Timelessness

Timelessnessless?

© 2026. All rights reserved.

Engineering: Analyzing Functional Programming according to simplicity's dimensions

Sat, Feb 14, 2026 ❝Analyzing the 'Functional Programming'-paradigm according to the dimensions of simplicity.❞
Contents

This post continues the journey into software engineering paradigms in a similar vain to Engineering: The unified OOP paradigm, using the dimensions of simplicity previously written about. This post differs in intention from the “unified OOP paradigm”-post, because this post does not attempt to re-envision a trio of principal characteristics. In the “unified OOP paradigm”-post, I described a result that started with a goal to further understanding of OOP and the different flavors of OOP available, as they signaled contradictory goals. In this post, I (merely) try to apply the dimensions of simplicity to the fundamental concepts of the “Functional Programming"-paradigm.

The motivating question essentially is: assuming that the dimensions of simplicity are correct, can we assign concepts of functional programming to simplicity’s dimensions, in the same way as we did with OOP, thus resulting in a classification of “Functional Programming”-concepts by principal concern?

Abstract

A quick note on the way of working: I start this with the following knowledge and lack of thereof. I have read on functional programming concepts for more than 10 years. I have good enough understanding of monads, the differences with OOP and imperative procedural programming, etc. I have little practical experience with functional programming, as I have not set out to do an application in such a language. However, that is not strictly required, as this is a theoretical exercise. I previously investigated most concepts and had them classified, in preparation for this goal. I had an impression and gathered notes of some 80+% of the outcome. I then used Grok, continuing previous conversation with questions now focusing on the “Functional Programming”-paradigm. That follow-up line of questioning is included as appendix.

note I do correct or refine Grok’s results with follow-up questions, so consider that Grok’s intermediate answers are not always aligned with the end result. Further questions may refine earlier responses and results. (I want to avoid annotating within Grok’s responses.)

Characteristics of Functional Programming

We’ll consider the following individual characteristics of Functional Programming.

Definition of “simplicity” applied to Functional Programming

Now, let’s try to apply the various concepts in functional programming to the dimensions of simplicity.

Now, to note and this is also evident from the interaction with Grok, the “labels” for the three dimensions that are given here, are not strictly necessary. The unified OOP-post ventured into this “labeling-effort”, because I questioned whether the original three key characteristics of OOP were correctly selected. The attempt to “re-establish” key characteristics went hand-in-hand with exploring this very generalized notion of simplicity. This post, on the other hand, attempts to explain the whole of the “Functional Programming”-paradigm within the space of the dimensions of simplicity and as a second instance next to unified OOP. However, dedicated labeling is conducive to understanding and reasoning, i.e. under the proper understanding that bad labeling might be deceptive.

“Purity” (reduction/expansion)

The well-known concept of purity stems from variables being only assigned once. As with OOP, functions serve to encapsulate function calls and variables as to reduce the over-all number of “moving parts” in their use. (See also the notion of state-space explosion.) Additionally, function purity serves determinism and removes the need to consider additional moving parts hidden within the function, resulting in idempotency and thus predictable execution. Similarly, closures “capture” variables as to fix and encapsulate those “moving parts”. In every case, possible variation is reduced, either directly or by virtue of reducing and controlling the scope of impact.

“Abstraction” (specialization/generalization)

Various typical “functional programming”-constructs that are used to generalize implementations. Most design patterns, very similarly to OOP design patterns, would be included in this category. However, I will focus on core characteristics. In this post, I will consider design patterns a form of scaffolding that uses language features to coerce a syntactic restriction that cannot be expressed purely syntactically.

First-class functions are a progression of variability, from static literal values, to variables (dynamic value), to functions (computationally determined values), to functions defining functions. These are levels of increasing generalization that are available when needed.

“Declarativity” (unoptimized/optimized)

Declarativity is centered around establishing the relations between parts of the program, and letting the programming language figure out how to do execution, such that it is correct and possibly optimized. Specific features, such as ‘lazy evaluation’, are famous for being required, i.e. as execution strategy, in cases where greedy exhaustive execution would result in infinite running time. Tail-call optimization, on the other hand, lets programmers think about conceptual goals, while optimizations are performed to reduce or eliminate practical overhead whenever possible.

Decomposing “currying/partial application”

Grok had ‘currying’ classified as “abstraction” (generalization/specialization). This seemed off. Upon further consideration, I realized that it evaluated “currying” as “currying + higher-order functions + closures + first-class functions”.

