Difference between revisions of "Trains"

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</tr>
 
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   <td><apll>L</apll> and <apll>R</apll> are arbitrary arrays, <apll>f</apll>, <apll>g</apll>, <apll>h</apll>, etc, are arbitrary functions of any type:  primitive, user-defined, system, and/or derived.</td>
+
   <td><apll>L</apll> and <apll>R</apll> are arbitrary arrays, <apll>f</apll>, <apll>g</apll>, <apll>h</apll>, etc, are arbitrary functions of any type:  primitive, user-defined, system, anonymous, and/or derived.</td>
 
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<p>For example,</p>
 
<p>For example,</p>
  
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(,⍎)'2+3'</apll><br />
+
<apll>     (,⍎)'2+3'</apll><br />
<apll>←→&nbsp;&nbsp;&nbsp;&nbsp;'2+3',⍎'2+3'</apll><br />
+
<apll>←→   '2+3',⍎'2+3'</apll><br />
<apll>←→&nbsp;&nbsp;&nbsp;&nbsp;'2+3',5</apll><br />
+
<apll>←→   '2+3',5</apll><br />
 
<apll>2+3 5</apll><br />
 
<apll>2+3 5</apll><br />
  
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;avg{is}(+⌿ ÷ ≢)</apll>  defines a function that computes the average of a numeric vector.<br />
+
<apll>     avg{is}(+⌿ ÷ ≢)</apll>  defines a function that computes the average of a numeric vector.<br />
<apll>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;avg 1 2 3 4</apll><br />
+
<apll>     avg 1 2 3 4</apll><br />
<apll>←→&nbsp;&nbsp;&nbsp;&nbsp;(+⌿ ÷ ≢) 1 2 3 4</apll><br />
+
<apll>←→   (+⌿ ÷ ≢) 1 2 3 4</apll><br />
<apll>←→&nbsp;&nbsp;&nbsp;&nbsp;(+⌿1 2 3 4) ÷ ≢1 2 3 4</apll><br />
+
<apll>←→   (+⌿1 2 3 4) ÷ ≢1 2 3 4</apll><br />
<apll>←→&nbsp;&nbsp;&nbsp;&nbsp;10 ÷ 4</apll><br />
+
<apll>←→   10 ÷ 4</apll><br />
 
<apll>2.5</apll>
 
<apll>2.5</apll>
  
 
<p>Longer Trains are defined as follows:</p>
 
<p>Longer Trains are defined as follows:</p>
  
<apll>&nbsp;&nbsp;(e f g h) ←→ &nbsp;&nbsp;(e (f g h))</apll><br />
+
<apll> (e f g h) ←→   (e (f g h))</apll><br />
 
<apll>(d e f g h) ←→ (d e (f g h))</apll><br />
 
<apll>(d e f g h) ←→ (d e (f g h))</apll><br />
  
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{|border="0"
 
{|border="0"
|Even length:  || <apll>(a b c ...) ←→  (a (b &nbsp;c ...))</apll>
+
|Even length:  || <apll>(a b c ...) ←→  (a (b c ...))</apll>
 
|-
 
|-
|Odd  length:  || <apll>(a b c ...) ←→  (a &nbsp;b (c ...))</apll>
+
|Odd  length:  || <apll>(a b c ...) ←→  (a b (c ...))</apll>
 
|}
 
|}
  

Latest revision as of 19:32, 15 April 2018

Z←  (f g) R is called a Monadic HookZ ≡ R f g R
Z←L (f g) R is called a Dyadic HookZ ≡ L f g R
Z←  (f g h) R is called a Monadic ForkZ ≡ (f R) g h R
Z←L (f g h) R is called a Dyadic ForkZ ≡ (L f R) g L h R
Z←  (f g h ...) R
Z←L (f g h ...) R
is also defined for longer Trains
L and R are arbitrary arrays, f, g, h, etc, are arbitrary functions of any type: primitive, user-defined, system, anonymous, and/or derived.


This clever idea from the designers of J is called Trains where a parenthesized sequence of functions (which normally would signal a SYNTAX ERROR) can be interpreted as per the above descriptions. Very nicely, they fit into and extend the spectrum of function definition syntax from user-defined to dynamic to trains to operator expressions. They are another and very interesting form of functional programming.

Note that the spacing between functions is for visual purposes only — it has no effect on the interpretation.

For example,

(,⍎)'2+3'
←→ '2+3',⍎'2+3'
←→ '2+3',5
2+3 5

avg←(+⌿ ÷ ≢) defines a function that computes the average of a numeric vector.
avg 1 2 3 4
←→ (+⌿ ÷ ≢) 1 2 3 4
←→ (+⌿1 2 3 4) ÷ ≢1 2 3 4
←→ 10 ÷ 4
2.5

Longer Trains are defined as follows:

(e f g h) ←→ (e (f g h))
(d e f g h) ←→ (d e (f g h))

and in general

Even length: (a b c ...) ←→ (a (b c ...))
Odd length: (a b c ...) ←→ (a b (c ...))

For more applications of this concept, see the discussion in the Learning J manual.

There is also a series of tables of common function expressions and their corresponding Train.