in computability theory, it states that all non-trivial semantic properties of programs are undecidable:
a semantic property is one about the program’s behavior (e.g. does the program terminate for all inputs)
a syntactic property (e.g. does the program contain an if-then-else statement)
a property is non-trivial if it is neither:
true for every partial computable function
false for every partial computable function
can be put into terms of functions: for any non-trivial property of partial functions, no general and effective method can decide whether an algorithm computes a partial function with that property. Hence, a property of partial functions is called trivial if it holds for all partial computable functions or for none, and an effective decision method is called general if it decides correctly for every algorithm