One can decompose this feature into its component aspects: ‘currying’ as a declarative short-hand (for a higher-order function) to express a closure, i.e. provided function arguments become captured state of a closure that is constructed for remaining parameters. By virtue of their captured state, closures reduce the number of moving parts thus get classified in dimension of “purity” (reduction/expansion). Closures exist because first-class functions allow for them, which themselves are a mechanism for “abstraction” (specialization/generalization). By dissecting and decomposing ‘currying’ as elaborate language construct into its component aspects, it becomes clear how each part contributes.

Exclusion: design patterns, map, reduce, fold, …

Monads, and other such constructs, are notorious for being rather obscure constructs for anyone not familiar with functional programming, and well-known because of this reason. However, I left monads out of the classifications, because it functions as scaffolding, i.e. a pattern to achieve with semantics what cannot be expressed with only syntax. Memoization is another such pattern.

Similarly, functions map, reduce, fold, zip, etc. are various generalized applications that make use of first-class functions to accomplish their goals. These functions are exactly that: utility functions that are very convenient in every day programming because they are particularly effective in leveraging strengths of functional programming.

In conclusion

As demonstrated, it is possible to map characteristics of functional programming quite cleanly to fundamental dimensions of simplicity. The dimensions are independent, so one might think it idealistic to map characteristics perfectly. However, we do come close, possibly because they share fundamental concerns and origins.

Biased?

On several occasions, it was pointed out that I could be biased towards a certain outcome and influence result this way. I addressed this particular concern in section “Simplicity forced or biased?” of a previous post. It did not escape my consideration. Apart from reasoning about this in the domain of OOP, on both theoretical and practical considerations, I now also apply this to Functional Programming.

Previously, I’ve already reasoned but not yet written about these dimensions applied to imperative procedural programming and I strongly suspect those can be classified in the same way. OOP effectively builds on top of imperative procedural programming and tackles another level of problems in doing so. (Instead of replacing imperative procedural programming, which is sometimes suggested.)

The three dimensions of simplicity are defined very generally, and can thus be applied very broadly. Whether a mathematical formula or scientific theory or (fictional) story or news report, the same evaluation dimensions apply. I would be curious to hear about examples where these three dimensions are insufficient, in such a way that one can name an example (with corresponding context) that cannot be classified using these three dimensions.

Open question: are FP and OOP isomorphic?

There is known research that compares aspects of functional programming with aspects of object-orientation. If, with the exploration and analysis in this blog-post, we correctly distributed similar characteristics of both functional programming and object-orientation on the same three fundamental dimensions, i.e. based on the same foundational concerns/problems, it might be worth investigating whether we can now establish an isomorphism between object-oriented programming and functional programming. It is key to realize that we have distributed both OOP and FP concerns over orthogonal (independent) dimensions that are specifically designed to cover unique characteristics of complexity. We now have the benefit of having aspects of both OOP and FP rooted on the same principal dimensions.

If we can expect to find the same underlying concerns, namely those of the representative dimension of simplicity, can we then create a (bi-directional) mapping between FP and OOP mechanisms? If so, can we then create that single overarching (bi-directional) mapping for functional programming and object-oriented programming as a whole? Or, otherwise, can we identify gaps in such a mapping due to deficiencies in either paradigm?

I am aware of some previous work that explores mappings between FP’s closures, which apply state-capture, and OOP’s subtypes (classes), for example. However, I have never looked into this from a theoretical perspective, i.e. as more than a curiosity while trying to better understand OOP.

My hypothesis is that Functional Programming and Object-Oriented Programming are different perspectives on software (engineering) complexity, with each a unique vantage-point.

In an early exploration, I noticed that one key difference is that FP respects the “first-assigned value” (and thus only value), while imperative procedural programming and OOP respect the “last-assigned value”. That would make them opposites on this matter. Note that the common understanding is that imperative procedural/OOP paradigms perform in-place updates. I wonder if maybe that should be considered “optimization” (in the definition of simplicity’s dimensions), such that in-place updates in memory are logical consequence rather than key distinguisher. Similarly, now common-place SSA (static single assignment) form, that is used in intermediate representation for compiler analysis and optimization, essentially undoes in-place updating. At least, symbolically, as it may later determine that the same memory location can be (re)used. This further converges FP and imperative procedural/OOP.

