lambdaspeech :: javascript

_h1 javascript

_p Following the λ-calculus style, we build data and control structures, for instance pairs, lists and recursion, exclusively using {b lambda}s and {b def}s without any {b '{if bool then one else two}} structure. We begin with {b speech} and translate code into the {b JS} syntax.

_h2 1) using speech

{prewrap °° 
1) words

{def pair  {lambda {:x :y :z} {:z :x :y}}}
{def left  {lambda {:z} {:z {lambda {:x :y} :x}}}}
{def right {lambda {:z} {:z {lambda {:x :y} :y}}}}

{def HI {pair hello world}}
{left {HI}}  -> hello
{right {HI}} -> world

{def nil   {lambda {:f :x} :x}}
{def isnil {lambda {:z} {:z {lambda {:x} right} left}}}

{isnil nil}  -> left
{isnil {HI}} -> right

{def list.disp
 {lambda {:list}
  {{{isnil :list}
   {pair
    {lambda {:list} .}
    {lambda {:list} {left :list} {list.disp {right :list}}
   }}} :list}}}

{def fruits
 {pair apple
  {pair banana
   {pair lemon
    {pair grapes
     {pair orange nil}}}}}}

{list.disp {fruits}}
-> apple banana lemon grapes orange .

2) numbers as lists

{def succ {lambda {:n} {pair | :n}}} 
{def pred 
 {lambda {:n}
  {{{isnil :n}   
   {pair {lambda {:n} :n} 
         {lambda {:n} {right :n}}
  }} :n}}}

{def zero nil}
{def one {succ {zero}}}
{def two {succ {one}}}
{def three {succ {two}}}
{def four {succ {three}}}
{def five {succ {four}}}
{def six {succ {five}}}

{def add
 {lambda {:a :b}
  {{{isnil :b}
   {pair
    {lambda {:a :b} :a}
    {lambda {:a :b} {add {succ :a} {pred :b}}}
  }} :a :b}}}

{def mul
 {def mul.rec
  {lambda {:a :b :c}
   {{{isnil :b}
    {pair
     {lambda {:a :b :c} :a}
     {lambda {:a :b :c}
      {mul.rec {add :a :c} {pred :b} :c}}
   }} :a :b :c}}}
 {lambda {:a :b} {mul.rec :a {pred :b} :a}}}

{def fac
 {lambda {:n}
  {{{isnil :n}
   {pair
    {lambda {:n} {one}}
    {lambda {:n} {mul :n {fac {pred :n}}}}
  }} :n}}}

{def tfac
 {lambda {:a :b}
  {{{< :b 1}
   {pair
    {lambda {:a :b} :a}
    {lambda {:a :b} {tfac {* :a :b} {- :b 1}}
   }}} :a :b}}}

{list.disp {tfac {one six}}} -> 
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°°}

_p Stack overflow after 8 or 9.

_h2 2) using javascript

_p The translation must follow these points:
_ul Javascript has closures but no native partial application, we have to modify slightly the speech {b pair} function. 
_ul words must be protected between quotes. 
_ul everything else is identical.

{pre °°

// 1) words

var nil   = function(s,z) { return z };
var isnil = function(n) { return n( function(x) { return right }, left ) };

var list_disp = function(list) {
  return isnil(list)( 
    pair(
     function(list) { return '.' },
     function(list) { return left(list) + ' ' + list_disp(right(list)) }
    ))(list)  
};

var fruits =
 pair( 'apple',
  pair( 'banana',
   pair( 'lemon',
    pair( 'grapes',
     pair( 'orange', nil)))));

list_disp( fruits );
// -> apple banana lemon grapes orange .

// 2) numbers as lists

var succ = function(n) { return pair( '|', n ) }; 
var pred = function(n) {
  return isnil(n)( 
    pair(   
     function(n) { return n }, 
     function(n) { return right(n) }
  ))(n) 
};

var zero = nil; 
var one = succ(zero);
var two = succ(one);
var three = succ(two);
var four = succ(three);
var five = succ(four);
var six = succ(five);

var fac = function(n) {
  return isnil(n)(
   pair( function(n) { return one },
         function(n) { return mul( n, fac( pred(n) )) }
   ))(n)
};
var tfac = function(a,b) {
  return isnil(b)(
   pair( function(a,b) { return a },
         function(a,b) { return tfac( mul(a,b), pred(b) ) }
   ))(a,b)
};

var display = function() {
  document.getElementById('output').innerHTML = tfac( one, six ); 
};

// setTimeout( display, 1 ); 
°°}

_p Output from javascript

{prewrap 
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}

_p Much more faster than speech but stack overflow after 8 or 9, asame. Syntaxes are similar, but the speech's syntax looks more uniform, more simple.

{script ;;
var pair  = function(x,y) { return function(z) { return z(x,y) } };
var left  = function(z)   { return z( function(x,y) { return x }) };
var right = function(z)   { return z( function(x,y) { return y }) };

var nil   = function(s,z) { return z };
var isnil = function(n) { return n( function(x) { return right }, left ) };

var list_disp = function(list) {
  return isnil(list)( 
    pair(
     function(list) { return '.' },
     function(list) { return left(list) + ' ' + list_disp(right(list)) }
    ))(list)  
};

var fruits =
 pair( 'apple',
  pair( 'banana',
   pair( 'lemon',
    pair( 'grapes',
     pair( 'orange', nil)))));

// numbers

var succ = function(n) { return pair( '|', n ) }; 
var pred = function(n) {
  return isnil(n)( 
    pair(   
     function(n) { return n }, 
     function(n) { return right(n) }
  ))(n) 
};

var zero = nil; 
var one = succ(zero);
var two = succ(one);
var three = succ(two);
var four = succ(three);
var five = succ(four);
var six = succ(five);

var display = function() {
  document.getElementById('output').innerHTML = list_disp( tfac( one,six ) ); 
};

// setTimeout( display, 1 ); 
}