Early LISP Part II (Apply redux)

By Joe Marshall

By April of 1959, issues with using subst to implement β-reduction became apparent. In the April 1959 Quarterly Progress Report of the Research Laboratory of Electronics, McCarthy gives an updated definition of the universal S-function apply:

 apply[f;args]=eval[cons[f;appq[args]];NIL]
where appq[m]=[null[m]→NIL;T→cons[list[QUOTE;car[m]];appq[cdr[m]]]]
and eval[e;a]=[
atom[e]→eval[assoc[e;a];a];
atom[car[e]]→[
car[e]=QUOTE→cadr[e];
car[e]=ATOM→atom[eval[cadr[e];a]];
car[e]=EQ→[eval[cadr[e];a]=eval[caddr[e];a]];
car[e]=COND→evcon[cdr[e];a];
car[e]=CAR→car[eval[cadr[e];a]];
car[e]=CDR→cdr[eval[cadr[e];a]];
car[e]=CONS→cons[eval[cadr[e];a];eval[caddr[e];a]];
T→eval[cons[assoc[car[e];a];evlis[cdr[e];a]];a]];
caar[e]=LABEL→eval[cons[caddar[e];cdr[e]];cons[list[cadar[e];car[e]];a]];
caar[e]=LAMBDA→eval[caddar[e];append[pair[cadar[e];cdr[e]];a]] and evcon[c;a]=[eval[caar[c];a]→eval[cadar[c];a];T→evcon[cdr[c];a]]
and evlis[m;a]= [null[m]→NIL;T→cons[list[QUOTE;eval[car[m];a]];
evlis[cdr[m];a]]

I find this a lot easier to understand if we transcribe it into modern Common LISP:

;;; Hey Emacs, this is -*- Lisp -*- (in-package "CL-USER") ;; Avoid smashing the standard definitions.
(shadow "APPLY")
(shadow "ASSOC")
(shadow "EVAL") (defun apply (f args) (eval (cons f (appq args)) nil)) (defun appq (m) (cond ((null m) nil) (t (cons (list 'QUOTE (car m)) (appq (cdr m)))))) (defun eval (e a) (cond ((atom e) (eval (assoc e a) a)) ((atom (car e)) (cond ((eq (car e) 'QUOTE) (cadr e)) ((eq (car e) 'ATOM) (atom (eval (cadr e) a))) ((eq (car e) 'EQ) (eq (eval (cadr e) a) (eval (caddr e) a))) ((eq (car e) 'COND) (evcon (cdr e) a)) ((eq (car e) 'CAR) (car (eval (cadr e) a))) ((eq (car e) 'CDR) (cdr (eval (cadr e) a))) ((eq (car e) 'CONS) (cons (eval (cadr e) a) (eval (caddr e) a))) (t (eval (cons (assoc (car e) a) (evlis (cdr e) a)) a)))) ((eq (caar e) 'LABEL) (eval (cons (caddar e) (cdr e)) (cons (list (cadar e) (car e)) a))) ((eq (caar e) 'LAMBDA) (eval (caddar e) (append (pair (cadar e) (cdr e)) a))))) (defun evcon (c a) (cond ((eval (caar c) a) (eval (cadar c) a)) (t (evcon (cdr c) a)))) (defun evlis (m a) (cond ((null m) nil) (t (cons (list 'QUOTE (eval (car m) a)) (evlis (cdr m) a))))) ;;; Modern helpers
(defun assoc (k l) (cadr (cl:assoc k l))) (defun pair (ls rs) (map 'list #'list ls rs)) (defun testit () (apply '(label ff (lambda (x) (cond ((atom x) x) ((quote t) (ff (car x)))))) (list '((a . b) . c))))

There are a few things to notice about this. First, there is no code that inspects the value cell or function cell of a symbol. All symbols are evaluated by looking up the value in the association list a, so this evaluator uses one namespace. Second, the recursive calls to eval when evaluating combinations (the last clause of the inner cond and the LABEL and LAMBDA clauses) are in tail position, so this evaluator could be coded up tail-recursively. (It is impossible to say without inspecting the IBM 704 assembly code.)

What is most curious about this evaluator is the first clause in the outer cond in eval. This is where variable lookup happens. As you can see, we look up the variable by calling assoc, but once we obtain the value, we call eval on it. This LISP isn't storing values in the environment, but rather expressions that evaluate to values. If we look at the LAMBDA clause of the cond, the one that handles combinations that begin with lambda expressions, we can see that it does not evaluate the arguments to the lambda but instead associates the bound variables with the arguments' expressions. This therefore has call-by-name semantics rather than the modern call-by-value semantics.

By April 1960 we see these changes:

(defun eval (e a) (cond ((atom e) (assoc e a)) ((atom (car e)) (cond ((eq (car e) 'QUOTE) (cadr e)) ((eq (car e) 'ATOM) (atom (eval (cadr e) a))) ((eq (car e) 'EQ) (eq (eval (cadr e) a) (eval (caddr e) a))) ((eq (car e) 'COND) (evcon (cdr e) a)) ((eq (car e) 'CAR) (car (eval (cadr e) a))) ((eq (car e) 'CDR) (cdr (eval (cadr e) a))) ((eq (car e) 'CONS) (cons (eval (cadr e) a) (eval (caddr e) a))) (t (eval (cons (assoc (car e) a) (evlis (cdr e) a)) a)))) ((eq (caar e) 'LABEL) (eval (cons (caddar e) (cdr e)) (cons (list (cadar e) (car e)) a))) ((eq (caar e) 'LAMBDA) (eval (caddar e) (append (pair (cadar e) (evlis (cdr e) a)) a)))))
Note how evaluating an atom now simply looks up the value of the atom in the association list and evaluation of a combination of a lambda involves evaluating the arguments eagerly. This is a call-by-value interpreter.