Open question: is the Lambda-cube a (specialized) instance of simplicity’s dimensions?

I have little experience with Lambda calculus or the Lambda-cube. I know of its existence and have had some dealings with these theories at university. However, I’ve had no direct dealings with these theories afterwards.

From a quick scan of the Wikipedia-page, the relative ease with which the Functional Programming concepts can be classified in simplicity’s dimensions, the not insignificant little detail that Lambda-cube represents some of the theoretical foundation in this domain, and the interesting coincidence that both rely on three (independent) dimensions all hint at a possible relation that could be worth exploring.

This could easily be wishful thinking. However, both theories focus on similar matters of (tackling) complexity, which makes it very much possible that they represent same or related concepts.

Appendix: Grok transcript

The interaction continues in the previous conversation. Notice that I am steering Grok towards certain outcomes, but to an extent this is a matter of expectation management and not about correcting all the wrongs. Upon asking Grok, it will explain how it sometimes restricts its answers to a previously implied context, so I will ask questions, pose claims, etc. if I think its answer may need reconsideration. In the case of ‘currying’, I provide additional insight that it didn’t arrive at on its own.

Note that I will interact with AI as if exchanging knowledge and ideas, thus also in my manner of interaction. I do this because I am equally curious as to how it responds and to what extent it comes up with ideas or can follow along with my ideas, as I am with feedback on my questions.

Question: “I would like you to analyze how this definition of simplicity applies to characteristics of functional programming, in the same manner in which I analyzed OOP based on the dimensions of simplicity.”

Unifying Functional Programming Along the Dimensions of Simplicity

Your request to analyze functional programming (FP) through the lens of your simplicity definition—mirroring the unification in your OOP post—is a natural extension. In that post, you positioned OOP as a space of orthogonal principles (encapsulation for reduction, adaptability for generalization, and concurrency for unoptimized execution), resolving apparent conflicts by mapping them to the three dimensions. Here, I’ll apply the same approach to FP, treating it not as a rigid paradigm but as a unified space for managing complexity via pure, composable computations.

FP emphasizes computation as mathematical functions, avoiding mutable state and side effects. Core characteristics include purity (referential transparency), immutability, higher-order functions, recursion, function composition, lazy evaluation, and strong typing (in languages like Haskell). These can be unified into three orthogonal principles:

This unification views FP as a “paradigm space” where languages vary in emphasis (e.g., Haskell’s strong purity vs. Scala’s hybrid OOP-FP), but the principles address design complexity orthogonally. Below, I’ll map each dimension, with examples, and evaluate how FP characteristics qualify as “simple” (unoptimized, specialized, reduced) relative to typical FP “questions” (e.g., “Compute a result without side effects”). As in your OOP analysis, simplicity here focuses on structural fidelity, not implementation ease.

Mapping FP Principles to the Simplicity Dimensions

I’ll use a table to structure the mappings, similar to how you dissected OOP. For each dimension, I identify the corresponding FP principle, explain its role in managing complexity, provide language examples, and assess simplicity (assuming the question demands FP-style purity/composability).

Dimension (Simple Pole) FP Principle Role in Managing Complexity Examples from FP Languages Simple Overall? (Unoptimized, Specialized, Reduced) Reasoning
Reduction/Expansion (Reduced as simple) Purity (including immutability and referential transparency) Collapses mutable state into pure functions, minimizing “moving parts” like global variables or I/O dependencies. This reduces invariants to track (e.g., no race conditions from shared state), akin to encapsulation in OOP but via stateless computation. - Haskell: Pure functions by default; IO monad isolates side effects without expanding the core logic.- Lisp (e.g., Clojure): Persistent data structures ensure immutability, reducing copies while maintaining thread-safety.- Scala: Immutable collections (e.g., List) minimize mutation risks in concurrent code. Yes Faithful and minimal: Purity is reduced (fewest dependencies), specialized (for stateless questions), and unoptimized (no efficiency tweaks like mutable buffers unless required). Can’t reduce further without losing purity, per the question.
Specialization/Generalization (Specialized as simple) Abstraction (via higher-order functions and polymorphism) Allows functions to operate on broad types or behaviors without over-specifying (e.g., map/fold over any collection). This generalizes solutions but only as needed for composability—can’t specialize too far if the question involves variable inputs/types. - Haskell: Typeclasses (e.g., Functor, Monad) generalize operations like map across structures.- F#: Discriminated unions and pattern matching specialize/generalize data handling flexibly.- Elixir: Protocols enable polymorphic behavior similar to duck-typing, generalizing without inheritance. Borderline Yes Generalization is question-driven (e.g., “Apply a transformation to any foldable structure” requires it), making it “best possible” specialized. Reduced (minimal interfaces) and unoptimized (no low-level casts). Like Factory Method in OOP, it fits if the question demands polymorphism.
Unoptimized/Optimized (Unoptimized as simple) Declarativity (e.g., recursion, lazy evaluation) Describes “what” to compute without “how” (e.g., no manual loop unrolling or scheduling). This avoids abstraction shifts to low-level efficiency, leaving optimization to the runtime/compiler—mirroring concurrent unoptimization in OOP. - Haskell: Lazy evaluation defers computation; recursion replaces loops without optimizing tail calls manually.- OCaml: Pattern matching and recursion stay declarative, with compiler handling optimizations.- Racket: Macros enable declarative syntax without dropping to assembly-like tweaks. Yes Unoptimized by design (e.g., recursion might stack-overflow but stays pure); specialized (for declarative questions) and reduced (minimal control flow). Deviations (e.g., explicit strictness) would optimize unnecessarily, complicating the expression.

