Inconsistent behavior of thread on empty llists

Question

Consider the following:

Quit[]
Thread[g[{1, 2}, 3]]
(* {g[1, 3], g[2, 3]} *)

Thread[g[{}, 3]]
(* {} *)

This works similarly if instead $g$ takes only one parameter. Now look at the following:

Quit[]
f1[x_] := x+3;
f2[x_,y_] := x + y + {1,0};

Thread[f1[{1,2}]]
(* {4, 5} *)
Thread[f1[{}]]
(* {} *)

Thread[f2[{1,2},5]]
(* {7, 7} *)
Thread[f2[{},5]]
(* Thread::tdlen: Objects of unequal length in {}+5+{1,0} cannot be combined. *)
(* Thread::tdlen: Objects of unequal length in 5+{}+{1,0} cannot be combined. *)
(* 5 + {} + {1, 0} *)

All of these make sense except for the last one. If threading works on $f1$ with an empty list, why shouldn't it work on $f2$ with an empty list?

(BTW, there was no tag for threading.)

Answer 1

The message you see does not come from Thread but instead from the failed application of the Listable Attribute of Plus.

f2[{}, 5];

Thread::tdlen: Objects of unequal length in {}+5+{1,0} cannot be combined. >>

Listable does not work over empty lists in the way that Thread does, despite the message name being Thread::tdlen:

Attributes[foo] = Listable;

foo[{}, {1, 2, 3}]

Thread::tdlen: Objects of unequal length in foo[{},{1,2,3}] cannot be combined. >>

foo[{}, {1, 2, 3}]

If you want Thread to work in the example you give you'll need to control evaluation, e.g.

Thread[Unevaluated @ f2[{}, 5]]

{}