Consider Gödel's equational calculus contained in all of them: it allows the substitution of variables by arbitrary numerals in one step, and arbitrarily complex terms can be replaced by their numerical value
The validity of the trace (both w.r.t. the applicability of the computation steps and the numerical correctness of the result) can be established o ine by a trusted checker. For tools used at design time, we argue that this approach has several advantages over proving the calculator correct...
foundational systems is that meta-mathematical arguments (for example, abbreviations that are external to the system or inductions over the syntactical form of an expression) are usually introduced early on, and without these simplifying meta-arguments, the vehicle stalls, never making it up the ste...