If so, these snippets of code which I shared on gitbub might please you.
What is a formal style of programming
Formal "code", like formalism in mathematics, is to solidly tie what you write to what you mathematically mean. And that connection goes both ways: from math to expression, from expression to math.
The traditional way to write formal code is to prove as much as you can 'along the way' of writing code. The difficulty of this approach is that proofs are hard, which either limits the complexity of your code, or limits your ability to be productive.
Another way to write code with mathematical properties is to assemble pieces of code that already have mathematical properties. When this assembly preserves these mathematical properties, and even better when it scales them, the resulting code has mathematical properties. A key concept here is that these "pieces of code with mathematical property" are "at different levels", as it is the interplay between these levels that give the code its semantic depth. (This last point explains why languages like Prolog are hard to scale).
Dualities are good place to find mathematical properties. An example of duality is symmetry: something can be 'one way' and 'the other', and we know "mathematically" what that means. This is why reversible code, reversible types, adjoint structures, and pretty much anything that goes 'one way' and 'the other' (e.g. like rows and columns) are a good basis on which to build systems with formal properties.
What is reversible programming?
Reversible expressions can be evaluated 'one way' and 'another'. This might be execution evaluation that might be reversed, yet might also mean that the interpretation of the expression can be seen from a reversed perspective at different semantic level (e.g. types, external view).
Reversibility is also a way to approach multi-party programming: Say I am party Alice having received B from Bob, after having previously shared A with Bob. Alice can reverse compute B to A to validate that Bob computed B from A. That is a simplified view of things, but it captures the idea that reversibility enables trust.
Reversibility is much like immutability that has been weakened, but which has not lost its magical properties.
What is point-free style?
A point-free (or tacit) style of programming traditionally means coding by composition without naming arguments (and without assignments). In a Python centric view that could mean to only use 'positional arguments', and to use only Callable objects (so as not to have method names), but you need to ask yourself: "Is that important"? In fact within the scope of reversible programming, point-free is best approached as composable and reversible. That you name things or not is of lesser importance. In fact, it is of lesser importance also because the traditional point-free is to focus on 'expression space'. Yet modern programming happens much at the type level, or the meta-type level, and a strict point-free approach would lead us to writing code where types are nameless, as well as meta-types. That would be tricky!
Note here: Point-free much leads to array, stream and structural oriented programming. This is not lost here. In fact a main reason to write code like this in Python is to write structural oriented ML. Reversibility is also a vital piece of blockchain and smart contracts theory too.
Why should you care?
Wikipedia's programming paradigm page enumerates many ways to code. Reversibility is one of the concepts that brings together all of these different ways of expressing software. Putting reversibility 'underneath' a paradigm gives it bridges to other paradigms that have also been given reversibility properties.
All original content copyright James Litsios, 2021.
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