Theorems · Theorem · logic and foundations
Nat.Partrec.Code.exists_code
∀ {f : ℕ →. ℕ}, Nat.Partrec f ↔ ∃ c, c.eval = fA function is partial recursive if and only if there is a code implementing it. Therefore,
eval is a universal partial recursive function.
- Defined in
- Mathlib.Computability.PartrecCode
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- PFunstatement and proof · cited by 207
- Part.someproof · cited by 111
- Part.bindproof · cited by 70
- Nat.Partrec.Codestatement and proof · cited by 66
- Part.mapproof · cited by 65
- Nat.pairproof · cited by 62
- Part.bind_someproof · cited by 49
- Nat.unpair_pairproof · cited by 30
- Part.map_someproof · cited by 27
- Nat.Partrec.Code.evalstatement and proof · cited by 25
- Nat.unpairedproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- Partrec.condproof · cited by 3
- Nat.Partrec'.of_partproof · cited by 2
- Nat.Partrec.merge'proof · cited by 1
- Nat.Partrec.Code.fixed_pointproof · cited by 1
- Nat.Partrec.Code.fixed_point₂proof · cited by 1