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Refal (“Recursive capabilities algorithmic language”) “is a purposeful programming language oriented toward symbolic computations”, alongside side “string processing, language translation, [and] synthetic intelligence“.[1] It is one among the oldest contributors of this household, first conceived of in 1966 as a theoretical instrument, with the first implementation exhibiting in 1968. Refal used to be supposed to combine mathematical simplicity with practicality for writing spacious and complex capabilities.

One amongst the first purposeful programming languages to attain so, and never like Screech of its time, Refal is in accordance with sample matching. Its sample matching works alongside side time-frame rewriting.

The basic recordsdata structure of Screech and Prolog is a linear listing built by cons operation in a sequential manner, thus with O(n) salvage admission to to listing’s nth side. Refal’s lists are built and scanned from each ends, with sample matching working for nested lists as neatly as the prime-level one. In attain, the final recordsdata structure of Refal is a tree in space of a listing. This gives freedom and convenience in creating recordsdata structures whereas the usage of only mathematically straightforward retain a watch on mechanisms of sample matching and substitution.

Refal moreover features a way known as the freezer to spice up surroundings generous partial evaluation.

Refal can also merely moreover be applied to the processing and transformation of tree structures, equally to XSLT.[2]


A Refal Hello World instance is proven under.

$ENTRY Hasten { = ;}
Hello {
   = ;

This system above includes two capabilities named Hasten and Hello. A way is written as the title of the way followed by the way physique in curly braces. The Hasten way is marked as the entry point of this design the usage of the $ENTRY directive.

One can also heart of attention on expressions within the way bodies as way “calls” in Screech-adore syntax. As an instance, the Hello way appears to be like to name the built-in Prout way with the string ‘Hello world’ as the argument. The which manner and the mechanism of the resolution, nevertheless, is extraordinarily rather about a. To illustrate the variation, gather into consideration the following way that determines whether or no longer a string is a palindrome.

 Buddy { = Correct;
    s.1 = Correct;
    s.1 e.2 s.1 = ;
    e.1 = Mistaken;  }

This case shows a way with a extra complex physique, consisting of four sentences (clauses). A sentence begins with a sample followed by an equal signal followed by a usual expression on the trusty hand side. A sentence is terminated with a semicolon. As an instance, the sample of the second sentence of the way is “s.1” and the expression is “Correct”.

As the instance shows, patterns consist of sample variables that gather the invent of a character figuring out the form of the variable (what the variable fits) followed by the variable identifier. The variables that starting up up with an “s” match a single symbol, of us that starting up up with an “e” match an arbitrary expression. The variable identifier can also merely moreover be an arbitrary alphanumeric sequence optionally separated from the kind identifier by a dot.

A way executes by comparing its argument with the patterns of its sentences within the describe they look within the definition, except the first sample that matches. The way then replaces the argument with the expression on the trusty hand side of the matched sentence.

If the outcomes of a way utility features a subexpression in angle brackets (as it could per chance well well after the third sentence of our instance is applied), the outcome is extra processed by Refal by invoking the way identified by the first symbol within the brackets. Execution stops when the outcome has no extra angle brackets to enlarge on this means.

The way Buddy can thus be study informally as: “If the expression is empty, change it with Correct. Otherwise if the expression is a single symbol, change it with Correct. Otherwise if the expression is an emblem followed by an arbitrary expression e.2 followed by the same symbol, change it with the expression . (In other words, throw away the 2 same symbols firstly and the prime and recurse). Otherwise change the expression with Mistaken. (The sample e.1 constantly fits).”

The next are three step-by-step execution traces annotated with the sentence numbers applied at every step to salvage the following


We are capable of now look that the Hello World instance genuinely executes as the sequence of the following expression transformations:

      Seed the machine with the initial expression marked by $ENTRY:
                  (apply the sentence in Hasten)
               (apply the sentence in Hello)
  (Prout is a built-in that prints and expands to nothing)
                       (nothing to apply; live)

Other examples[edit]


 Truth { 0 = 1;
    s.N = >>; }

Here 0 fits 0 the number and produces 1. On every other symbol which is a host, multiply it with the outcomes of (Truth (- s.N 1))
Present the prefix form of operators.

Factorial with loops[edit]

 Truth { s.n = ; };
 Loop {
    0 s.f = s.f;
    s.n s.f =  >; }

As can also merely moreover be seen s.n acts as the loop counter.


 Equal {
    (e.1)(e.1) = T;
    (e.1)(e.2) = F; }

Here the way is defined as, if given two terms, and the terms are same then the first clause fits and produces Correct.
else the second clause fits and produces Mistaken.

A crucial property of Refal is that all capabilities in refal are single argument. (However will seemingly be
decomposed into terms in an expression as above.)


Defining retain a watch on structures is easy

 If {
    T Then (e.1) Else (e.2) = e.1;
    F Then (e.1) Else (e.2) = e.2;  }

Here the e1 is evaluated only when the expression entered fits ‘Correct’ Then e1 Else e2
the same for e2.

Squeeze blanks[edit]

 Squeeze {
    e.1'__'e.2 = ;
    e.1 = e.1; }

(Utilizing ‘_’ as opposed to living char in converse to provide the way name certain.)
The predominant clause fits at any time when the way Squeeze encounters double
blanks in its input expression, and replaces it with a single blank.
The second clause fits only when the first one did no longer, and returns the
resultant price which is the fresh expression.

Squeeze the usage of converse looping[edit]

 Squeeze {
    '__'e.1 = ;
    s.A e.1 = s.A ;
    = ; };


External links[edit]

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