[mithametacs]

Sounds like a page worth another search if you don't mind. I'll give you Internet Points in return!

-- my attempt:

Imperative defines the order and semantics of each step.

Declarative defines the prerequisites and intent of each step.

The algorithms each can implement are equivalent.

[Mikhail_Edoshin]

Found it:

https://existentialtype.wordpress.com/2013/07/18/what-if-any...

Semantic is another word that is hard to define.

[mithametacs]

I read that and the followup. It’s good writing but I slightly disagree. Imperative is actually a closer mathematical formalism for some things.

I find imperative better for expressing state machines. I find declarative better for backtracking.

You can write a state machine with just a loop, an assignable, and conditions. Writing state in prolog is irritating.

[Mikhail_Edoshin]

You don't even need a loop. Steps, conditions, and a 'goto'. Loop are actually a design mistake. They try to bound 'goto' by making it structured. They are declarative, by the way. As a special case or even as a common case they are fine, but not when they try to completely banish 'goto'. They are strictly secondary.

Similarly declarative programming is strictly secondary to imperative. It is a limited form of imperative that codifies some good patterns and turns them into a structure. But it also makes it hard or impossible not to use these patterns.

[Mikhail_Edoshin]

(I would also say that state machine is a foundational model for programming.)