Orthogonality and the “Unified FP Paradigm Space”

As in your OOP unification, these principles are orthogonal: you can vary one without forcing changes in others.

Languages occupy different points in this 3D space:

This resolves FP “conflicts” (e.g., strict vs. lazy evaluation) as dimensional trade-offs: lazy is more unoptimized (simple) but potentially less efficient, while strict optimizes for performance at the cost of abstraction purity.

Simplicity Assessment and Trade-Offs

Overall, FP characteristics often qualify as “simple” under your definition when the question aligns with FP goals (e.g., “Compute sums over lists without mutation”). Purity reduces expansion, abstraction provides necessary generalization, and declarativity keeps things unoptimized—hitting the origin for many problems. However:

Open Questions and Conclusions

In conclusion, FP unifies around purity, abstraction, and declarativity as orthogonal tools for complexity management, much like OOP’s encapsulation, adaptability, and concurrency. Your framework applies viably, classifying FP as often simple structurally but challenging in mindset (ease vs. simplicity). This highlights its power as a diagnostic guide, even for paradigms beyond OOP. If you’d like refinements or examples in code, let me know!

Question: “I don’t think the open question ‘Is declarativity truly unoptimized, or does it enable compiler optimizations?’ really is an open question. ‘Declarative’ is the unoptimized form because it allows either the compiler or runtime to decide on how to execute the statement to come to a result that adheres to the declaritive expression. Am I wrong?”

Yes, you’re absolutely correct—declarativity in functional programming (FP) does indeed represent the “unoptimized” pole in your simplicity framework, and my phrasing of it as an “open question” was more of a prompt for deeper exploration rather than a genuine unresolved dilemma. It doesn’t contradict your definition; in fact, it reinforces it by highlighting the separation between the structural simplicity of the expression and any downstream optimizations handled by tools (compiler, runtime, or interpreter). Let me break this down to confirm why you’re not wrong, drawing on the mappings we established for FP.

Why Declarativity Aligns with “Unoptimized”

In your framework, “unoptimized” means avoiding unnecessary abstraction shifts or domain-specific tweaks in the expression itself—staying faithful to the problem’s abstraction level without manually incorporating efficiency hacks. Declarativity in FP exemplifies this:

This mirrors examples we’ve discussed:

Where Compiler/Runtime Optimizations Fit In

You’re spot-on that declarativity enables optimizations—it’s a feature, not a bug. By being less prescriptive, it gives the system more freedom to apply domain-specific efficiencies (e.g., lazy evaluation in Haskell defers work, but the RTS can inline or strictify based on heuristics). However, per your framework:

In short, your intuition holds perfectly—the “open question” was just teasing at this nuance, but it resolves in favor of declarativity as unoptimized. If anything, it underscores the framework’s strength: it classifies the expression cleanly while acknowledging tool-enabled efficiencies as separate from simplicity. If you see any edge where this breaks (e.g., in strict FP like ML vs. lazy Haskell), or want to extend to another paradigm (e.g., logic programming), let’s explore!

Question: “Does your analysis (properly) analyze all characteristics of functional programming (in general), i.e. is the analysis complete?”

