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It sounds like he's stating that a UTM can't simulate an arbitrary lambda function then The concept doesn't make sense. Lambda functions don't do anything, the
by davidmathers 18y ago
It sounds like he's stating that a UTM can't simulate an arbitrary lambda function then
The concept doesn't make sense. Lambda functions don't do anything, they're just notations. The process of beta reduction is what causes things/computation to happen. Beta reduction rewrites all the lambda functions, hence they're no longer the same functions. What you're saying is something like: a computer can't compute "computation".
- frisco 18y agoExample: a function accepts as input the source of another program (assume it's computable and halts). Thus, the original function is variable; can it be simulated by a UTM for any arbitrary valid input? I'm probably using the wrong terminology here, but the overall logic is what I'm getting at.
- davidmathers 18y agoThe input to a function can't change (it's a fixed set). If the input changes then you've defined a new function. That's the mathematical definition of a function. You're talking about a set/class of functions, so you would need 1 UTM per function.