every expression that can be replaced by another expression that denotes the same value is referentially transparent. With referential transparency there’s no distinction between the name of a thing and the value it denotes, so we benefit of optimizations like: memoization, parallelization, common subexpression elimination, etc.
identity introducing a new dimension of bugs: side-effect bugs • By introducing assignment is just philosophically harder to define equality • By introducing assignment we brought our time perspective into our programs • By introducing assignment we just make our lives more difficult
and better modularity • We can move in all three dimensions of space, yet we are prisoners of the present, that is, we need assignment to work with time because mathematical functions are timeless, static • We could think that our temporal existence is what imposes state on any system
infinite streams that are computed as needed, the downside is that we lose a bit of modularity and some functions depending on what they do might have a version that accepts deferred arguments normal order evaluation One way to avoid that problem would be to automatically deferring all function arguments giving us a language with normal order evaluation, yet it would complicate the cases where our program depends on the order of events Scalability The same interface can be used to solve different problems (sync vs async).
quantity which let us benefit from mathematical properties. Modularity It restores back the same encapsulation we had when using assignment but without using it and with better semantics. Combinatorial interface The interface we obtain is highly expressive and very powerful constructs can be made out of simple combinators, it also can be used to solve different domain problems (sync vs async) maintaining almost the same interface.