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Instead of writing thick directly, I can prove an elimination rule for fin sn which, for any given w performs case analysis between `patterns' w and (thin w j). If this rule eliminates over datatypes, I can use it to write programs. In particular, the program for thick moves a great deal closer to its specification.

Extending this idea, I can prove an elimination rule for trees which internalises the search involved in check. The patterns (put (leaf w) there) and ((thin w) |> t) are certainly exhaustive and disjoint. The problem is that a tree containing several (leaf w)'s gives rise to an ambiguous match for there. We may get different interpretations depending on whether we want, say

This suggestion bears a strong resemblance to Phil Wadler's neat idea of allowing different `views' of a datatype. He gives various examples, eg viewing cons-lists as snoc-lists, all of which are expressible as nonstandard elimination rules for datatypes. I go further in two ways:

I speak not without some experience here. Along with a selection of genetic disorders, I inherited Fred McBride's 1970 implementation of LISP with pattern matching. Patterns consisted of atomic constants, atomic variables and cons of patterns, and may be elaborated with side-conditions: nonlinear patterns are interpreted via the decidable intensional equality on s-expressions (`EQUAL' to lispers).

In 1989, I extended this pattern language to admit the `append' symbol. (Note, list is its own position type and append is the put-function.) Parsers for simple grammars follow the productions transparently, line by line. The interpreter also ran internalised search a lot faster than explicitly recursive search, although it is hard to tell whether this speedup would survive compilation.

I'm fed up with constructor patterns. I want the programs I had when I was a kid, and I hope I can get them without general recursion. Except for the six line Turing machine simulator, of course.

Moving on, it's fairly clear that much of the syntax manipulation equipment I built for trees generalises. Indeed, it's not that hard to add binding. Maybe it's worth automating its construction.

There are three examples I have in mind for further study:

And that's that. There's a lot more in this commentary than there was in any instance of my talk. More detail in my thesis...

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