Is an empty initializer list valid C code?

No, an empty initializer list is not allowed. This can also be shown by GCC when compiling with -std=c99 -pedantic:

a.c:4: warning: ISO C forbids empty initializer braces

The reason is the way the grammar is defined in §6.7.9 of the 2011 ISO C Standard:

initializer:
         assignment-expression
         { initializer-list }
         { initializer-list , }
initializer-list:
         designation(opt) initializer
         initializer-list , designation(opt) initializer

According to that definition, an initializer-list must contain at least one initializer.

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