Discussion 12: Programs as Data

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Scheme Programs as Data

All Scheme programs are made up of expressions. There are two types of expressions: primitive expressions and combinations.

  • Primitive expression examples: #f, 1.7, +
  • Combinations examples: (fact 10), (/ 8 3), (not #f)

Scheme's built-in list data structure can be used to represent combinations.

  • Example: (list 'fact 10) results in the combination (fact 10).


The normal quote ' and the quasiquote ` are both valid ways to quote an expression. However, the quasiquoted expression can be unquoted with the "unquote" , (represented by a comma). When a term in a quasiquoted expression is unquoted, the unquoted term is evaluated.

scm> (define a 5)
scm> (define b 3)
scm> `(* a b)
(* a b)
scm> `(* a ,b)
(* a 3)
scm> '(* a ,b)
(* a (unquote b))

Q1: WWSD? Quasiquotation

scm> '(1 x 3)
scm> (define x 2)
scm> `(1 x 3)
scm> `(1 ,x 3)
scm> '(1 ,x 3)
scm> `(,1 x 3)
scm> `,(+ 1 x 3)
scm> `(1 (,x) 3)
scm> `(1 ,(+ x 2) 3)
scm> (define y 3)
scm> `(x ,(* y x) y)
scm> `(1 ,(cons x (list y 4)) 5)

Eval Procedure

The eval procedure forces evaluation of a given expression in the current environment. Since a quote supresses evaluation, calling eval on a quoted expression (quote expr) will evaluate the expression expr.

scm> (define a '(1 2 3))
scm> (quote a) ; equivalently, 'a
scm> (eval 'a)
(1 2 3)

Apply Procedure

When evaluating an expression, once the operator and operands have been fully evaluated, the operator is apply'd using the operands as arguments. This can also be done outside of the implicit context of evaluations using the apply procedure. The apply procedure applies a given operator to a list of operands.

scm> (apply + '(2 3))
scm> (apply (lambda (x) (* 2 x)) (list 1))

Q2: WWSD? Eval and Apply

scm> (define add-numbers '(+ 1 2))
scm> add-numbers
scm> (eval add-numbers)
scm> (apply + '(1 2)) ; Is this similar to the previous eval call?
scm> (define expr '(lambda (a b) (+ a b)))
scm> expr
scm> (define adder-func (eval expr))
scm> (apply adder-func '(1 2))
scm> (define make-list (cons 'list '(1 2 3)))
scm> make-list
scm> (eval make-list)
scm> (apply list '(1 2 3)) ; Is this similar to the previous eval call?

Q3: Geometric Sequence

Implement the procedure geom, which takes in a nonnegative integer n and a factor f that is an integer greater than 0. The procedure should create a program as a list that, when passed into the eval procedure, evaluates to the nth number of the geometric sequence that starts at 1 and has a factor of f. The sequence is zero-indexed.

For example, the geometric sequence starting at 2 is 1, 2, 4, 8, and so on. The expression (geom 5 2) returns a program as a list. When eval is called on that returned list, it should evaluate to the 5th number of the geometric sequence that has a factor of 2 (and starts at 1), which is 32.

Run in 61A Code

Q4: Make Or

Implement make-or, which returns, as a list, a program that takes in two expressions and or's them together (applying short-circuiting rules). However, do this without using the or special form. You may also assume the name v1 doesn't appear anywhere outside this function. For a quick reminder on the short-circuiting rules for or take a look at slide 18 of Lecture 3 on Control.

The behavior of the or procedure is specified by the following doctests:

scm> (define or-program (make-or '(print 'bork) '(/ 1 0)))
scm> (eval or-program)
scm> (eval (make-or '(= 1 0) '(+ 1 2)))
Run in 61A Code

Q5: Make "Make Or"

The above code generates a program that evaluates an or expression without using any or statements. However, we can take it even one step further: let's create a program which generates make-or, the program you created which generates an or expression.

Implement make-make-or, a program which generates a program which, when eval'd, can be apply'd to make an or expression with differing varibles. You may find the code you wrote above to be useful.

Hint: recall that you want to construct a list that resembles the program. Do you know what this list would look like?

Run in 61A Code

Now, given this function, determine the outputs from the following expressions:

scm> (make-make-or)
scm> (eval (make-make-or))
scm> (eval (eval (make-make-or)))
scm> (apply (eval (eval (make-make-or))) '(#t (/ 1 0)))
scm> (eval (apply (eval (eval (make-make-or))) '(#t (/ 1 0))))