Suppose we declare that
y = x + 1[This is not an assignment. Imagine a val in front if that is fits your language preferences]. This declares a relationship between x and y, but it does it in a functional style. It would look more functional still if we wrote "y = add 1 x", but that is just sugar.
But what if we have y and we want x? Since we are just declaring a relationship it isn't obvious why we have to change this. But in functional style this has to be changed to:
x = y - 1Functional programs can only run forward, they can't run backwards. Haskell has, of course, a big exception to that: Constructors can be run forward (to construct) or backward (to deconstruct). But perhaps everything that can run backwards should be allowed to (and hence be useable in case statements). In addition to convenience there is a dodgy philosophical point.
When we look at the way the world works it is rather like a giant computer program. And it is particularly like a program in that, on a large scale it pushes forward in an irreversible way. Entropy increases and broken plates never reassemble themselves. And yet at the core is quantum mechanics which is completely reversible.
Haskell and Mercury are two languages in which the interaction with the external world (including mutable data in memory) is explicit. This is a consequence of the fact that both languages are declarative. In non-declarative languages the textual order of the program specifies an order of execution (optimisers alter that, but they are constrained to preserve the semantics, and are forced to make conservative decisions as a result). In declarative languages the compiler generates execution when required, and the thing that brings about that requirement is interaction with the outside world. Since that interaction is explicit, one would hope that the optimiser is never constrained by worrying about what separately compiled code might do.
So it seems that programming should have three levels.
- A core language that is reversible. This specifies what can be handled by cases, though if you allow multiple returns (as Mercury does) then you can expand that.
- Reducing operations (like summing a list) which are intrinsically irreversible.
- Interaction with the unforgiving world which forces an order of execution.
But maybe its not quite that simple. It seems that if the part of the real world you are dealing with is quantum then it might be reversible and you might conceivably be able to interact with that in the reversible part of the language. Perhaps more practically: When two programs interact with each other then they might sometimes be able to do that while each stays within the reversible core.
I should have another go at learning Mercury. Last time was 15 years ago.