The Magnificent Seven


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The Magnificent Seven

  1. 1. The Magnificent Seven by Michael Fogus creating a Lisp variant in seven forms Who am I? Michael Fogus Software Programmer 12 years experience Lisp, C, CLIPS, Prolog, C++, Java, Jess, Python, Scala, Clojure Co-author of The Joy of Clojure @fogus on the Intertweets Lisp History John McCarthy
  2. 2. 1958 Massachusetts Institute of Technology (MIT) IBM 704 (origin of car and cdr) Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I [1] [1] Lisp Innovations Dynamic types Garbage collection if-then-else (via cond) Tree data structures Homoiconicity... McCarthy's Magnificent Seven McCarthy's Seven [2] Had car cdr cons cond label and lambda, dynamic scoping [3] , lists (kinda) atom eq quote Didn't Have closures, macros, numbers [2] [3] Building from parts (label and (lambda (and_x and_y) (cond (and_x (cond (and_y t) (t nil))) (t nil)))) (and t nil) ;=> nil
  3. 3. (and t t) ;=> t Building from parts (continued) (label list (lambda (x y) (cons x (cons y (quote ()))))) (def append (lambda (append_x append_y) (cond ((null append_x) append_y) (t (cons (car append_x) (append (cdr append_x) append_y)))))) (append (list 1 2) (list 3 4)) ;=> (1 2 3 4) You can see where this is going... Meta-circular Evaluator FTW (def eval (lambda (expr binds) (cond ((atom expr) (assoc expr binds)) ((atom (car expr)) (cond ((eq (car expr) (quote quote)) (cadr expr)) ((eq (car expr) (quote atom)) (atom (eval (cadr expr) binds))) ((eq (car expr) (quote eq)) (eq (eval (cadr expr) binds) (eval (caddr expr) binds))) ((eq (car expr) (quote car)) (car (eval (cadr expr) binds))) ((eq (car expr) (quote cdr)) (cdr (eval (cadr expr) binds))) ((eq (car expr) (quote cons)) (cons (eval (cadr expr) binds) (eval (caddr expr) binds))) ((eq (car expr) (quote cond)) (eval-cond (cdr expr) binds)) (t (eval (cons (assoc (car expr) binds) (cdr expr)) binds)))) ((eq (caar expr) (quote def)) (eval (cons (caddar expr) (cdr expr)) (cons (list (cadar expr) (car expr)) binds))) ((eq (caar expr) (quote lambda)) (eval (caddar expr) (append (pair (cadar expr) (eval-args (cdr expr) binds)) binds))) (t (assoc expr binds))))) note: not all code shown Breathtaking!
  4. 4. Fojure
  5. 5. Feajures 7 core funcjions and 2 spejial fjorms Symbolj Lajy Single immutable data strucjure Funcjional Lexical Scopjure Closures The Magnificent Seven fn def No Need For car and cdr (def CAR (fn [[h & _]] h)) (def CDR (fn [[_ & t]] t)) (CAR [1 2 3]) ;=> 1 (CDR [1 2 3]) ;=> (2 3) Wait! What?!? I never mentioned anything about vectors No Need For cons (def CONS (fn [h t] (fn ([] h) ([_] t)))) (CONS 1 (CONS 2 (CONS 3 nil))) ;=> #<user$CONS$fn__85 user$CONS$fn__85@445e228> A closure over the head and tail
  6. 6. A good start... Closure: A Poor Man's Object Closure Dissection (def CONS (fn [h t] (fn ([] h) ([_] t)))) A closure head tail A closure is an Object with a single method .apply(...) The New first and rest (def FIRST (fn [s] (s))) (def REST (fn [s] (s nil))) (def a (CONS 1 (CONS 2 (CONS 3 nil)))) (FIRST a) ;=> 1 (REST a) ;=> #<user$CONS$fn__85 user$CONS$fn__85@375e293a> (FIRST (REST a)) ;=> 2 Saplings 1. 1 = 2. 2 if 3. 3 ' 4. 4 :keywords Yet Another CONS (def CONS
  7. 7. (fn [h t] (fn [d] (if (= d :type) 'CONS (if (= d :head) h t))))) (def $ (CONS 'a (CONS 'b nil))) ;=> #<user$CONS$fn__4 user$CONS$fn__4@61578aab> ($ :type) ;=> CONS ($ :head) ;=> a (($ :tail) :head) ;=> b Now what does this look like? Cons Cell Object: A Poor Man's Closure A Protocol for seqs Call with :type to inspect the seq type Return CONS when type is a cons cell Call with :head to get the head Call with antyhing else to get the tail first and rest (def FIRST (fn [x] (if x (if (= (x :type) 'CONS) (x :head)
