Add luarrow.monad module with Identity, Maybe, and Either monads

[Copilot]

Overview

This PR implements the luarrow.monad module, adding support for monadic programming with three core monads: Identity, Maybe, and Either. The module provides Haskell-inspired monadic operations with Lua's operator overloading for elegant composition.

What's New

Three Monad Implementations

1. Identity Monad

The simplest monad that wraps values in a computational context, enabling applicative-style function composition:

local identity = require('luarrow').identity

local f = function(x) return x + 1 end
local g = function(x) return x * 10 end
local h = function(x) return x - 2 end

-- Applicative-style composition and application
local result = identity(f) * identity(g) * identity(h) % 42
print(result)  -- 401

Note: pure is available as an alias for identity for backward compatibility.

2. Maybe Monad

Represents optional values with just(value) for values and nothing() for absence:

local just = require('luarrow').just
local nothing = require('luarrow').nothing

-- Safe division
local safe_divide = function(x)
  return function(y)
    if y == 0 then return nothing() else return just(x / y) end
  end
end

local result = just(10) % safe_divide(5)  -- just(2.0)
print(result:or_else(0))  -- 2.0

3. Either Monad

Represents computations that may fail with right(value) for success and left(error) for failures:

local right = require('luarrow').right
local left = require('luarrow').left

-- Parse and validate
local parse_int = function(str)
  local n = tonumber(str)
  if n and math.floor(n) == n then
    return right(n)
  else
    return left("Not an integer: " .. str)
  end
end

local result = parse_int("42")  -- right(42)
print(result:or_else(0))  -- 42

How It Works

Each monad provides:

• fmap (via * operator): Map functions over wrapped values
• bind (via % operator): Chain monadic computations
• or_else: Extract value with a default fallback
• Method style: Explicit method calls for all operations

Implementation Details

New Files

• src/luarrow/monad/identity.lua: Identity monad implementation
• src/luarrow/monad/maybe.lua: Maybe monad implementation
• src/luarrow/monad/either.lua: Either monad implementation
• src/luarrow/monad.lua: Main module exporting all three monads
• spec/luarrow/monad/identity_spec.lua: Identity monad tests
• spec/luarrow/monad/maybe_spec.lua: Maybe monad tests (9 tests)
• spec/luarrow/monad/either_spec.lua: Either monad tests (11 tests)

Updated Files

• src/luarrow.lua: Exports all monad functions (identity/pure, just, nothing, right, left)
• doc/api.md: Complete API documentation for all three monads with examples
• README.md: Added monad overview and examples
• doc/examples.md: Added practical monad usage examples
• spec/luarrow/monad_spec.lua: Original tests maintained for backward compatibility
• Minor style fixes in src/luarrow/fun.lua, src/luarrow/arrow.lua, and scripts/benchmark.lua

Design Philosophy

The implementation follows Haskell's monad conventions while maintaining luarrow's patterns:

• Uses operator overloading (* for fmap, % for bind)
• Provides both operator-style and method-style APIs
• Includes LuaCATS type annotations for better IDE support
• Maintains zero external dependencies
• Minimal overhead with lightweight wrappers
• Backward compatible: pure still works as an alias for identity

Testing

All tests pass (20+ tests total):

• Identity monad: 5 tests
• Maybe monad: 9 tests
• Either monad: 11 tests
• Backward compatibility tests
• All existing tests continue to pass

The test suite covers:

• Basic monadic operations
• Function mapping and chaining
• Error handling and edge cases
• Method-style and operator-style APIs
• Backward compatibility with original pure implementation

Documentation

Complete documentation has been added following the existing style:

• API reference in doc/api.md with detailed monad explanations and type signatures
• Real-world examples in doc/examples.md showing practical use cases
• Quick start guide in README.md
• Examples for safe division, parsing, and error handling

Closes

Closes #7

Original prompt

---

This section details on the original issue you should resolve

<issue_title>Future: Add utils for Applicative style function application</issue_title>
<issue_description>Implement in the future.

Like

pure(f) * pure(g) % m
```</issue_description>

<agent_instructions>'luarrow.monad'モジュールを作って、件名のことをそのモジュールで達成してください。他のコミットと既存のドキュメントを参考にしてドキュメントも作成してね！</agent_instructions>

## Comments on the Issue (you are @copilot in this section)

<comments>
<comment_new><author>@aiya000</author><body>
Currently, it can implement by Fun class and writing some utils.</body></comment_new>
</comments>

Fixes #5

---

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[aiya000]

@copilot

実装してくれたのは多分Identityモナドだね？
そしたらMaybeモナドとEitherモナドも実装してもらっていい？

今の実装は
luarrow.monad.identity
に移動。
Maybeは
luarrow.monad.maybe
に。
Eitherは
luarrow.monad.either
に。

[Copilot]

@copilot

実装してくれたのは多分Identityモナドだね？
...

Done! I've refactored the monad implementation:

• Identity monad (what you implemented originally) is now at luarrow.monad.identity
• Maybe monad is now at luarrow.monad.maybe with just(value) and nothing()
• Either monad is now at luarrow.monad.either with right(value) and left(error)

All three are exported from the main luarrow.monad module and the root luarrow module. Backward compatibility is maintained - pure still works as an alias for identity.

Each monad includes appropriate methods (fmap, bind, or_else, etc.) and comprehensive tests. Documentation has been updated in all relevant files.

Commit: Refactor monad module into Identity, Maybe, and Either monads

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[aiya000]

メモ:
必要性を感じなくなっているためペンディング。
モナドとしてではなく、それぞれのユーティリティ関数（ちょうど今list向けにはあるように）を作る方向にした方がいい気がする。
特にMaybeはnil向けにできる。
EitherもLuaCATSのよくある和型にすればできる。
Identityは⋯この文脈だと不要になりそう。