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Computers

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What are they even?

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@igorwhiletrue

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A little history

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brb inventing programming

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computers they’re so great <3 Alonzo Church

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John McCarthy

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I <3 computers but hate assembly language

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(

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( ) parentheses are hugs

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❤ ( )

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How to read lisp code, in one easy step

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foo(1, 2)

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(foo 1 2)

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(+ 1 2)

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3

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Growing a language

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a bar foo atom

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cons

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first

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rest

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a b

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(a . b)

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a

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(a . nil)

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a b c

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(a . (b . (c . nil)))

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(a b c)

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(foo (bar) (baz qux))

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foo bar baz qux

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foo(bar(), baz(qux))

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foo bar baz qux fn arg 0 arg 1 fn fn arg 0 call call call

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(foo (bar) (baz qux))

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(foo (bar) (baz qux)) fn arg 0 arg 1

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(foo (bar) (baz qux)) fn arg 0 fn

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(quote (a b c))

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'(a b c)

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(first '(a b c)) !

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(first '(a b c)) ! 'a

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a b c

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(rest '(a b c)) !

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(rest '(a b c)) ! '(b c)

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a b c

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(cons 'a '(b c)) !

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(cons 'a '(b c)) ! '(a b c)

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a b c

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5 3.14 "fubar" variable :keyword

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(fn [x] x)

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(fn [x] x) arguments

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(fn [x] x) body

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(def answer 42)

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(def hello (fn [name] (str "Hello " name)))

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(hello “Laracon”)

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No loops

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Recursive functions

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in order to understand rec ursion, one must first understand re cursion,

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll)))))

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(member? 'c '(a b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d)) (member? 'c '(c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d)) (member? 'c '(c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d)) (member? 'c '(c d))

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d)) (member? 'c '(c d)) => true

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) (member? 'c '(b c d)) => true

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(defn member? [x coll] (cond (empty? coll) false :else (or (= (first coll) x) (member? x (rest coll))))) ! (member? 'c '(a b c d)) => true

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true

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Macros

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(foo (bar) (baz qux))

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"(+ 1 2)" Reader + 1 2 + 1 2 Eval 3 Compile-time Runtime x 0 y 1 z 2

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"(a 1 2)" Reader a 1 2 Compile-time Macro b 5 6 a 1 2

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(defn id [x] x) ! (def id (fn [x] x)) =>

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(-> '(foo bar baz) reverse first name string/reverse) (string/reverse (name (first (reverse '(foo bar baz)))) =>

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class Foo ($bar) { } class Foo { private $bar; function __construct($bar) { $this->bar = $bar; } } =>

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Backporting?

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function () use ($foo) { return qux($foo); } => () ==> qux($foo)

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hhvm 5.6 5.5 5.4 FI ...

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Computer Science

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Computer Science

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Computer Science

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Y-Combinator

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(defn Y [le] ((fn [f] (f f)) (fn [f] (le #((f f) %)))))

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(defn fac [f] (fn [x] (if (zero? x) 1 (* x (f (dec x))))))

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((Y fac) 5)

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((Y ) 5) (fn [f] (fn [x] (if (zero? x) 1 (* x (f (dec x))))))

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(( ) 5) (fn [f] (fn [x] (if (zero? x) 1 (* x (f (dec x)))))) (fn [le] ((fn [f] (f f)) (fn [f] (le #((f f) %)))))

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Lambda Calculus

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0: (fn [f] identity) 1: (fn [f] f) 2: (fn [f] #(f (f %))) 3: (fn [f] #(f (f (f %))))

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((n inc) 0)

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(( inc) 0) (fn [f] identity)

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( 0) identity

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0

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(( inc) 0) (fn [f] f)

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( 0) inc

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1

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(( inc) 0) (fn [f] #(f (f %)))

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( 0) #(inc (inc %))

