Idris中能否基于Hex简易定义开发库，编译后转高效同构表示？

1. Can we define functions for a type and compile it to an isomorphic representation? #

Absolutely! This is a core pattern in dependently typed languages like Idris, where we can balance ergonomic, easy-to-reason-about code for developers with efficient runtime representations. Here's how it works:

The key is to work with a developer-friendly algebraic data type (ADT) in your public API, then use Idris's type system and compiler optimizations to map it to a more efficient isomorphic type under the hood. Common approaches include:

• Isomorphism Proofs: Define both types, then write conversion functions (to/from) paired with proofs that they're inverses (e.g., to . from = id). Idris can often optimize these conversions away if marked %inline, since it recognizes the isomorphism is trivial.
• Abstract Data Types (ADTs): Hide the efficient implementation behind a module boundary. Export only the friendly type and its interface functions, while internally using the optimized representation. Users never see the efficient type, but benefit from its performance.
• Erased Dependent Types: For types with compile-time guarantees (like your refined string), the proof terms are erased at runtime, leaving only the efficient primitive (e.g., a JS string) while maintaining type safety during development.

2. Can we use the List HexDigit interface but compile to the refined String type for JS efficiency? #

Yes, this is a perfect use case for the pattern above. Here's a step-by-step implementation plan:

Step 1: Expose the Friendly Public Interface #

First, define the simple HexDigit and Hex types in a public module, along with all the functions your users will need (parsing, serialization, manipulation):

module Hex.Public

data HexDigit = H0 | H1 | H2 | H3 | H4 | H5 | H6 | H7 | H8 | H9 | HA | HB | HC | HD | HE | HF

Hex : Type
Hex = List HexDigit

-- Example: Convert Hex to a human-readable string
hexToString : Hex -> String
hexToString [] = "0x"
hexToString digits = "0x" ++ concatMap digitToChar digits
  where
    digitToChar : HexDigit -> Char
    digitToChar H0 = '0'
    digitToChar H1 = '1'
    -- ... implement for all digits (H2 to HF)
    digitToChar HF = 'f'

-- Example: Parse a string to Hex (with error handling)
parseHex : String -> Maybe Hex
parseHex s = case unpack s of
  '0'::'x'::rest => traverse charToDigit rest
  _ => Nothing
  where
    charToDigit : Char -> Maybe HexDigit
    charToDigit '0' = Just H0
    charToDigit '1' = Just H1
    -- ... handle both lowercase and uppercase hex chars
    charToDigit 'F' = Just HF
    charToDigit _ = Nothing

Step 2: Define the Efficient Internal Representation #

In a private module, define the refined string type (with compile-time validity proofs) and establish the isomorphism with the friendly Hex type:

module Hex.Internal

import Hex.Public

-- Proof that a character is a valid hex nibble
data IsNib : Char -> Type where
  IsNib0 : IsNib '0'
  IsNib1 : IsNib '1'
  -- ... up to IsNibF : IsNib 'f'

-- Proof that a string is a valid hex string (starts with "0x", followed by nibbles)
data IsHex : String -> Type where
  IsHexNil : IsHex "0x"
  IsHexCons : IsHex s -> IsNib c -> IsHex (s ++ singleton c)

-- Efficient runtime type: string + compile-time validity proof
EfficientHex : Type
EfficientHex = (s : String ** IsHex s)

-- Convert friendly Hex to EfficientHex (with proof of validity)
toEfficient : Hex -> EfficientHex
toEfficient hex = 
  let str = Public.hexToString hex
      proof = isHexValid hex
  in (str ** proof)
  where
    isHexValid : Hex -> IsHex (Public.hexToString hex)
    isHexValid [] = IsHexNil
    isHexValid (d::ds) = IsHexCons (isHexValid ds) (nibProof d)
    nibProof : HexDigit -> IsNib (Public.digitToChar d)
    nibProof H0 = IsNib0
    nibProof H1 = IsNib1
    -- ... map each HexDigit to its corresponding IsNib proof

-- Convert EfficientHex back to friendly Hex (safe, since proof guarantees validity)
fromEfficient : EfficientHex -> Hex
fromEfficient (str ** _) = 
  -- Since str is guaranteed valid, parseHex will always return Just Hex
  case Public.parseHex str of
    Just hex => hex
    Nothing => impossible -- Compiler knows this case can't happen

Step 3: Optimize for JS Compilation #

• Erased Proofs: Idris automatically erases dependent types like IsHex and IsNib at runtime. So EfficientHex compiles directly to a plain JS string—no extra overhead!
• Inline Conversions: Mark toEfficient and fromEfficient as %inline to let the compiler eliminate any conversion overhead. The optimizer will strip out the intermediate List HexDigit entirely in the JS output.
• Foreign Interop: Use %foreign to pass the efficient string directly to JS functions, avoiding any unnecessary conversions.

Final Result #

Users interact with the simple List HexDigit type, writing clean, easy-to-debug code. Meanwhile, the JS compiler outputs optimized native strings, with all type safety guarantees enforced at compile time.

内容的提问来源于stack exchange，提问作者MaiaVictor