  8. 8. (if (x) ((x) :head)))))) (def REST (fn [x] (if x (if (= (x :type) 'CONS) (x :tail) (if (x) ((x) :tail)))))) (FIRST $) ;=> a (REST $) ;=> #<user$CONS$fn__17 user$CONS$fn__17@2eb0a3f5> (FIRST (REST $)) ;=> b We can do a ton with only CONS , FIRST and REST ! seq (def SEQ (fn [x] (if x (if (= (x :type) 'CONS) x (if (x) (SEQ (x))))))) (SEQ $) ;=> #<user$CONS$fn__97 user$CONS$fn__97@293b9fae> (FIRST (SEQ $)) ;=> a (SEQ (REST (REST $))) ;=> nil prn (def PRN (fn [s] (if (SEQ s) (do (print (FIRST (SEQ s))) (print " ") (recur (REST s))) (println)))) (PRN $)
  9. 9. ; a b (PRN (CONS 'a nil)) ; a This doesn't count append (def APPEND (fn app [l r] (if (FIRST l) (CONS (FIRST l) (app (REST l) r)) r))) (PRN (APPEND (CONS 'x nil) (CONS 'y (CONS 'z nil)))) ; x y z But this is not a convenient way to deal with lists Lists 1. 5 apply list (def LIST (fn ls ([h] (CONS h nil)) ([h t] (CONS h (CONS t nil))) ([h m & [f & r]] (if (CAR r) (if (CAR (CDR r)) (APPEND (LIST h m) (apply ls f (CAR r) (CDR r))) (APPEND (LIST h m) (LIST f (CAR r)))) (CONS h (LIST m f)))))) (PRN (LIST 'a 'b 'c 'd 'e 'f)) ; a b c d e f (SEQ (REST (LIST 'a))) ;=> nil (PRN (APPEND (LIST 'a 'b) (LIST 'x 'y))) ; a b x y Using CAR, CDR, and destructuring as the primordial first and rest
  10. 10. Being Lazy Being Lazy TODO Lazy seqs Lazy seq (def LAZY-SEQ (fn [f] (fn ([x] (if (= x :type) 'LAZY-SEQ)) ([] (f))))) (FIRST ((LAZY-SEQ (fn [] (LIST 'a 'b 'c))))) ;=> a (PRN ((LAZY-SEQ (fn [] (LIST 'a 'b 'c))))) ; a b c Now we have a protocol for lazy seqs A Protocol for lazy seqs Wrap the part that you want to be lazy in a fn Pass that fn to LAZY-SEQ Conform to the semantics of :type Deal with the extra level of indirection when dealing with lazy seqs map (def MAP (fn [f s] (LAZY-SEQ (fn [] (if (SEQ s) (CONS (f (FIRST s)) (MAP f (REST s)))))))) (PRN (MAP keyword (LIST 'a 'b 'c))) ; :a :b :c
  11. 11. (PRN (MAP LIST (LIST 'a 'b))) ; #<user$CONS$fn__356 user$CONS$fn__356@54cb2185> ... (PRN (FIRST (MAP LIST (LIST 'a 'b)))) ; a Control Structures 6 defmacro 7 ` let (let [a 1] (let [b 2] (println [a b])) (println [a b])) ; java.lang.Exception: Unable to resolve symbol: b in this context Defines a scope for named values LET (defmacro LET [[bind val] & body] `((fn [~bind] ~@body) ~val)) (LET (a 1) (LET (b 2) (println [a b]))) produces... ((fn [a] ((fn [b] (println [a b])) 2)) 1) more or less More LET
  12. 12. (FIRST (LET (x 'a) (CONS x nil))) ;=> a (PRN (LET (x 'x) (LET (y 'y) (CONS x (CONS y $))))) ; x y a b And the rest is mechanical but... We didn't need keywords... Symbols would have worked just as well (def CONS (fn [a b] (fn ([x] (if (= x 'lazy) 'CONS (if (= x 'head) a b)))))) (def $$ (CONS 'a (CONS 'b nil))) ($$ 'head) ;=> a ($$ 'tail) ;=> #<user$CONS$fn__91 user$CONS$fn__91@58e22f2b> The Magnificent 6 = if ' :keywords apply defmacro `
  13. 13. and... We didn't need apply... defmacro gives us that for free (defmacro APPLY [f args] `(~f ~@args)) (APPLY + [1 2 3 4]) ;=> 10 (PRN (APPLY LIST '[a b c d e])) ; a b c d e The Magnificent 5 = if ' :keywords apply defmacro ` and... We didn't need defmacro and `... why not?
  14. 14. Meta-circular Evaluator FTW (def EVAL (fn (expr binds) (COND ((ATOM expr) (ASSOC expr binds)) ((ATOM (FIRST expr)) (COND ((= (FIRST expr) 'quote) (SECOND expr)) ((= (FIRST expr) 'ATOM) (ATOM (EVAL (SECOND expr) binds))) ((= (FIRST expr) '=) (= (EVAL (SECOND expr) binds) (EVAL (THIRD expr) binds))) ((= (FIRST expr) 'FIRST) (FIRST (EVAL (SECOND expr) binds))) ((= (FIRST expr) 'REST) (REST (EVAL (SECOND expr) binds))) ((= (FIRST expr) 'CONS) (CONS (EVAL (SECOND expr) binds) (EVAL (THIRD expr) binds))) ((= (FIRST expr) 'COND) (EVAL-COND (REST expr) binds)) ('true (EVAL (CONS (ASSOC (FIRST expr) binds) (REST expr)) binds)))) ((= (CAAR expr) 'def) (EVAL (CONS (CADDAR expr) (REST expr)) (CONS (LIST (CADAR expr) (FIRST expr)) binds))) ((= (CAAR expr) 'fn) (EVAL (CADDAR expr)
  15. 15. (APPEND (PAIR (CADAR expr) (EVAL-ARGS (REST expr) binds)) binds))) ('true (ASSOC expr binds))))) note: not all code shown The Magnificent 3 = if ' :keywords apply defmacro ` The Magnificent 3!?! Our Options deftype defprotocol reify intern . defmulti defmethod defrecord first rest [] ^ {} delay force new defclass proxy list* fn* fn? seq clojure.lang.RT and so on... The Garden of Forking Paths
  16. 16. Thank You