; In this article, I'll show how John McCarthy's Lisp can be interpreted ; in McCarthy's Lisp, which is interpreted in McCarthy's Lisp ... ; and so on, n times. ; ; One of the reasons for harder understanding of early Lisps is ; McCarthy's decision to use same identifiers for Lisp implemented ; in machine code, and for Lisp interpreted by EVAL function. ; ; For example, if McCarthy-60 Lisp expression ; ; ; (EVAL (QUOTE ((LAMBDA (XX) (CONS XX (CONS XX (QUOTE ())))) ; (QUOTE somedata))) ; (QUOTE ())) ; ; ; is evaluated, the first and the last oocurences of QUOTE are ; evaluated as special operators defined in base language (in my ; case Newlisp, in original implementation it was machine code), ; while second and third occurence of QUOTE are interpreted ; following the rules defined in John McCarthy-60 EVAL function. ; ; McCarthy's decision isn't incorrect, but using slightly ; different symbols is not wrong either and it certainly contributes ; to easier understanding. In second article I redefined EVAL so ; it evaluates expressions containing symbols like CONS.1, QUOTE.1 ; ... for example: ; ; ; (EVAL (QUOTE ((LAMBDA.1 (XX) (CONS.1 XX (CONS.1 XX (QUOTE.1 ())))) ; (QUOTE.1 somedata))) ; (QUOTE ())) ; ; ; If we can define LAMBDA.1, QUOTE.1, ... then, why not EVAL.1 as well? ; ; That definition was described in previous article on this topic. It is very ; dry and formal definition, because definition of EVAL.1, and ; all needed helper functions should be written in limited McCarthy-60 ; Lisp EVAL interpreter, and given to EVAL in the form of quoted ; association list. ; ; ; (EVAL <quoted expression to be evaluated> ; <quoted association list> ;<======= HERE ; ) ; ; ; If quoted association list is named McCarthy-60-interpreter.1, ; then example of such expressions is ; ; ; (EVAL (QUOTE (EVAL.1 (QUOTE.1 ((LAMBDA.2 (XX) ; (CONS.2 XX (CONS.2 XX (QUOTE.2 ())))) ; (QUOTE.2 somedata))) ; (QUOTE.1 ()) ; ) ; ) ; <McCarthy-60-interpreter.1> ; ) ; ; ; This is how McCarthy-60-interpreter.1 looks like: ; (McCarthy-60-Lisp in Newlisp library first.) (load (append "http://www.instprog.com/McCarthy-60-LISP/" "McCarthy-60-LISP-in-Newlisp.lsp")) (setf McCarthy-60-interpreter.1 '(QUOTE ( ;------------------------- (EVAL.1 (LABEL.1 EVAL.1 (LAMBDA.1 (e a) (COND.1 ((ATOM.1 e) (ASSOC.1 e a)) ;------------------------- ((ATOM.1 (CAR.1 e)) (COND.1 ((EQ.1 (CAR.1 e) (QUOTE.1 QUOTE.2)) (CAR.1 (CDR.1 e))) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 ATOM.2)) (ATOM.1 (EVAL.1 (CAR.1 (CDR.1 e)) a))) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 EQ.2)) (EQ.1 (EVAL.1 (CAR.1 (CDR.1 e)) a) (EVAL.1 (CAR.1 (CDR.1 (CDR.1 e))) a))) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 COND.2)) (EVCON.1 (CDR.1 e) a)) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 AND.2)) (EVAL.1 (CONS.1 (QUOTE.1 COND.2) (CONS.1 (CDR.1 e) (QUOTE.1 (((QUOTE.2 T) (QUOTE.2 F)))))) a)) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 CAR.2)) (CAR.1 (EVAL.1 (CAR.1 (CDR.1 e)) a))) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 CDR.2)) (CDR.1 (EVAL.1 (CAR.1 (CDR.1 e)) a))) ;------------------------- ((EQ.1 (CAR.1 e) (QUOTE.1 CONS.2)) (CONS.1 (EVAL.1 (CAR.1 (CDR.1 e)) a) (EVAL.1 (CAR.1 (CDR.1 (CDR.1 e))) a))) ;------------------------- ((QUOTE.1 T) (EVAL.1 (CONS.1 (ASSOC.1 (CAR.1 e) a) (CDR.1 e)) a)))) ;------------------------- ((EQ.1 (CAR.1 (CAR.1 e)) (QUOTE.1 LABEL.2)) (EVAL.1 (CONS.1 (CAR.1 (CDR.1 (CDR.1 (CAR.1 e)))) (CDR.1 e)) (CONS.1 (LIST.1 (CAR.1 (CDR.1 (CAR.1 e))) (CAR.1 e)) a))) ;------------------------- ((EQ.1 (CAR.1 (CAR.1 e)) (QUOTE.1 LAMBDA.2)) (EVAL.1 (CAR.1 (CDR.1 (CDR.1 (CAR.1 e)))) (APPEND.1 (PAIR.1 (CAR.1 (CDR.1 (CAR.1 e))) (EVLIS.1 (CDR.1 e) a)) a))) )))) ;------------------------- (APPEND.1 (LABEL.1 APPEND.1 (LAMBDA.1(X Y) (COND.1 ((NULL.1 X) Y) ((QUOTE.1 T) (CONS.1 (CAR.1 X) (APPEND.1 (CDR.1 X) Y))))))) ;------------------------- (ASSOC.1 (LABEL.1 ASSOC.1 (LAMBDA.1 (X Y) (COND.1 ((EQ.1 (CAR.1 (CAR.1 Y)) X) (CAR.1 (CDR.1 (CAR.1 Y)))) ((QUOTE.1 T) (ASSOC.1 X (CDR.1 Y))))))) ;------------------------- (PAIR.1 (LABEL.1 PAIR.1 (LAMBDA.1 (X Y) (COND.1 ((AND.1 (NULL.1 X) (NULL.1 Y)) (QUOTE.1 NIL)) ((AND.1 (NOT.1 (ATOM.1 X)) (NOT.1 (ATOM.1 Y))) (CONS.1 (LIST.1 (CAR.1 X) (CAR.1 Y)) (PAIR.1 (CDR.1 X) (CDR.1 Y)))))))) ;------------------------- (EVLIS.1 (LABEL.1 EVLIS.1 (LAMBDA.1 (m a) (COND.1 ((NULL.1 m) (QUOTE.1 NIL)) ((QUOTE.1 T) (CONS.1 (EVAL.1 (CAR.1 m) a) (EVLIS.1 (CDR.1 m) a))))))) ;------------------------- (EVCON.1 (LABEL.1 EVCON.1 (LAMBDA.1 (c a) (COND.1 ((EVAL.1 (CAR.1 (CAR.1 c)) a) (EVAL.1 (CAR.1 (CDR.1 (CAR.1 c))) a)) ((QUOTE.1 T) (EVCON.1 (CDR.1 c) a)))))) ;------------------------- (NULL.1 (LAMBDA.1 (X) (AND.1 (ATOM.1 X) (EQ.1 X (QUOTE.1 NIL))))) ;------------------------- (NOT.1 (LAMBDA.1 (X) (COND.1 (X (QUOTE.1 F)) ((QUOTE.1 T)(QUOTE.1 T))))) ;------------------------- (LIST.1 (LAMBDA.1 (X Y) (CONS.1 X (CONS.1 Y (QUOTE.1 NIL))))) ) ) ) ; variable McCarthy-60-interpreter.1 cannot be used directly. It ; has to be replaced with its value first. ; ; Once McCarthy-60-interpreter.1 is defined, it is easy to generalize ; it and define McCarthy-60-interpreter.2, McCarthy-60-interpreter.3,... ; Just respective indexes should be changed. ; ; Here is Newlisp function that calculate these interpreters, for ; given n: (define (McCarthy-60-interpreter n) (if (= n 1) McCarthy-60-interpreter.1 (letn((symbols-in-McCarthy-60-interpreter.1 (difference (unique (flat McCarthy-60-interpreter.1)) '(T F NIL))) (assoc-list1 (map (lambda(x) (list x (if (find x '(QUOTE e a X Y m c)) (sym (append "°" (string x) "." (string (- n 1)))) (let ((parsed-x (parse (string x) "."))) (case (last parsed-x) ("1" (sym (append "°" (first parsed-x) "." (string n)))) ("2" (sym (append "°" (first parsed-x) "." (string (+ n 1)))))))))) symbols-in-McCarthy-60-interpreter.1)) (assoc-list2 (map (lambda(x) (list (last x) (sym (rest (string (last x)))))) assoc-list1))) (local(result) (setf result (expand McCarthy-60-interpreter.1 assoc-list1)) (setf result (expand result assoc-list2)) result)))) ; And this is an example how these interpreters could be used (setf McCarthy-60-interpreter.2 (McCarthy-60-interpreter 2)) (debug-wrap EVAL) (eval (expand '(EVAL (QUOTE (EVAL.1 (QUOTE.1 (EVAL.2 (QUOTE.2 (QUOTE.3 somedata)) (QUOTE.2 ()) ) ) McCarthy-60-interpreter.2 ) ) McCarthy-60-interpreter.1 ) 'McCarthy-60-interpreter.1 'McCarthy-60-interpreter.2 ) ) ; McCarthy's EVAL is, however, very inefficient - its purpose was ; purely theoretical, so, if you want to really evaluate this simple ; expression prepare yourself on long waiting. (Less than one hour ; on modern PC, however.) |
Part of the output of the program
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