A fundamental property of stack languages is that the concatenation of two programs `X`

and `Y`

-- `X Y`

-- is the program that applies `Y`

to the result of `X`

, that is, the *composition* of `X`

and `Y`

. This means that certain common quotation patterns can be written very concisely.

For example, in Factor we can filter a sequence by a predicate using the `filter`

combinator:

( scratchpad ) { 1 2 3 4 5 6 7 8 } [ even? ] filter . { 2 4 6 8 }

If we want to remove elements matching the predicate instead, we can compose the predicate with the `not`

word:

( scratchpad ) { 1 2 3 4 5 6 7 8 } [ even? not ] filter . { 1 3 5 7 }

Partial application works out very nicely too: write a quotation which pushes some of the parameters before calling a word:

( scratchpad ) { 1 2 3 4 5 6 7 8 } [ 4 > ] filter . { 5 6 7 8 }

Compare these three quotations,

[ even? ] [ even? not ] [ 4 > ]

This is shorter than the equivalent in an applicative language, because we have to name the input argument, that is only used once. In Common Lisp:

(function evenp) (lambda (x) (not (evenp x))) (lambda (x) (> x 4))

In Haskell:

(even) (not . even) (4 >)

Since concatenative languages do not have named parameters (let's ignore Factor's `locals`

vocabulary for now), talking about free variables does not make sense. The nearest equivalent in a concatenative language is constructing new quotations from existing quotations.

In Factor, quotations look like a sequence of objects; for example, `[ 2 2 + ]`

has three elements, the integer `2`

, the integer `2`

again, and the word `+`

; the latter is itself an object which can be introspected and executed. This means that we can use sequence operations to construct quotations.

Suppose we have the quotation `[ + ]`

. When executed, it takes two numbers from the stack, adds them, and leaves the result on the stack. If we prefix the quotation with the integer 5, we get a new quotation, `[ 5 + ]`

, which adds 5 to the top of the stack. This is similar to *currying* in applicative languages, so Factor calls this operation `curry`

.

Another fundamental operation on quotations is composition: suppose we take the quotation `[ 2 + ]`

and the quotation `[ 0 > ]`

; their composition is `[2 + 0 > ]`

. Of course, this is just the concatenation of the two quotations.

These two fundamental operations -- `curry`

and `compose`

-- have very simple and intuitive semantics. Note that quotations are printable objects, whereas in applicative languages, closures are typically opaque.

Examples of `curry`

:

( scratchpad ) 5 [ + ] curry . [ 5 + ]

Compare with lisps applicative version; note the closure does not print readably:

* (let ((x 5)) (lambda (y) (+ x y))) #<FUNCTION (LAMBDA (Y)) {11682335}>

or Haskell:

(5+) Functions cannot be printed in Haskell

Examples of `compose`

:

( scratchpad ) [ 3 = ] [ not ] compose . [ 3 = not ]

Applicative version:

* (let ((f (lambda (x) (= x 3)))) (lambda (y) (not (funcall f y)))) #<FUNCTION (LAMBDA (Y)) {11680B3D}>

(not . (3 ==)) Again, functions cannot be printed

As you can see, function composition and partial application feels a lot more natural in stack languages, because of the duality between composition and concatenation.

*This revision created on Wed, 26 Oct 2011 19:56:28 by DanielSwe
*