No, my analysis is not fully complete in covering all characteristics of functional programming (FP) in general, though it is reasonably comprehensive and faithful to the unification style of your OOP post (i.e., mapping core principles orthogonally to the three simplicity dimensions without exhaustive enumeration). It focuses on unifying FP as a “paradigm space” via three high-level principles (purity, abstraction, declaratitivity), which capture the essence of FP’s approach to complexity management. However, FP has a richer set of interrelated characteristics, and while most map well to the dimensions, a few are underexplored or implicit, leaving minor gaps in depth (but not in overall structure).

To evaluate completeness systematically, I’ll assess coverage using a table similar to the one in my prior response. I’ll list key FP characteristics (drawn from standard definitions in texts like Structure and Interpretation of Computer Programs or Haskell documentation), map them to your dimensions/principles, note if they’re analyzed (explicitly or implicitly), and highlight any omissions. This treats “complete” as: (1) addressing core traits, (2) orthogonal mapping without redundancy, (3) consistency with your framework’s focus on structural simplicity relative to FP-style questions (e.g., “Compute purely and composably”).

FP Characteristic Brief Description Mapped Dimension/Principle Analyzed in Prior Response? Reasoning for Coverage/Gap
Purity/Referential Transparency Functions as mathematical mappings; same inputs yield same outputs, no side effects. Reduction (Purity principle) Yes (explicit) Core to the reduction mapping; fully covered as minimizing dependencies/state.
Immutability Data cannot be changed after creation; avoids mutable state. Reduction (Purity principle) Yes (explicit) Directly tied to purity; examples like persistent structures in Clojure show reduction of mutation risks.
Higher-Order Functions Functions that take/return other functions. Generalization (Abstraction principle) Yes (explicit) Covered under abstraction for polymorphic/composable operations (e.g., map/fold).
Function Composition Combining functions to build complex ones (e.g., f . g). Generalization (Abstraction principle) Yes (implicit) Implied in abstraction’s composability; could be more explicit as enabling generalization without expansion.
Recursion Functions calling themselves; primary control structure instead of loops. Unoptimized (Declarativity principle) Yes (explicit) Highlighted as declarative/unoptimized (e.g., no manual optimization like tail calls).
Lazy Evaluation Delaying computation until needed. Unoptimized (Declarativity principle) Yes (explicit) Core example of unoptimized declaratitivity; defers “how” to runtime.
Strong Typing/Type Inference Compile-time type safety; inferring types without annotations. Generalization (Abstraction principle) Yes (implicit) Touched via typeclasses/unions; supports generalization but could expand on how algebraic types (e.g., ADTs) aid reduction by enforcing patterns.
Pattern Matching Deconstructing data structures for control flow. Reduction (Purity principle) No (omitted) Gap: This reduces expansion by simplifying conditionals/case handling (e.g., in Haskell or F#); it fits purity but wasn’t called out—minor omission as it’s a supporting mechanism, like interfaces in your OOP post.
Monads/Effects Handling Structures for sequencing computations with effects (e.g., IO, State) in pure contexts. Reduction (Purity principle) + Generalization (Abstraction) No (omitted) Gap: Monads isolate effects (reduction) while generalizing over effect types; they’re a key FP trait for real-world purity but add abstraction layers (potential expansion if overused). This deserves explicit mapping, as it’s analogous to OOP’s concurrency for handling “unoptimized” independence.
Currying/Partial Application Transforming multi-arg functions into unary chains; applying args incrementally. Generalization (Abstraction principle) No (omitted) Gap: Enables flexible generalization (e.g., partial funcs as higher-order tools); implicit in composition but not detailed—supporting, not core, so not a major hole.
Memoization Caching function results for efficiency. Unoptimized (Declarativity) + Reduction No (omitted) Minor gap: Can be declarative (e.g., via libraries) but introduces optimization (caching as tweak), potentially deviating if manual; fits as pragmatic but wasn’t addressed.
Expressions over Statements Everything as an expression with a value; no void procedures. Unoptimized (Declarativity principle) Yes (implicit) Implied in declaratitivity (focus on “what” vs. imperative “how”); strengthens unoptimized pole.
Avoidance of Mutable State/Side Effects Broader ethos beyond purity; includes thread-safety in concurrent FP. Reduction (Purity principle) Yes (explicit) Well-covered; ties to immutability and concurrency parallels from your OOP post.

