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ZOWIE is a programming language where all control flow is both
memory-mapped and structured. It is memory-mapped in the sense that
changes in flow are triggered by changes made to memory locations, and
it is structured in the sense of structured programming – the programmer
never deals with
gotos, offsets, or labels of any kind.
The primary design goal of ZOWIE was to have memory-mapped structured control flow. This goal was inspired by Jeffry Johnston's unsuccessful attempt to reduce the number of instructions in BitChanger (while retaining Turing-completeness) by memory-mapping the loop operation.
I initially thought that the difficulty lay in BitChanger's minimalism. To do memory-mapped flow control in general sounded easy – just start a loop when one memory location is written, and end it when some other location is written, right? But no. It's not that simple, as I attempt to explain below. ZOWIE is the last of several, sometimes painful, attempts over the summer of 2009 to realize this design goal (and it is not clear that the techniques used in ZOWIE could be usefully imported back into BitChanger.) The final, workable idea crystallized at about the time September turned into October.
The thing with loop structures is that there is usually some way to jump to a known point in the loop (say, the start, or the end) – really, that's what makes them structured. And to jump to a point in a loop, you have to know where that point is. And if you can analyze the loop structure statically, for example if your semantics are directed by syntax as in almost all high-level languages, then it's not difficult to know where that point is.
But if that point is defined by when some memory location is changed, it is not in general possible to detect it statically (by Rice's Theorem, which is just a generalization of the Halting Problem.) So it is not, in general, possible to know ahead of time where the loop begins or ends.
There are a few things to note about this.
One is that by "statically" I do not necessarily mean "at compile-time". Many Brainfuck and Mouse interpreters seek out the end of the loop only when they know they must exit it. However, because they are looking through the program text, it is still a kind of static analysis.
Another thing is that it would of course be possible to detect some kind of (fixed) command to change the memory location associated with ending a loop – but that would be cheating! (Also, if memory locations can be computed, it is still not fully general, because we cannot look for all possible computations that would result in that memory location.)
Lastly, note that we really don't have a problem detecting the start of a loop. As soon as we execute the start of a loop, we know it's a loop, and we know where it is, so we can record that location. The problem is any other point in the loop, like the end. A little reflection will reveal that this means it will be more difficult to do a "WHILE" loop or a structured conditional ("IF-THEN-ENDIF") than a "REPEAT" loop (where the condition is at the end of the loop.) However, it is widely known that "REPEAT" loops alone are not sufficient for a Turing-complete language. We'll see below that ZOWIE manages to create generalized loops through the use of transactions.
The secondary design goal of ZOWIE was to strike the perfect balance between It's a Mad Mad Mad Mad World and The Party. It is generally considered a morbid failure in that regard, what with not being a madcap 60's movie and all.
Syntax and Semantics
To mitigate retooling costs, ZOWIE borrows much of its archiecture and instruction repertoire from SMITH. There are an unlimited number of registers, numbered from 0 upward; each register contains a non-negative integer value of unbounded extent. The contents of a register before it has ever been written is guaranteed to be 0.
There are five instruction forms. The first register is the destination register, and is written to; the second register (or immediate value) is read from. As in SMITH, square brackets indicate indirect register access. All instruction forms are case-sensitive; they must be given using capital letters.
MOV register, immediate e.g. MOV R8, 141 MOV register, register MOV R8, R9 MOV [register], register MOV R[R8], R9 MOV register, [register] MOV R8, R[R9] MOV [register], [register] MOV R[R8], R[R9]
Not only flow control, but in fact all operations in ZOWIE are memory-mapped. The lowest-numbered nine registers have special behaviour when written to or read from:
When a value is written into R0, the Unicode symbol represented by the value is sent to the standard output channel.
Reading from R0 waits until a Unicode symbol is available on the standard input, then offers its value as the value of this register.
This is similar to the
TTY pseudo-register of SMITH.
Note: although implementations should make a best effort, the external
encoding and representation of Unicode characters is ultimately
implementation-defined, especially on systems which are only capable of
accurately displaying a subset of the Unicode character set. For
example, on a strict ASCII teletype or other device incapable of
displaying the DOWNWARDS ARROW (↓) symbol, it would be reasonable to
↓ or some similar "escape sequence" when executing
MOV R0, 8595.
When a value is written into R1, a BEGIN TRANSACTION occurs; conceptually, a copy of the program state, including all registers and the location of the currently executing instruction, is made, and pushed onto a stack.
Reading from R1 always offers the value 1.
When a value is written into R2, what happens depends on the value.
If the value is greater than zero, the current transaction is COMMITted; conceptually, the topmost program state is popped from the stack and discarded.
If the value is equal to zero, the current transaction is ROLLBACKed. Conceptually, the topmost program state is popped; the contents of all registers are reset to what they were in the popped program state; but the location of the currently executing instruction is unchanged.
Reading from R2 always offers the value 2.
When a value is written into R3, what happens depends on the value.
If the value is greater than zero, the current transaction is COMMIT AND REPEATed; conceptually, the topmost program state is popped from the stack; the location of the currently executing instruction is reset to what it was in the program state; and a copy of this new program state is pushed once more onto the stack.
If the value is equal to zero, the current transaction is COMMITed (described previously in R2).
Reading from R3 always offers the value 3.
When a value is written into R4, that value is added to the value in R8, and the result is written into R8. Reading from R4 always offers the value 4.
When a value is written into R5, that value is subtracted from the value in R8, and the result is written into R8. If the result would be negative, the result will be zero. Reading from R5 always offers the value 5.
When a value is written into R6, the product of that value and the value in R8 is written into R8. Reading from R6 always offers the value 6.
When a value is written into R7, the boolean negation of that value is written into R8: 1 if the value was 0, and 0 otherwise. Reading from R7 always offers the value 7.
Not really memory-mapped, but used as an "accumulator" by the registers R4 through R7.
Because the reading and writing of registers can have side-effects, the order of reads and writes during the execution of a single instruction is strictly defined as follows:
- The indirect source register, if any, is read (to discover the direct source register.)
- The direct source register is read.
- The indirect destination register, if any, is read (to discover the direct destination register.)
- The direct destination register is written.
I believe ZOWIE is Turing-complete because the transactions can simulate both "IF" and "REPEAT" control structures, which, taken together, can simulate a "WHILE", which is widely known to be sufficient, along with the usual arithmetical operations on an unbounded number of unbounded integer registers, to have a system that is Turing-complete.
For example, a crude translation of Brainfuck into ZOWIE might go like:
preamble MOV R10, 100 ; the Brainfuck tape index MOV R11, 101 ; the saved-test-value stack pointer > MOV R8, R10 ; inc tape index by two MOV R4, R2 MOV R10, R8 < MOV R8, R10 ; dec tape index by two MOV R5, R2 MOV R10, R8 + MOV R8, R[R10] ; inc value on tape MOV R4, R1 MOV R[R10], R8 - MOV R8, R[R10] ; dec value on tape MOV R5, R1 MOV R[R10], R8 . MOV R0, R[R10] ; output , MOV R[R10], R0 ; input [ MOV R1, R1 ; BEGIN TRANSACTION for "REPEAT" MOV R8, R11 ; bump up the saved-value stack pointer MOV R4, R2 MOV R11, R8 MOV R[R11], R[R10] ; save the value we are testing MOV R1, R1 ; BEGIN TRANSACTION for "IF" ] MOV R2, R[R11] ; COMMIT if non-zero or ROLLBACK otherwise MOV R12, R11 ; retain a copy of the saved-stack pointer MOV R8, R11 ; bump down the saved-stack pointer MOV R5, R2 MOV R11, R8 MOV R3, R[R12] ; COMMIT AND REPEAT if non-zero
Three things to note:
- In this translation, the simulated Brainfuck tape and the saved-value stack are interleaved.
- It is important to save the value being tested before the "IF" transaction is begun – otherwise, the value will be rolled back before it can be tested for the COMMIT AND REPEAT.
- The input-output behaviour of ZOWIE programs produced by this translation does differ from Brainfuck. If the value on the tape is initially zero, a Brainfuck "while" loop will never be executed at all, whereas a ZOWIE transaction will be executed, but afterwards undone – everything, that is, except input and output, because being interactions with the outside world, those can't be undone. This limitation does not affect whether ZOWIE is Turing-complete or not (you could just refrain from outputting anything until the very end of the computation), but it does imply that ZOWIE has limitations on how it can communicate.
Happy «deleted by black helicopters»!
December 29th, 2009 CE