Hypothesis: if you can write a compiler in a given programming language, then that language must be Turing-complete.
Only if it compiles from C to C by passing on the pointer to the source code. As soon as you implement even just repeated search/replace you got the lambda calculus.
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I think you misunderstood my example. The language used to implement the compiler has only one instruction called "compile" which takes one argument, the string representing the program to be compiled. This language lets you compile a program but nothing else.
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