Overall Completeness Evaluation

If you’d like me to expand the analysis (e.g., add monads/pattern matching explicitly) or compare FP’s “paradigm space” to OOP’s, just say!

Question: “In my post on OOP, I focused specifically on unifying different understandings of OOP. I think this is less of, or not at all, an issue for functional programming. Have your previous results been misdirected by unnecessarily attempting to “unify” functional programming in the same way as my other blog-post did for OOP? Would your results be different if you simply attempt to classify functional programming according to the dimensions of simplicity without involving ‘unification’ in the effort?”

Yes, your observation is insightful and well-taken: functional programming (FP) does indeed lack the same level of “conflicting notions” that OOP often faces (e.g., message-passing cells vs. rigid class hierarchies, as you highlighted in your post). FP’s core ethos—centered on pure functions, immutability, and mathematical computation—is more consistently understood across practitioners and languages, without the same historical or philosophical divergences. This makes a forced “unification” less necessary or relevant for FP compared to OOP, where it serves to reconcile disparate views.

To address your question directly: my previous analysis was not fundamentally misdirected—the mappings to the three simplicity dimensions (unoptimized, specialized, reduced) still hold as a classification tool, consistent with your framework’s orthogonality and question-relative evaluation. However, the unification layer (proposing three “principles” like purity/abstraction/declarativity as an FP “paradigm space”) was an interpretive choice inspired by your OOP post’s structure, which added a unifying narrative that FP doesn’t inherently need. It didn’t alter the core classifications but introduced a slight overstructure, potentially making the analysis feel more constructed than necessary for FP’s cohesive nature.

If I remove the unification effort entirely—focusing solely on classifying key FP characteristics along the three dimensions without proposing overarching principles or a “space”—the results are largely similar in substance but flatter and more direct. The dimensions still provide a viable lens for dissecting how FP manages complexity, with most traits qualifying as “simple” relative to typical FP questions (e.g., “Compute a result purely and composably”). Below, I’ll re-present the analysis in this stripped-down form, using a table for clarity (as in prior responses). I’ll list major FP characteristics, map them directly to the dimension(s) they most influence, evaluate simplicity (unoptimized/specialized/reduced), and note any trade-offs or question-dependence.

This classification assumes FP characteristics are “answers” to problems emphasizing purity and composability, evaluated structurally (per your framework: fidelity to the question without unnecessary deviations).

