The Fundamental Concept of Programming language X

[L.J.Dickey]

In article <1782 at aipna.ed.ac.uk> sean at aipna.ed.ac.uk (Sean Matthews) writes:

>I have also listed a section 2a, of combinatory logic, which is where
>we could put languages like FP, and even APL.  FP is clearly
>combinatory, while I would argue that the way that APL works is much
>more influenced by the combinatory style that it encourages than by
>the fact that it works with arrays (and I know that there is
>assignment in APL, but in practice people try to avoid it, and write
>one liners instead, since that is the more powerful, and natural way
>to think in APL, the pity is that it has such a limited set of
>combinators).

Readers are encouraged to track the progress of SAX (Sharp APL for UNIX),
which has introduced some new combinators.  Their vocabulary uses words
like "noun", "verb", "adverb", and "conjunction".  An adverb corresponds
to a mathematical operator because it acts on a function ("verb") and 
returns a function as a result.  Their new adverbs and conjunctions
are (for me) the most interesting combinators.  Some APL users are as
concerned about the proliferation of parentheses as, apparently,
some combinatory logicians were, and so find practical use for the
commute adverb, for instance.

A recent research paper on this topic by some involved one way or another
with SAX, appears in APL Quote Quad, Volume 19, Number 4, August 1989,
on page 197.

-- 
    L. J. Dickey, Faculty of Mathematics, University of Waterloo.
	ljdickey at water.UWaterloo.ca	ljdickey at water.BITNET
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	ljdickey at water.waterloo.edu