nwave-ai/nw-fp-principles

FP Principles

Core functional programming thinking patterns. Language-agnostic.

Cross-references: fp-domain-modeling | fp-hexagonal-architecture | fp-algebra-driven-design

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1. Higher-Order Functions as Problem Decomposition

[STARTER]

Three operations replace most loops:

| Operation | Purpose | Replaces | |-----------|---------|----------| | Map | Transform each element, preserve structure | Loop building new collection | | Filter | Keep elements matching condition | Loop with conditional | | Fold | Accumulate elements into single result | Loop with running total |

When to use Map: Transform every element without changing collection shape. Nested maps handle nested structures. When to use Filter: Select elements without changing their values. When to use Fold: Reduce collection to single value. Accumulator IS your state. Combining function IS your state transition. Folds make state machines explicit.

Decision: "Am I transforming, selecting, or accumulating?" Pick matching operation. If none fit, compose two.

Why: These operations communicate intent. Map says "same shape, different values." Fold says "many inputs, one output." Loops say nothing about intent until you read every line.

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2. Type-Driven Design

[STARTER]

Write the type signature before implementation. The type tells you what the function can and cannot do.

Process:

1. Declare what the function consumes and produces
2. Ask: "which type-specific operations do I actually use?"
3. Replace concrete types with type variables for everything you don't inspect
4. Add constraints only for capabilities you use (equality, ordering, display)

Design progression: Concrete types -> type variables -> constrained type variables. Each step increases reuse while documenting minimal assumptions.

Why: Function's type signature is a contract. Narrower types mean fewer possible implementations, fewer bugs.

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3. Pattern Matching as Decision Decomposition

[STARTER]

Decompose decisions by data shape, not boolean conditions. Each clause handles one concrete case. Compiler verifies exhaustiveness.

When to use pattern matching: "What shape is this data?" When to use guards/conditions: "What property does this value have?" When to use named bindings: Intermediate results need a name to avoid repetition.

Heuristic: Prefer small extracted functions over giant match expressions. Pattern match on top-level shape, delegate to named functions for sub-decisions.

Exhaustiveness as safety net: When you add a new variant to a choice type, compiler flags every match that doesn't handle it.

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4. Composition Patterns

[INTERMEDIATE]

Partial Application

Fix some arguments of a general function to create specialized version. Eliminates throwaway helper functions.

When: General function exists and you need specialized version for specific context.

Function Composition (Pipelines)

Chain functions where output of one feeds into next. Each function has single responsibility.

Why: Composition reveals architecture of computation. Pipelines read as sequence of steps, making business process visible.

Point-Free Style

Omit explicit argument when function is just a composition. Use when it reveals intent. Avoid when it obscures meaning.

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5. Container Abstractions

[INTERMEDIATE] -> [ADVANCED]

Progressive hierarchy for working with values inside containers (nullables, lists, futures, results).

[INTERMEDIATE] Transformable Container (Functor)

What: Apply function to values inside container without changing structure. Plain English: "I have a value in a box. Transform the value without opening the box." When: You have nullable/optional/list/future and want to transform contents without inspecting the container. Guarantees: Transforming with identity does nothing. Can fuse or split transformations freely.

[INTERMEDIATE] Combinable Containers (Applicative)

What: Apply a function inside a container to values inside other containers. Plain English: "I have a function in a box AND values in boxes. Combine them." When: Validation -- check multiple fields independently, combine results only if all succeed. Doesn't short-circuit; collects all errors.

[INTERMEDIATE] Combinable Values (Monoid)

What: Combine two values of same type into one, with default element that changes nothing. Plain English: "I have many values. Smash them together into one." When: Folding/reducing collections. Combining operation must be associative, enabling parallelism. Examples: String concatenation with empty string | addition with zero | list append with empty list.

[ADVANCED] Chainable Operations (Monad)

What: Chain operations where each step produces wrapped value, next step depends on previous result. Plain English: "Step 1's output determines what step 2 does. Each step might fail/branch/have effects." When: Sequential dependent operations where each step can fail, branch, or produce effects.

Decision Tree: Which Abstraction Do I Need?

Do I need to transform values inside a container?
  YES, one function, one container --> Transformable (Functor)
  YES, combine multiple independent containers --> Combinable Containers (Applicative)
  YES, chain dependent operations sequentially --> Chainable Operations (Monad)
Do I need to combine values of the same type?
  YES --> Combinable Values (Monoid)

Progression Summary

Each level adds a new kind of combination:

• Transformable: one function, one container
• Combinable Containers: one function, multiple containers (independent)
• Chainable: sequential dependent operations, each producing container
• Combinable Values: same-type values collapsed into one

Runnable Example: Map, Filter, Fold on Domain Objects

orders = [Order(100, "pending"), Order(250, "shipped"), Order(50, "pending")]

pendingTotals = orders
  |> filter (o -> o.status == "pending")    -- [Order(100, "pending"), Order(50, "pending")]
  |> map (o -> o.amount)                    -- [100, 50]
  |> fold 0 (acc, x -> acc + x)            -- 150

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6. Specialized Chainable Patterns

[ADVANCED]

| Pattern | What It Manages | When to Use | |---------|----------------|-------------| | Optional (Maybe/Option) | Possible absence | Operations that can fail without explanation | | Result (Either) | Failure with context | Operations that fail with error details | | Environment (Reader) | Shared read-only config | Dependency injection, configuration threading | | Accumulator (Writer) | Side-channel output | Logging, auditing, collecting metadata | | Stateful (State) | Sequential state changes | Counters, parsers, accumulators |

These compose: real applications stack multiple patterns. See fp-hexagonal-architecture for DI patterns.

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7. Lazy Evaluation as Design Pattern

[INTERMEDIATE]

Separate WHAT to compute from WHEN it gets computed. Define potentially infinite sequences and let consumer determine how much to evaluate.

When: Generating candidates then selecting results | pagination and streaming | decoupling producers from consumers | build systems that only rebuild what changed.

Separation principle: Generate all possibilities, then filter. Declarative style says WHAT you want, not HOW to search.

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8. The FP Problem-Solving Method

[STARTER]

1. Start with type signature: What does this function consume and produce?
2. Identify traversal pattern: Map, filter, fold, or search?
3. Recognize accumulator: If folding, what is the state and how does each element change it?
4. Decompose by data shape: Pattern match on constructors, handle each case independently
5. Compose small functions: Build complex behavior from simple, tested pieces

Mindset shift: Describe WHAT to compute (transformations, compositions, constraints) rather than HOW (loops, mutations, control flow).

| Imperative Thinking | Functional Thinking | |---------------------|---------------------| | Loop through items | Map/filter/fold over collections | | Mutate variables | Transform immutable values | | Check conditions with if/else | Pattern match on data shapes | | Inherit from base class | Satisfy capability constraints | | Call methods on objects | Compose functions into pipelines | | Handle errors with try/catch | Use Optional/Result for explicit failure in types | | Pass dependencies explicitly | Use Environment pattern for implicit config |