Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Computable program transformers
Definition
Fix a numbering of the partial computable functions.
A computable program transformer is a total computable function
It acts on indices rather than directly on extensional partial functions: the transformed program with input index is the index .
Remarks
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A transformer may change syntax without changing the computed partial function.
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The recursion theorem concerns fixed points of such transformers at the level of computed behavior.
Depends on
Used by
Dependency tree · two levels
2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Robert I. Soare, Turing Computability: Theory and Applications (standard reference, not scraped)
- Lawrence S. Moss, Invitation to Computability and Recursion, The Recursion Theorem (standard reference, not scraped)