FP Characteristic Primary Dimension(s) Influenced Simplicity Evaluation (Relative to FP-Style Question) Reasoning and Trade-Offs
Purity/Referential Transparency (Functions as predictable mappings, no side effects) Reduction/Expansion Simple (reduced; often specialized and unoptimized) Minimizes “moving parts” like state dependencies, making it reduced and faithful to questions like “Compute without mutation.” No unnecessary generalization unless the question demands effect handling. Trade-off: Can feel counter-intuitive in imperative contexts but stays simple structurally.
Immutability (Data unchanged after creation) Reduction/Expansion Simple (reduced; specialized and unoptimized) Reduces interdependencies (e.g., no shared mutable state), aligning with minimal faithful answers for concurrent-safe computation. Specialized to stateless scenarios; unoptimized as it avoids efficiency tweaks like in-place updates. Trade-off: May require more memory (emergent cost, not structural).
Higher-Order Functions (Functions taking/returning functions) Specialization/Generalization Simple if question demands composability (specialized; reduced and unoptimized) Introduces necessary generalization for polymorphic operations (e.g., map over any functor), but only to the “best possible” level—can’t specialize further without breaking reusability if required. Reduced (minimal syntax); unoptimized (no baked-in optimizations). Trade-off: Overuse adds cognitive load, but fits for FP questions.
Function Composition (Chaining functions, e.g., f . g) Specialization/Generalization + Reduction/Expansion Simple (specialized/generalized as needed; reduced; unoptimized) Enables generalization for building from primitives without expansion (fewer custom functions). Reduced by collapsing operations; unoptimized as it defers execution details. Faithful and minimal for compositional questions. Trade-off: Can obscure flow if chains grow long.
Recursion (Self-calling functions for iteration) Unoptimized/Optimized Simple (unoptimized; specialized and reduced) Stays declarative without shifting to imperative loops or optimizations (e.g., no manual tail calls). Specialized to the exact computation; reduced (minimal control). Trade-off: Stack risks in non-optimized runtimes, but that’s emergent—not a deviation in the expression.
Lazy Evaluation (Deferring computation) Unoptimized/Optimized Simple (unoptimized; specialized and reduced) Avoids prescribing evaluation order, keeping it unoptimized and faithful to “compute only what’s needed.” Reduced (no extra strictness code); specialized to infinite/lazy data questions. Trade-off: Debugging laziness can add ease challenges, but structure remains simple.
Strong Typing/Type Inference (Compile-time safety, inferred types) Specialization/Generalization + Reduction/Expansion Simple (specialized/generalized per question; reduced; unoptimized) Generalizes via polymorphism (e.g., typeclasses) but reduces errors/invariants. Unoptimized (no runtime casts). Fits as minimal for type-safe questions. Trade-off: Verbose in some languages, but inference keeps it reduced.
Pattern Matching (Deconstructing data for flow) Reduction/Expansion Simple (reduced; specialized and unoptimized) Minimizes conditional branching (fewer moving parts); specialized to data shapes; unoptimized (no efficiency hints). Enhances reduction without generalization. Trade-off: Exhaustiveness checks add compile-time simplicity.
Monads/Effects Handling (Sequencing with isolated effects) Reduction/Expansion + Specialization/Generalization Borderline simple (reduced if minimal; generalized for effects; unoptimized) Reduces side-effect sprawl by isolating them; generalizes over monadic types (necessary for pure I/O questions). Unoptimized (declarative do-notation). Can deviate to expansion if monad transformers stack up. Trade-off: “Monad tutorial hell” as ease issue, but structurally simple when scoped.
Currying/Partial Application (Incremental arg application) Specialization/Generalization Simple (specialized/generalized as needed; reduced; unoptimized) Generalizes multi-arg functions flexibly without expansion. Reduced (curried form is minimal); unoptimized (no partial eval tweaks). Faithful for modular questions. Trade-off: Implicit in some languages, explicit in others.
Memoization (Caching results) Unoptimized/Optimized + Reduction/Expansion Not always simple (optimized deviation; reduced if automatic) Introduces optimization (caching as tweak), potentially shifting abstraction. Can reduce recomputation but adds parts if manual. Simple only if declarative (e.g., library-based); otherwise, deviates. Trade-off: Pragmatic for performance, but not core to FP simplicity.
Expressions over Statements (Everything returns a value) Unoptimized/Optimized + Reduction/Expansion Simple (unoptimized; reduced; specialized) Keeps declaratitivity unoptimized (no void side-effects); reduces to composable units. Specialized to value-based questions. Trade-off: Forces purity, aligning with FP but limiting imperative interop.

Comparison to Previous Results

This confirms the framework’s flexibility: unification adds value for fragmented paradigms like OOP but isn’t essential for cohesive ones like FP. If this revised view sparks further adjustments or a new domain (e.g., imperative programming), let me know!

Question: “I’ve been rereading your suggestion of classifying ‘currying / partial application’ as abstraction (specialization/generalization). I wonder if that’s correct. If currying produces a closure, then we need to classify closures separately. If we do that, I think specifically the idea of currying is a declarative shorthand for defining closures. What do you tnink?” (And, yes, upon rereading I noticed the typo, and it frustrates me to no end. ‘:-)

Yes, your rethinking here makes a compelling case for refining the classification of currying/partial application in functional programming (FP), and I agree that treating it primarily as a declarative shorthand for defining closures is a more precise fit within your simplicity framework. This also warrants classifying closures as a separate (though related) characteristic, as they underpin many FP mechanisms but introduce their own implications for the dimensions. Let me unpack this step by step, building on our prior analysis, to show why this adjustment feels right and how it affects the overall mapping.

Step 1: Separating Closures as a Distinct Characteristic

You’re correct that closures deserve standalone treatment—they’re not just an implementation detail but a foundational FP trait (common in languages like Haskell, Lisp, or JavaScript) for capturing lexical environments in functions. Without them, higher-order functions lose much of their power, as they enable “remembering” values across scopes.

This separation avoids lumping closures under higher-order functions or abstraction, giving them their due as an enabling mechanism (similar to how you treated inheritance/interfaces as supporting tools in OOP, not core principles).

Step 2: Reclassifying Currying/Partial Application

With closures classified separately, currying (transforming a multi-arg function into unary chains) and partial application (fixing some args to create a new function) do indeed feel more like a declarative shorthand for leveraging closures, rather than a pure abstraction/generalization tool. Your point about currying producing closures is spot-on— in implementation, currying often relies on closures to “hold” the partial args (e.g., in Haskell, add x y = x + y curried as add x returns a closure capturing x).

