xtype

xtype, or Extended Type, is a dynamic type system library for Lua.

Sometimes, advanced type checking code is needed to implement specific abstractions; xtype aims to fulfill that need.

Incentives:

• Simplification: Prevent writing redundant type checking code.
• Interoperability: Having a general low-level type system library can ease the interactions of third-party code.
• Metaprogramming / Genericity: Exploit the dynamic nature of Lua to generate definitions on-the-fly.

See src/, rockspecs/ or luarocks.

Concepts

Type

A xtype's type is either primitive or non-primitive.

A primitive type is a string. It can be any Lua types from type() or additional types like xtype or multifunction.

A non-primitive type is a table defining the type. It contains the xtype_name, xtype_stack and xtype_set fields and should identify as a xtype.

Value

Any Lua value has a type; we will call this the terminal type of the value as opposed to inherited types.

If the metatable of a table or userdata value has a xtype field, then the type is the value of that field.

If the value is a cdata, its type is defined by xtype.ctype() or the __xtype field (e.g. through the metatype __index) which will call xtype.ctype() when encountered.

Otherwise, the type is the Lua type returned by type().

Inheritance

A non-primitive type can inherit from other types, building a stack of types. This stack defines the order in which the types are evaluated, from the terminal type to the least specific inherited types.

Multifunction

A multifunction is a function that can have multiple definitions, each associated to a specific signature. When called, it resolves the call by selecting a matching definition from the call signature.

Metaprogramming

We can use Lua as its own metaprogramming language: we can generate Lua code from Lua.

A multifunction can have generators that are called when no definitions could be found, allowing to generate definitions for specific call signatures on-the-fly.

API

xtype

-- Create a type.
--
-- The created type is a table with 3 fields: xtype_name, xtype_stack and xtype_set.
-- The table can be modified as long as the xtype fields are left untouched.
-- A default metatable is set; it can be replaced at the condition that the
-- type would still be recognized as a "xtype".
--
-- name: human-readable string (doesn't have to be unique)
-- ...: base types, ordered by descending proximity, to the least specific type
-- return created type
xtype.create(name, ...)

-- Get/bind a type to a ctype (LuaJIT FFI).
--
-- This can't be changed afterwards.
-- The same type can be bound to different ctypes; it can be useful when
-- different ctype qualifiers should match the same type.
--
-- ctype: cdata ctype object
-- t: (optional) type
-- return bound type
xtype.ctype(ctype, t)

-- Check if a value is a valid type.
xtype.check(t)

-- Get the name of a type.
-- return string or nothing if not a type
xtype.name(t)

-- Get terminal type of a value.
xtype.get(v)

-- Check if a value is of type t.
xtype.is(v, t)

-- Check if a type is of type ot.
xtype.of(t, ot)

-- Create a multifunction.
xtype.multifunction()

-- Global multifunctions namespace for binary operators.
-- For interoperability between third-party types.
-- Equality (eq) has a default behavior defined as: eq(any, any) -> false
--
-- map of Lua binary op name => multifunction
-- (add, sub, mul, div, mod, pow, concat, eq, lt, le, idiv, band, bor, bxor, shl, shr)
xtype.op

-- Low-level API.

-- The type's xtype_stack field is a list of types ordered from the terminal
-- type to the least specific inherited types.

-- Stack distance to another type from a terminal type.
-- ot: support "any" keyword
-- return distance or nil/nothing if not of type ot
xtype.typeDist(t, ot)

-- Check and return signature (list of types).
-- ...: types
xtype.checkSign(...)

-- Distance to another signature from a call signature.
-- osign: support "any" keyword
-- return distance or nothing if not generalizable to osign
xtype.signDist(sign, osign)

-- Return formatted signature string.
xtype.formatSign(sign)

-- Code generation tools.

-- Generate "a1, a2, a3, a4..." list string.
-- tpl: string where "$" will be replaced by the index
-- i: start index
-- j: end index
-- separator: (optional) default: ", "
xtype.tpllist(tpl, i, j, separator)

-- Template substitution.
-- tpl: string with $... parameters
-- args: map of param => value
-- return processed template
xtype.tplsub(tpl, args)

Multifunction

-- Define a multifunction signature.
-- The keyword "any" matches any type. It is the least specific match for a
-- given terminal type.
--
-- f: definition function; nil to undefine
-- ...: signature, list of types
multifunction:define(f, ...)

-- Add a generator function.
--
-- All generators are called when no matching definition has been found to
-- eventually define new signatures.
--
-- f(multifunction, ...): called to generate new definitions
--- ...: call signature, list of (terminal) types
multifunction:addGenerator(f)

-- Get the resolved function for a specific signature.
-- ...: call signature, list of (terminal) types
-- return function or nil without a matching definition
multifunction:resolve(...)

-- Call the multifunction.
multifunction(...)
multifunction:call(...)

-- Low-level API.

multifunction.definitions = {} -- map of sign hash => {.f, .sign}

-- Hash function signature.
-- sign: signature, list of types
-- return number
multifunction:hashSign(sign)