Before the idea of postmodern programming can begin to be investigated, the question of whether anything like modernist and classical programming even exists needs to be asked.
It is not surprising that the question of how to define postmodern programming is reframed by the OO contingent (reflecting their ignorance as much as their immature self-obsession) as literally "what comes after object-orientation?" That is a silly question to ask when you don't know what object-oriented means or what came before.
James Noble and Robert Biddle attempted to address the issue in their Notes on Postmodern Programming, but focused on the act of writing programs and left the question of programming paradigms unexamined.
One possible interpretation gives surprisingly straightforward definitions: the development of the idea of algorithms constitutes the age of classical programming, while procedural and data abstraction, being the rationalization of the construction and application of algorithms, constitute modern programming.
What then is the narrative of a modern program? The evaluation strategy. Algorithms are executed in steps. Modernist programming promotes rationalization in laying out these steps. Postmodern programming rejects the linear evaluation strategy.
Curiously, we can arrive at the same conclusion by framing the relationship between procedural and functional programming in terms of a dialectic:
The thesis of procedural programming is the description of programs in terms of time (sequential execution of instructions/sequential branching) and behavior (the semantics of instructions), as entities operating on data - object identity, and state of addressable (nameable) places (registers, variables, arrays, etc.).
Functional programming presents an antithesis: programs are described in terms of data - identity (named functions) and state (first-class functions) - and operate on time (persistent/immutable data structures) and behavior (monads).
The synthesis is a nondeterministic, reified (homoiconic), first-class program. The program exists for the sake of itself, becomes the object of study and center of efforts. The computational narrative of the evaluation strategy escapes control, and so from the point of view of the programmer becomes irrelevant.
How, when, and why certain parts of the program are evaluated becomes subjective.
Perl was not the first postmodern programming language; Prolog was.
Non-determinism as the rejection of computational narrative and the reification of time arise naturally from physical constraints when attempting to reason about concurrency. Most of the modernist concurrency techniques concern themselves with maintaining what I call the global state illusion, or quite literally forcing a single narrative on a distributed system. Not only does the current state of the system remain unknown and unknowable, but its past history permits an exponential number of equally valid, relative interpretations.
Rich Hickey's 2009 JVM summit presentation explores these concepts of concurrency and time in a thought-provoking manner.