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2

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(defn INC [n] (fn [p] (fn [x] (p ((n p) x))))) ! ! (defn DEC [n] (fn [f] (fn [x] (((n (fn [g] (fn [h] (h (g f))))) (fn [y] x)) (fn [y] y))))) ! ! (defn ADD [m] (fn [n] ((n INC) m))) ! ! (defn MUL [m] (fn [n] ((n (ADD m)) ZERO)))

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Meta-circular evaluator

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(defun null. (x) (eq x '())) ! (defun and. (x y) (cond (x (cond (y 't) ('t '()))) ('t '()))) ! (defun not. (x) (cond (x '()) ('t 't))) ! (defun append. (x y) (cond ((null. x) y) ('t (cons (car x) (append. (cdr x) y))))) ! (defun list. (x y) (cons x (cons y '()))) ! (defun pair. (x y) (cond ((and. (null. x) (null. y)) '()) ((and. (not. (atom x)) (not. (atom y))) (cons (list. (car x) (car y)) (pair. (cdr x) (cdr y)))))) ! (defun assoc. (x y) (cond ((eq (caar y) x) (cadar y)) ('t (assoc. x (cdr y))))) (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) '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))) ((eq (car e) 'cond) (evcon. (cdr e) a)) ('t (eval. (cons (assoc. (car e) a) (cdr e)) 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))))) ! (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) '()) ('t (cons (eval. (car m) a) (evlis. (cdr m) a)))))

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62 LOC

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function evaluate($expr, $env = []) { if (is_string($expr)) { if (is_numeric($expr)) { $val = (float) $expr; return [$val, $env]; } if ('true' === $expr) { return [true, $env]; } if ('false' === $expr) { return [false, $env]; } if ('null' === $expr) { return [null, $env]; } $var = $expr; return [$env[$var], $env]; } $fn = array_shift($expr); $args = $expr; if ('define' === $fn) { list($var, $val) = $args; list($val, $env) = evaluate($val, $env); $env = array_merge($env, [$var => $val]); return [null, $env]; } if ('lambda' === $fn) { list($lambda_args, $code) = $args; $closure = ['closure', $lambda_args, $code, $env]; return [$closure, $env]; } if ('if' === $fn) { list($cond, $then, $else) = $args; $cond = evaluate($cond, $env)[0]; if ($cond === true) { $val = evaluate($then, $env)[0]; } else { $val = evaluate($else, $env)[0]; } return [$val, $env]; } ! $fn = evaluate($fn, $env)[0]; $args = array_map(function ($arg) use ($env) { return evaluate($arg, $env)[0]; }, $args); return apply($fn, $args, $env); } ! function apply($fn, $args, $env) { list($_, $lambda_args, $code, $closure_env) = $fn; ! $env = array_merge($env, $closure_env); $env = array_merge($env, array_combine($lambda_args, $args)); return evaluate_code($code, $env); } function evaluate_code($code, $env = []) { foreach ($code as $expr) { list($val, $env) = evaluate($expr, $env); } return [$val, $env]; }

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68 LOC

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PHPPHP: 6208 LOC github.com/ircmaxell/PHPPHP

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PHPPHP: 6208 LOC github.com/ircmaxell/PHPPHP (parser +6169 LOC)

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)

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Questions? • joind.in/11697 • github.com/igorw • lambda-php • lusp • ilias • galapagos • @igorwhiletrue

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References • Lisp Logo by Conrad Barski
 lisperati.com/logo.html • Jesus bleibet meine Freude by Jeffrey Campbell • Programming with Nothing by Tom Stuart
 codon.com/programming-with-nothing • The Magnificent Seven by Michael Fogus
 fogus.me/static/preso/magnificent7/

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• Recursive functions of symbolic expressions and their computation by machine, Part I by John McCarthy
 www-formal.stanford.edu/jmc/recursive.pdf • Growing a Language by Guy Steele
 youtube.com/watch?v=_ahvzDzKdB0 • The Lambda Papers by Guy Steele and Gerald Sussman
 library.readscheme.org/page1.html • SICP lectures by Hal Abelson and Gerald Sussman
 groups.csail.mit.edu/mac/classes/6.001/abelson- sussman-lectures/