Re: [stack] the concatenative wikipedia article

On Dec 31, 2008, at 3:21 PM, William Tanksley, Jr wrote:

> OTOH, can a concatenative language ever be infix? I'd find it odd...

The general idea that I've had for a prefix/infix language is as  
follows:

1. 'f g' denotes the composition of 'f' and 'g'
2. 'f g h' denotes the composition of 'g' with the construction of 'f'  
and 'h' (construction is basically a cleave combinator)
3. Grouping is to the right such that 'f g h i j k == f g (h i (j k))'
4. Composition is associative such that '(f g) h == f (g h)'
5. Literals (e.g. '42') are constant functions such that '42 f == 42'
6. Multiple arguments are passed via lists
7. 'a == head', 'b == head tail', 'c == head (head tail)', etc --  
these are essentially used to index into lists

As such, you write functions like this:

    discriminant = (sq b) - 4 * a * c

And here's the definition in use

    # composition of discriminant and the construction [1,3,-4]
    discriminant [1,3,-4]
    # expansion of discriminant
    ((sq b) - 4 * a * c) [1,3,-4]
    # fully parenthesized
    ((sq b) - (4 * (a * c))) [1,3,-4]
    # replacing infix with composition + construction
    (- [sq b, * [4, * [a, c]]) [1,3,-4]
    # law of associativity: (f g) h == f (g h)
    - ([sq b, * [4, * [a, c]]) [1,3,-4])
    # law of distributivity: [f0..fN] g == [f0 g..fN g]
    - [(sq b) [1,3,-4], * [4 [1,3,-4], (* [a, c]) [1,3,-4]]
    # simplification
    - [(sq b) [1,3,-4], * [4, (* [a, c]) [1,3,-4]]
    - [(sq b) [1,3,-4], * [4, * [1, -4]]
    - [sq (b [1,3,-4]), * [4, * [1, -4]]
    - [sq 3, * [4, * [1, -4]]
    - [sq 3, * [4, -4]]
    - [sq 3, -16]
    - [9, -16]
    25

The infix syntax makes the manipulation a little awkward, but I've  
found it often makes the definitions shorter and more readable. The  
fact that any function can be used infix is a nice touch.

So, is this concatenative? It's just composition and cleave combinators.

- John