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Structured program theorem w/o selection

I don't think there is anything wrong with your reasoning. I don't think selections (if statements) are necessary, as you prove. So why is the theorem stated that way? Here comes some speculation on ...
D.W.'s user avatar
  • 161k
1 vote

Are there minimum criteria for a programming language being Turing complete?

This should at least be part of the answer to the question. And the answer is no. Intuitively, a specification of programming language can be arbitrarily complex such that it may encode any decidable ...
Clément Dato's user avatar
0 votes

Constraints on the order of program semantics given by an enumeration of turing-complete system programs

A Tuing-complete programming language has the property that there is a surjection $c : \mathbb{N} \to \mathsf{Prog}$ (the set of all valid programs in whatever model of computation you have). We call $...
Andrej Bauer's user avatar
  • 30.8k
0 votes

What are quines (layman friendly)?

A fixed point is a solution $x$ to a fixed-point equation $x = f(x)$. The Kleene Recursion Theorem states that there is a Universal Recursive Function $f(P(φ),y)$ that includes every other recursive ...
NinjaDarth's user avatar
0 votes

Looping and branching with Algorithmic Differentiation

As explained in the other responses, AD alone cannot capture the effects of input-dependent control flow. Regarding your second and third questions, there are some recent tools that extend AD to still ...
justinnk's user avatar

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