> You should not approach problems in functional languages with imperative techniques. It's fitting a square peg in a round hole.
This might be part of the problem with FP. Every popular CPU architecture is imperative.
This might be part of the problem with FP. Every popular CPU architecture is imperative.
Everything is a tradeoff. FP gives you a lot of flexibility in how you trade space and time of the execution of your program. It's also not a magic wand, just a really powerful tool.
Imperative systems are "fitting a square peg in a round hole" by introducing hacks like 'clock signals', 'pipeline flushes', etc.
One of the many ways to demonstrate this: all linear circuits have duals (voltage <-> current, series <-> parallel, and so on), but in a cartesian closed category only the terminal object is dualizable.
What you're probably thinking of is the fact that this category is compact closed. The corresponding internal language is going to be some sort of process calculus (I think the pi calculus is too strong, but not sure), not the lambda calculus.
That's arguable, given that every (deterministic) imperative computation can be expressed as a pure functional program. "Imperative" is more of a viewpoint that the developer is using to understand the behavior of the computer, rather than a property of the machine itself.
A pure functional analysis will describe a computation on that "imperative" architecture as an inmutable, monotonic sequence of all the states that the CPU goes through over time; or maybe, if you know enough PL theory, as a chain of rewritings of a program-long expression that is updated, one term at a time, when each expression is replaced by the result of a function as it consumes its input parameters.
And no viewpoint is inherently better than the other (except that the functional version can be analyzed in a natural way with mathematical tools, which is often difficult with the imperative description).
Just because both lambda calculus and assembly are Turing complete does not mean that CPU architecture isn't clearly imperative.
Also, this: https://news.ycombinator.com/item?id=30883863
The same is true of CPUs, which at their base level execute instructions line-by-line to move and load things in and out of stateful registers as well as doing simple mathematics.
Not going to keep arguing, as I can see from your other comments that you are going to try to hold this line, and also your reasoning doesn't really make sense.
Everyone has heard of Turing completeness. It does not imply that all distinctions between the semantics of languages and the structure of hardware thus are collapsed. It means that you can write an equivalent program using different semantics or different hardware.
No, it means that every computable program or device can be described through functional semantics, and therefore that very same program running on that same hardware can be described mathematically with them (not an 'equivalent' program, but the same program with the same runtime behaviour, just described in low level with a different format).
That's a core principle of computer science that predates computers themselves, and people arguing about the benefits of the imperative style tend to be unaware of this fact, making their arguments look weak.
Main memory is state. Registers and cache are state. The entire purpose of the CPU is to mutate state.
He's not really stretching the definition, that's just the lens through which FP looks at the world.
Of course there is state. FP doesn't prohibit state, it just makes it explicit and referentially transparent. But this is in the semantics, not the execution model of the program.
If we are going to nitpick syntax, nothing about `mov eax ebx` lists main memory as output. In fact, mov doesn't even have an 'output'.
If you want to model mov as a function with the implicit output of "all of main memory", then you can do the same with any arbitrary C function. If you can't make that leap for C, then you can't make that leap for assembly.
Functional programmers are simply choosing to use a different style of map, but we both represent the same reality.
Computers that do anything useful have all manner of I/O. Highly oversimplified in modern architecture, but you can think of I/O as a bunch of memory cells that are DMA'd by external forces. Literally the exact opposite of functional, IO registers are the epitome of global mutable state. Then you have interrupts and the CPU operates in response to these events.
The viewpoint of "computers are mutable state" is inherently better because of parsimony - it requires less degrees of indirection to explain what is happening. Just because you could shoehorn reality into a physical model, does not make it equally valid. You basically need to break it down to the Schrodinger equation level to have a purely functional model when even idealized gates are involved because propagation delay impacts things like how fast you can DMA.
Hey, physicists do it all the time. Having mathematical representations of how things work in the real world often turn out to give you complex devices that you wouldn't get by intuition alone. Thanks to doing it, we have Special Relativity and Schrodinger equations, that bring you advantages as GPS and insanely-high-speed networks.
There's nothing wrong with modelling interrupts and mutable state as static mathematical entities a.k.a. functions; and if you think it is, you don't know enough about functional programming - in fact, doing it allows for advanced tactics like automatic verification and very high scale generation of electronic devices.
Those less degrees of indirection may make it simple to build some kinds of programs; but they also introduce complexity in modelling the possible states of the system when you allow for arbitrary, unchecked side effects. So no, that representation is not inherently better - only most suited for some tasks than others; but the converse is also true for functional models of computation. If you think it is always better, it's because you're not taking all possible scenarios and utilities into account.
(Besides, as I already said elsewhere, "computers are mutable state" is not incompatible with functional representation; as mutable state can be represented with it). It seems that you're confusing mutable, wich is a property of computational devices, with 'imperative' which is a style of writing source code and defining relations between statements in your written program.
> Literally the exact opposite of functional, IO registers are the epitome of global mutable state.
Yup, you definitively don't know what functional programming is if you think you can't have global mutable state in it. In fact, every top-level Haskell program is defined as a global mutable IO monad...