Homoiconicity

In computer programming, homoiconicity (from the Greek words homo- meaning "the same" and icon meaning "representation") is a property of some programming languages. A language is homoiconic if a program written in it can be manipulated as data using the language, and thus the program's internal representation can be inferred just by reading the program itself. For example, a Lisp program is written as a regular Lisp list, and can be manipulated by other Lisp code.[1] In homoiconic languages, all code can be accessed and transformed as data, using the same representation. This property is often summarized by saying that the language treats "code as data".

In a homoiconic language, the primary representation of programs is also a data structure in a primitive type of the language itself. This makes metaprogramming easier than in a language without this property: reflection in the language (examining the program's entities at runtime) depends on a single, homogeneous structure, and it does not have to handle several different structures that would appear in a complex syntax.

As noted above, a commonly cited example is the programming language Lisp, which was created to be easy for lists manipulation and where the structure is given by S-expressions that take the form of nested lists. Lisp programs are written in the form of lists; the result is that the program can access its own functions and procedures while running, and programmatically alter itself on the fly. Homoiconic languages typically include full support of syntactic macros, allowing the programmer to express transformations of programs in a concise way. Examples are the programming languages Clojure (a contemporary dialect of Lisp), Rebol (also its successor Red), Refal, and more recently Julia.

History

The original source is the paper Macro Instruction Extensions of Compiler Languages,[2] according to the early and influential paper TRAC, A Text-Handling Language:[3]

One of the main design goals was that the input script of TRAC (what is typed in by the user) should be identical to the text which guides the internal action of the TRAC processor. In other words, TRAC procedures should be stored in memory as a string of characters exactly as the user typed them at the keyboard. If the TRAC procedures themselves evolve new procedures, these new procedures should also be stated in the same script. The TRAC processor in its action interprets this script as its program. In other words, the TRAC translator program (the processor) effectively converts the computer into a new computer with a new program language -- the TRAC language. At any time, it should be possible to display program or procedural information in the same form as the TRAC processor will act upon it during its execution. It is desirable that the internal character code representation be identical to, or very similar to, the external code representation. In the present TRAC implementation, the internal character representation is based upon ASCII. Because TRAC procedures and text have the same representation inside and outside the processor, the term homoiconic is applicable, from homo meaning the same, and icon meaning representation.

[...]

Following suggestion of McCullough, W. S., based upon terminology due to Peirce, C. S. s McIlroy. M. D., "Macro Instruction Extensions of Compiler Languages," Comm. ACM, p. 214-220; April, 1960.

Alan Kay used and possibly popularized the term "homoiconic" through his use of the term in his 1969 PhD thesis:[4]

A notable group of exceptions to all the previous systems are Interactive LISP [...] and TRAC. Both are functionally oriented (one list, the other string), both talk to the user with one language, and both are "homoiconic" in that their internal and external representations are essentially the same. They both have the ability to dynamically create new functions which may then be elaborated at the users's pleasure.

Their only great drawback is that programs written in them look like King Burniburiach's letter to the Sumerians done in Babylonian cuniform! [...]

Uses and advantages

One advantage of homoiconicity is that extending the language with new concepts typically becomes simpler, as data representing code can be passed between the meta and base layer of the program. The abstract syntax tree of a function may be composed and manipulated as a data structure in the meta layer, and then evaluated. It can be much easier to understand how to manipulate the code since it can be more easily understood as simple data (since the format of the language itself is as a data format).

A typical demonstration of homoiconicity is the meta-circular evaluator.

Implementation methods

All Von Neumann architecture systems, which includes the vast majority of general purpose computers today, can implicitly be described as homoiconic due to the way that raw machine code executes in memory, the data type being bytes in memory. However, this feature can also be abstracted to the programming language level.

Languages such as Lisp and its dialects,[5] such as Scheme,[6] Clojure, Racket employ S-expressions to achieve homoiconicity.

Other languages which are considered to be homoiconic include:

In Lisp

Lisp uses S-expressions as an external representation for data and code. S-expressions can be read with the primitive Lisp function READ. READ returns Lisp data: lists, symbols, numbers, strings. The primitive Lisp function EVAL uses Lisp code represented as Lisp data, computes side-effects and returns a result. The result will be printed by the primitive function PRINT, which creates an external S-expression from Lisp data.

Lisp data, a list using different data types: (sub)lists, symbols, strings and integer numbers.

((:name "john" :age 20) (:name "mary" :age 18) (:name "alice" :age 22))

Lisp code. The example uses lists, symbols and numbers.

(* (sin 1.1) (cos 2.03))      ; in infix: sin(1.1)*cos(2.03)

Create above expression with the primitive Lisp function LIST and set the variable EXPRESSION to the result

(setf expression  (list '* (list 'sin 1.1) (list 'cos 2.03)) )  
-> (* (SIN 1.1) (COS 2.03))    ; Lisp returns and prints the result

(third expression)    ; the third element of the expression
-> (COS 2.03)

Change the COS term to SIN

(setf (first (third expression)) 'SIN)
; The expression is now (* (SIN 1.1) (SIN 2.03)).

