Author here. The `<<` operator is being abused to mean "bind", so the right side is a normal expression (constructing a Foo and Bar) and the left side matches it to a particular "shape".

The purposes of pattern matching is to replace code that looks like this:

    if  (isinstance(tree, BinOp)
            and type(tree.left) is Name
            and type(tree.op) is Mod
            and tree.left.id in module.expr_registry):
        ...

with code that looks like this

    if BinOp(Name(id), Mod(), body) << tree 
            and id in module.expr_registry:
        ...

Which looks much nicer, and more clearly says what you want: that `tree` "looks like" a particular shape.

EDIT: Here's another example. Turning this:

    if  ((isinstance(tree, ClassDef) or isinstance(tree, FunctionDef))
            and len(tree.decorator_list) == 1
            and tree.decorator_list[0]
            and type(tree.decorator_list[0]) is Name
            and tree.decorator_list[0].id in module.decorator_registry):
        ...

into:

    if  ((isinstance(tree, ClassDef) or isinstance(tree, FunctionDef))
            and [Name(id)] << tree.decorator_list 
            and id in module.decorator_registry):
        ...

Doesn't quite work yet, but we're getting there