1), while (get-all-pairs 'bird pets) returns '().

  If lst is not an association list, then use the error function to stop the program, e.g. by calling something like (error "lst is not an association list").

  One way to implement get-first-pair is by calling (car (get-all-pairs key lst)). However, that’s inefficient for large lists, so implement it an a more efficient manner.

• (del-all-pairs key lst) returns an association list that is the same as lst but all pairs in lst whose first element is key have been removed. For example, (del-all-pairs 'cat pets) returns ((dog 1) (fish 1) (fish 2)).

  If lst is not an association list, then use the error function to stop the program, e.g. by calling something like (error "lst is not an association list").

• (del-first-pair key lst) returns a list that is the same as lst but the first pair in lst whose first element is keyhas been removed. For example, (del-first-pair 'cat pets) returns ((dog 1) (fish 1) (cat 2) (fish 2)).

  If lst is not an association list, then use the error function to stop the program, e.g. by calling something like (error "lst is not an association list").

No special function is needed for adding a pair. Just use cons, e.g.:

=> (cons '(frog 2) pets)
((frog 2) (cat 1) (dog 1) (fish 1) (cat 2) (fish 2))

Implement all these functions as described with the exact headers: they will be tested individually.

Part 2: An Expression Evaluator¶

In this part, your task is to implement a function called myeval that evaluates an infix arithmetic expression that might (or might not) have variables. The values for variables are stored in an association list that is passed to the evaluator.

Here are some examples:

=> (myeval '(2 + (3 * x))     ;; the expression
           '((x -1) (y 4))    ;; the environment
   )
-1

=> (myeval '(2 + (3 * 1))     ;; the expression
           '((x -1) (y 4))    ;; the environment
   )
5

=> (myeval '((m * a) - 0.1)   ;; the expression
           '((m 2.5) (a 2))   ;; the environment
   )
4.9

=> (myeval '(4 * (s * s))     ;; the expression
           '((q 3) (r 4))     ;; the environment
   )
;unknown variable             ;; call error if expression can't be evaluated

To make it easier for us to mark, your evaluator must be called exactly like this:

(myeval expr environment)

expr is an arithmetic expression (as defined below), and environment is an association list (see part 1) of the variables and their values that can appear in expr.

Here is an EBNF grammar for the expressions that myeval can evaluate:

expr   =   "(" expr "+" expr ")"
               | "(" expr "-" expr ")"
               | "(" expr "*" expr ")"
               | "(" expr "/" expr ")"
               | "(" expr "**" expr ")"  ;; e.g. (2 ** 3) is 8, (3 ** 3) is 27
               | var
               | number
      number = a Scheme number
      var    = a Scheme symbol

If you call myeval on an expression not generated by this grammar, or if the expression contains a variable not in the environment, then it should end with a call to the error function.

Marking Scheme¶

Part 1

• 6 marks for correctly implementing each of the given association list functions as described in Part 1. This includes both the behaviour of the functions, and the names and parameters of the functions.
• 2 marks for coding style. This includes consistent and sensible indentation, good variable names, good use of Scheme features, etc.

Part 2

• 10 marks for correctly evaluating all the expressions specified by the grammar.

  All invalid expressions (i.e. expressions not specified by the grammar) should result in a call to error.

  The evaluation function must have exactly the interface as described above. Otherwise, you will probably get 0 for this part.

• 2 marks for coding style. This includes consistent and sensible indentation, good variable names, good use of Scheme features, etc.

The maximum score for this assignment is 20 marks. There are no bonus marks.