Implementação simples de inferência do tipo Hindley-Milner em C #:
Inferência do tipo Hindley-Milner sobre expressões S (Lisp-ish), em menos de 650 linhas de C #
Observe que a implementação está no intervalo de apenas 270 linhas de C # (para o algoritmo W adequado e para as poucas estruturas de dados que o suportam).
Trecho de uso:
// ...
var syntax =
new SExpressionSyntax().
Include
(
// Not-quite-Lisp-indeed; just tolen from our host, C#, as-is
SExpressionSyntax.Token("\\/\\/.*", SExpressionSyntax.Commenting),
SExpressionSyntax.Token("false", (token, match) => false),
SExpressionSyntax.Token("true", (token, match) => true),
SExpressionSyntax.Token("null", (token, match) => null),
// Integers (unsigned)
SExpressionSyntax.Token("[0-9]+", (token, match) => int.Parse(match)),
// String literals
SExpressionSyntax.Token("\\\"(\\\\\\n|\\\\t|\\\\n|\\\\r|\\\\\\\"|[^\\\"])*\\\"", (token, match) => match.Substring(1, match.Length - 2)),
// For identifiers...
SExpressionSyntax.Token("[\\$_A-Za-z][\\$_0-9A-Za-z\\-]*", SExpressionSyntax.NewSymbol),
// ... and such
SExpressionSyntax.Token("[\\!\\&\\|\\<\\=\\>\\+\\-\\*\\/\\%\\:]+", SExpressionSyntax.NewSymbol)
);
var system = TypeSystem.Default;
var env = new Dictionary<string, IType>();
// Classic
var @bool = system.NewType(typeof(bool).Name);
var @int = system.NewType(typeof(int).Name);
var @string = system.NewType(typeof(string).Name);
// Generic list of some `item' type : List<item>
var ItemType = system.NewGeneric();
var ListType = system.NewType("List", new[] { ItemType });
// Populate the top level typing environment (aka, the language's "builtins")
env[@bool.Id] = @bool;
env[@int.Id] = @int;
env[@string.Id] = @string;
env[ListType.Id] = env["nil"] = ListType;
//...
Action<object> analyze =
(ast) =>
{
var nodes = (Node[])visitSExpr(ast);
foreach (var node in nodes)
{
try
{
Console.WriteLine();
Console.WriteLine("{0} : {1}", node.Id, system.Infer(env, node));
}
catch (Exception ex)
{
Console.WriteLine(ex.Message);
}
}
Console.WriteLine();
Console.WriteLine("... Done.");
};
// Parse some S-expr (in string representation)
var source =
syntax.
Parse
(@"
(
let
(
// Type inference ""playground""
// Classic..
( id ( ( x ) => x ) ) // identity
( o ( ( f g ) => ( ( x ) => ( f ( g x ) ) ) ) ) // composition
( factorial ( ( n ) => ( if ( > n 0 ) ( * n ( factorial ( - n 1 ) ) ) 1 ) ) )
// More interesting..
( fmap (
( f l ) =>
( if ( empty l )
( : ( f ( head l ) ) ( fmap f ( tail l ) ) )
nil
)
) )
// your own...
)
( )
)
");
// Visit the parsed S-expr, turn it into a more friendly AST for H-M
// (see Node, et al, above) and infer some types from the latter
analyze(source);
// ...
... que produz:
id : Function<`u, `u>
o : Function<Function<`z, `aa>, Function<`y, `z>, Function<`y, `aa>>
factorial : Function<Int32, Int32>
fmap : Function<Function<`au, `ax>, List<`au>, List<`ax>>
... Done.
Veja também a implementação JavaScript de Brian McKenna no bitbucket, que também ajuda a começar (funcionou para mim).
«HTH,