I think APL/J/K are typically implemented as interpreters rather than compilers, because the languages contain some ambiguity that you might not always be able

I think APL/J/K are typically implemented as interpreters rather than compilers, because the languages contain some ambiguity that you might not always be able to resolve statically. See for example: http://t3x.org/klong/ambiguity.html http://t3x.org/klong/ambiguity.html The J Incunabulum provides a glimpse of a toy interpreter and of Arthur Whitney's style: http://code.jsoftware.com/wiki/Essays/Incunabulum http://code.jsoftware.com/wiki/Essays/Incunabulum I've found it quite interesting in terms of data structures, parsing, evaluation and how the primitives are implemented. I reformatted it into a more readable style (more readable to me). Memory management is through reference counting I think (maybe not in this example, but I vaguely remember reading that somewhere). Interpreters for array languages are quite efficient because the primitives operate on arrays and you tend to not have explicit loops in the scripts themselves. The loops are "hidden" inside the optimized primitives in the interpreter. You can add further optimizations by recognizing certain idioms like +/ for "sum" and providing a special optimized implementation. Obviously that doesn't work for user-defined functions. I don't know if K etc can optimize those as well. Another thing to consider is how you represent intermediate values. If you're operating on large arrays, you don't want to create a lot of large intermediate arrays that you'll throw away immediately. You can probably detect situations where you can modify arrays in-place. This papers provides as different solution: http://dl.acm.org/citation.cfm?id=512761 http://dl.acm.org/citation.cfm?id=512761 Unfortunately I don't know if there's a free copy available anywhere, so I haven't actually read the paper. I'd be interested to know if there's a free legal copy available somewhere. It might be similar to stream fusion for lists in Haskell: http://fun.cs.tufts.edu/stream-fusion.pdf http://fun.cs.tufts.edu/stream-fusion.pdf Or how you might optimize SQL/relational queries for databases by pushing down projections through selects and joins to reduce the amount of data that you need to retrieve and work on. These approaches might also allow you to optimize user-defined functions. Finally, Timothy Budd implemented a compiler for a slightly modified version of APL and documented the result: http://www.springer.com/de/book/9780387966434 http://www.springer.com/de/book/9780387966434 Again, I don't know if there's a free legal PDF anywhere, so I haven't read the book. I'd be interested in a free legal copy of this book as well.