In constructive and intuitionistic frameworks (following Brouwer and Bishop), the existence of a computable f does not automatically yield an effective procedure without additional choice principles that are not constructively neutral.
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A approach to math and logic that only accepts something as true if you can actually build or demonstrate it step-by-step, rather than just proving it must exist in theory.
Constructively neutral(as a property of logical principles)
Something that doesn't contradict constructive thinking or require assumptions that constructivists reject as unproven.
Effective procedure(as the practical outcome being discussed)
A clear set of instructions that actually works in practice to solve a problem or accomplish a task.
Intuitionistic(as a logical framework)
A system of logic that rejects the idea that something must be either true or false if we can't actually verify which one it is; closely related to constructivism.
computable(As employed in the technical literature discussed in this passage)