Evaluate the expression

(eval expression)
-> 0.7988834

Print the expression to a string

(print-to-string expression)
->  "(* (SIN 1.1) (SIN 2.03))"

Read the expression from a string

(read-from-string "(* (SIN 1.1) (SIN 2.03))")
->  (* (SIN 1.1) (SIN 2.03))     ; returns a list of lists, numbers and symbols

In Prolog

1 ?- X is 2*5.
X = 10.

2 ?- L = (X is 2*5), write_canonical(L).
is(_, *(2, 5))
L = (X is 2*5).

3 ?- L = (ten(X):-(X is 2*5)), write_canonical(L).
:-(ten(A), is(A, *(2, 5)))
L = (ten(X):-X is 2*5).

4 ?- L = (ten(X):-(X is 2*5)), assert(L).
L = (ten(X):-X is 2*5).

5 ?- ten(X).
X = 10.

6 ?-

On line 4 we create a new clause. The operator :- separates the head and the body of a clause. With assert/1* we add it to the existing clauses (add it to the "database"), so we can call it later. In other languages we would call it "creating a function during runtime". We can also remove clauses from the database with abolish/1, or retract/1.

* The number after the clause's name is the number of arguments it can take. It is also called arity.

We can also query the database to get the body of a clause:

7 ?- clause(ten(X),Y).
Y = (X is 2*5).

8 ?- clause(ten(X),Y), Y = (X is Z).
Y = (X is 2*5),
Z = 2*5.

9 ?- clause(ten(X),Y), call(Y).
X = 10,
Y = (10 is 2*5).

call is analogous to Lisp's eval function.

In Rebol

The concept of treating code as data and the manipulation and evaluation thereof can be demonstrated very neatly in Rebol. (Rebol, unlike Lisp, does not require parentheses to separate expressions).

The following is an example of code in Rebol (Note that >> represents the interpreter prompt; spaces between some elements have been added for readability):

>> repeat i 3 [ print [ i "hello" ] ]


1 hello
2 hello
3 hello

(repeat is in fact a built-in function in Rebol and is not a language construct or keyword).

By enclosing the code in square brackets, the interpreter does not evaluate it, but merely treats it as a block containing words:

[ repeat i 3 [ print [ i "hello" ] ] ]

This block has the type block! and can furthermore be assigned as the value of a word by using what appears to be a syntax for assignment, but is actually understood by the interpreter as a special type (set-word!) and takes the form of a word followed by a colon:

>> block1: [ repeat i 3 [ print [ i "hello" ] ] ]
 ;; Assign the value of the block to the word `block1`
== [repeat i 3 [print [i "hello"]]]
>> type? block1
 ;; Evaluate the type of the word `block1`
== block!

The block can still be interpreted by using the do function provided in Rebol (similar to eval in Lisp).

It is possible to interrogate the elements of the block and change their values, thus altering the behavior of the code if it were to be evaluated:

>> block1/3
 ;; The third element of the block
== 3
>> block1/3: 5
 ;; Set the value of the 3rd element to 5
== 5
>> probe block1
 ;; Show the changed block
[repeat i 5 [print [i "hello"]]]
== [repeat i 5 [print [i "hello"]]]
>> do block1
 ;; Evaluate the block
1 hello
2 hello
3 hello
4 hello
5 hello

See also

References

  1. ↑ Wheeler, David A. "Readable Lisp S-expressions".
  2. ↑ McIlroy, Douglas (1960). "Macro Instruction Extensions of Compiler Languages". Comm. ACM. 3 (4): 214–220. doi:10.1145/367177.367223.
  3. ↑ Mooers, C.N.; Deutsch, L.P. (1965). "TRAC, A Text-Handling Language". Proceeding ACM '65 Proceedings of the 1965 20th national conference. pp. 229–246. doi:10.1145/800197.806048.
  4. ↑ Kay, Alan (1969). The Reactive Engine (PhD). University of Utah.
  5. 1 2 3 4 5 6 7 8 9 Homoiconic Languages
  6. 1 2 Homoiconic languages (archived), in true Blue blog at Oracle
  7. ↑ "Why we created Julia". julialang.org. We want a language that’s homoiconic, with true macros like Lisp, but with obvious, familiar mathematical notation like Matlab.
  8. ↑ "metaprogramming". docs.julialang.org. Like Lisp, Julia represents its own code as a data structure of the language itself.
  9. ↑ "Metaprogramming in mathematica". stackexchange. Mathematica is [...] Homoiconic language (programs written in own data structures - Mathematica expressions. This is code-as-data paradigm, like Lisp which uses lists for this)
  10. ↑ Shapiro, Ehud Y.; Sterling, Leon (1994). The art of Prolog: advanced programming techniques. MIT Press. ISBN 0-262-19338-8.
  11. ↑ Ramsay, S.; Pytlik-Zillig, B. (2012). "Code-Generation Techniques for XML Collections Interoperability". dh2012 Digital Humanities Conference Proceedings.
  12. ↑ "Notes for Programming Language Experts". Wolfram Language. Wolfram. 2017.
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