Babbage designed the first programs for the analytical engine.
> Grace Hopper was the first person to design a compiler for a programming language.
Hopper was the first person to use the word "compiler" for a program, but it was not a compiler by the modern meaning; it was a linker, and not the first.
> Throughout the 19th and early 20th century, and up to World War II, programming was predominantly done by women;
Not by the modern meaning; they manually entered programs designed by men.
> After the 1960s, the computing work that had been dominated by women evolved into modern software, and the importance of women decreased.
The design of programs has always been done by men mostly.