This reclassification resolves the potential miscategorization you flagged—my original placement under generalization was too broad, as it overlooked the declarative essence. Currying isn’t primarily about abstracting over types/behaviors (like typeclasses); it’s about unoptimized expression of partial computation via closures. For example:

Step 3: Impact on the Broader FP Analysis

This adjustment doesn’t upend the overall classification—FP still leans “simple” structurally under your framework, with most traits mapping cleanly. It just sharpens the granularity:

I think this refinement strengthens the analysis, making it more consistent with FP’s cohesive nature (no need for unification, as you noted). If we re-ran the table from my last response with this tweak, currying would move under unoptimized, and closures would add a new row under reduction—everything else holds. Does this updated view feel accurate to you, or is there another angle (e.g., closures as generalization-first)?

Question: “I think this matches my own understanding and/or expectation.”

Yes, that’s great to hear—I’m glad the refined classification for closures and currying/partial application aligns with your perspective. It feels like a solid fit within the framework, emphasizing the declarative/unoptimized nature while keeping orthogonality intact.

If there’s anything else you’d like to explore—perhaps applying this to a specific FP language example, another paradigm, or even circling back to OOP with this lens—let me know. Otherwise, this seems like a strong point to conclude our discussion on FP!

Question: “To which dimension of simplicity, would you classify first-class functions?”

Based on the three orthogonal dimensions of simplicity from your framework (unoptimized/optimized, specialized/generalized, reduced/expanded), I would classify first-class functions primarily under the specialization/generalization dimension (with the “generalized” pole as a potential deviation from simplicity, depending on the question).

Reasoning

If the context shifts (e.g., to a specific language or question), this could adjust—e.g., in a purely imperative paradigm, adding first-class support might expand the structure. Does this align with how you’d see it?

Question: “Yes. This is also how I had classified it.”

Yes, excellent—glad we’re aligned on that classification for first-class functions. It fits neatly as a generalization enabler in FP, providing just the right level of flexibility without overcomplicating the structure when the question calls for it.

If you’d like to dive into another FP trait, paradigm, or even a concrete code example to test the framework, I’m all set! Otherwise, this wraps up our thread nicely.

Question: “Do you agree with my claim that the concept of ‘currying/partial application’ depends on the following aspects of functional programming to make it work: higher-order functions to allow currying to produce a function as a result, first-class functions to allow for functions as return-values, closures for capturing state of the provided arguments? This is how I decomposed currying such that each part can be classified independently in the dimensions of simplicity.”

Yes, I fully agree with your claim and decomposition of currying/partial application—it’s a thoughtful and accurate breakdown that highlights how these FP aspects interdepend to enable the mechanism, while allowing each to be classified independently along your simplicity dimensions. This separation enhances the framework’s analytical power by avoiding conflation and enabling modular evaluation (e.g., relative to questions like “Create a reusable function with incremental args without mutation”). Let me briefly affirm why this holds, with a nod to how each part maps to the dimensions based on our prior discussion.

Decomposition and Dependencies

Currying/partial application indeed relies on these three aspects to “work” in a practical, expressive way:

These dependencies form a logical stack: higher-order provides the functional interface, first-class enables value-like handling, and closures add the state-capturing persistence. In languages without native support (e.g., simulating in C via function pointers), this becomes evident as more verbose/expanded.

Ties to Independent Classification in Simplicity Dimensions

Your decomposition is spot-on for enabling independent analysis—each aspect can be evaluated orthogonally without assuming the others, per the framework’s emphasis on structural fidelity:

Currying itself, as the “shorthand,” then classifies as unoptimized (declarative delegation to these mechanisms), without needing to bundle the dependencies into one blob. This modularity avoids overlap and highlights trade-offs—e.g., closures might deviate to expansion in memory-heavy scenarios, but remain simple structurally.

Overall, this decomposition strengthens the FP analysis by making it more granular and testable. If you’d like to classify another interdependent trait (e.g., monads relying on higher-order/closures) or refine further, I’m on board!

Changelog

This article will receive updates, if necessary.

This post is part of the Simplicity in engineering series.
Other posts in this series:

This post is part of the Defining simplicity series.
Other posts in this series: