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You need a high level relational projection system that can operate on multiple dimensions simultaneously, shaders or SQL are ideal for taking advantage of para

You need a high level relational projection system that can operate on multiple dimensions simultaneously, shaders or SQL are ideal for taking advantage of parallelism. Esp if you can operate symbolically, think triple nested loops where the inner loop is some expensive projection, if it is over a regular space, and can be decomposed as a tree. I think this language could be represented as a Wasm DAG of functions, map/pmap/apply/tree_call/reduce Having a spec and a body of software to run but no test oracles for how that software runs feels contrived. If you have megabytes or gigabytes of code but not even screenshots of how it should it should look when it runs isn't the same as having a book in a dead language and not knowing what it should sound like. > However, the third cart was a metacircular interpreter, so in some sense it potentially represents a kind of reference implementation — just, one you couldn't use until your UM was running well enough to run it. This is a great example of a test oracle. Fixed-point correctness.

kragen 4y ago
Hmm, I understand a "test oracle" to be a thing where, if you submit any arbitrary input to it, it will tell you what the correct output should be. The metacircular interpreter isn't such a thing: you can submit an input to it, and if its output is different from the output of the implementation it's running on, you know that implementation has a bug. Say my implementation is P and the metacircular interpreter (presumed correct) is M. If P[M[X]] outputs "foo", while P[X] outputs "bar", we know there is a bug in I. This is similar to a test oracle in some ways: given a test oracle O, if O[X] outputs "foo" and P[X] outputs "bar", we know I has a bug. The difference is that in the metacircular case, the correct output might actually be "foo". Worse, if P[M[Y]] outputs "baz" and P[Y] also outputs "baz", it does not therefore follow that "baz" is the correct output, as it would if O[Y] outputs "baz". It might just be that P has a bug that flows through to the metacircular interpreter. Maybe it rounds division the wrong way, or incorrectly considers negative zero to be unequal to positive zero. I agree that screenshots would be very useful, but a static repository of screenshots is also not a test oracle, for a slightly different reason: you cannot submit a novel input to it and find out what the correct screenshot would be. I agree that a DAG of functions is a useful representation that preserves significant degrees of parallelism that conventional machine-code representations expunge. However, Wasm also expunges them. The idea of using a relational rather than functional or imperative computing paradigm for archival is interesting. We should probably discuss this in a more amenable format.

kragen 4y ago

Hmm, I understand a "test oracle" to be a thing where, if you submit any arbitrary input to it, it will tell you what the correct output should be. The metacircular interpreter isn't such a thing: you can submit an input to it, and if its output is different from the output of the implementation it's running on, you know that implementation has a bug. Say my implementation is P and the metacircular interpreter (presumed correct) is M. If P[M[X]] outputs "foo", while P[X] outputs "bar", we know there is a bug in I. This is similar to a test oracle in some ways: given a test oracle O, if O[X] outputs "foo" and P[X] outputs "bar", we know I has a bug. The difference is that in the metacircular case, the correct output might actually be "foo". Worse, if P[M[Y]] outputs "baz" and P[Y] also outputs "baz", it does not therefore follow that "baz" is the correct output, as it would if O[Y] outputs "baz". It might just be that P has a bug that flows through to the metacircular interpreter. Maybe it rounds division the wrong way, or incorrectly considers negative zero to be unequal to positive zero. I agree that screenshots would be very useful, but a static repository of screenshots is also not a test oracle, for a slightly different reason: you cannot submit a novel input to it and find out what the correct screenshot would be. I agree that a DAG of functions is a useful representation that preserves significant degrees of parallelism that conventional machine-code representations expunge. However, Wasm also expunges them. The idea of using a relational rather than functional or imperative computing paradigm for archival is interesting. We should probably discuss this in a more amenable format.