4 ms·

Disclaimer: I am totally out of my field and I have no idea precise definitions of terms etc. Is it haulting really in conflict with linear types? If we inspe

by Risord 9y ago

Disclaimer: I am totally out of my field and I have no idea precise definitions of terms etc. Is it haulting really in conflict with linear types? If we inspect function from outside and we pick random time T after starting (but before finish) the event has been happen at most once. After function is finished event is done exactly once. I think conceptually situation is pretty much the same is T: 1ns | trillion years | infinite. So I feel that "It WILL happen after infinite time." is valid claim and therefore haulting by itself is not a problem. In real world issue seems to be that we cannot run our software from very long to infinite time whenever is it haulted or not => at some point we kill that process. Killing process on the other hand is harmful thing for promise to run exactly once since killed process won't product anything new for sure. So in practice haulting results always to killing process but if process is killed it don't mean that process was haulted. So I claim that you shouldn't proof that your system won't hault but instead you should proof that process cannot be killed if anything. At the end it depends how we want box our world. What you think?

chriswarbo 9y ago
You're right that proving that a program halts doesn't tell us whether or not it's practical to run (it could take 1 trillion years), but it can be useful for other reasons. For example, if a function claims to return a value of type T, and we can prove that the function halts, then we know that a value of type T must exist (it's whatever the function will return, however long that takes). This is how dependently typed languages can implement pre and post conditions: we can represent conditions as types, and put preconditions as extra argument types, and postconditions as extra return values (e.g. in a tuple). For example, we might have a function 'f1' which turns 'A' values into 'B' values: f1 : A -> B f1 myA = ... If we require some precondition 'PRE' to hold for the argument, and postcondition 'POST' to hold for the return value, we can use dependent types to represent them: f2 : (a : A) -> PRE a -> (b : B, POST b) f2 myA preProof = ... We can 'f1' by just giving it an 'A' argument, but the precondition won't be checked. Likewise, we learn nothing about whether the output satisfies the postcondition. With 'f2', we must give it an extra argument, representing a proof that the precondition holds for the given 'A' value. The function must also do more work: not only must it return a 'B' value, but it must also give us a proof that that 'B' value satisfies the postcondition (we can pass that proof around, e.g. if another function requires it as a precondition). If we can prove that these calculations will halt, then we don't actually need to run them at all! Knowing that 'PRE a' can be proved in a finite amount of time (however long) is itself a proof of 'PRE a'! (And likewise for 'POST b'). Hence we can "erase" this proof stuff after type checking, to generate code equivalent to 'f1'. If we don't know whether or not those proof calculations will halt, we can't use this shortcut, and we're forced to run the proof calculations in full at runtime (which may not halt, or might take a trillion years!).
- mcaruso 9y ago
  In your f2 example, could you ever use/inspect the preProof argument? If the proof calculation is erased, I assume preProof could never be used in any way. Although depending on what the type PRE really is it might not be something you could do anything useful with in the first place. I should probably learn Idris already, that would probably clear up these questions. :)
  - chriswarbo 9y ago
    > In your f2 example, could you ever use/inspect the preProof argument? Yes you could, but if your return value relies on details of the proof (e.g. branching on different cases) then it may no longer be erasable. Unless those parts of the return value can also be erased... it gets tricky :) You're right to mention Idris, since it treats proofs in this way. In languages like ATS, there is a clear separation between erasable "proof-like" things and runtime "value-like" things, which makes things more predictable, but can lead to duplication.

by Risord 9y ago

chriswarbo 9y ago

You're right that proving that a program halts doesn't tell us whether or not it's practical to run (it could take 1 trillion years), but it can be useful for other reasons. For example, if a function claims to return a value of type T, and we can prove that the function halts, then we know that a value of type T must exist (it's whatever the function will return, however long that takes). This is how dependently typed languages can implement pre and post conditions: we can represent conditions as types, and put preconditions as extra argument types, and postconditions as extra return values (e.g. in a tuple). For example, we might have a function 'f1' which turns 'A' values into 'B' values: f1 : A -> B f1 myA = ... If we require some precondition 'PRE' to hold for the argument, and postcondition 'POST' to hold for the return value, we can use dependent types to represent them: f2 : (a : A) -> PRE a -> (b : B, POST b) f2 myA preProof = ... We can 'f1' by just giving it an 'A' argument, but the precondition won't be checked. Likewise, we learn nothing about whether the output satisfies the postcondition. With 'f2', we must give it an extra argument, representing a proof that the precondition holds for the given 'A' value. The function must also do more work: not only must it return a 'B' value, but it must also give us a proof that that 'B' value satisfies the postcondition (we can pass that proof around, e.g. if another function requires it as a precondition). If we can prove that these calculations will halt, then we don't actually need to run them at all! Knowing that 'PRE a' can be proved in a finite amount of time (however long) is itself a proof of 'PRE a'! (And likewise for 'POST b'). Hence we can "erase" this proof stuff after type checking, to generate code equivalent to 'f1'. If we don't know whether or not those proof calculations will halt, we can't use this shortcut, and we're forced to run the proof calculations in full at runtime (which may not halt, or might take a trillion years!).

mcaruso 9y ago
In your f2 example, could you ever use/inspect the preProof argument? If the proof calculation is erased, I assume preProof could never be used in any way. Although depending on what the type PRE really is it might not be something you could do anything useful with in the first place. I should probably learn Idris already, that would probably clear up these questions. :)
- chriswarbo 9y ago
  > In your f2 example, could you ever use/inspect the preProof argument? Yes you could, but if your return value relies on details of the proof (e.g. branching on different cases) then it may no longer be erasable. Unless those parts of the return value can also be erased... it gets tricky :) You're right to mention Idris, since it treats proofs in this way. In languages like ATS, there is a clear separation between erasable "proof-like" things and runtime "value-like" things, which makes things more predictable, but can lead to duplication.