Theorems · Definition · logic and foundations
Computable
{α : Type u_1} → {σ : Type u_2} → [Primcodable α] → [Primcodable σ] → (α → σ) → PropComputable functions α → σ between Primcodable types:
a function is computable if and only if it is partially recursive (as a partial function)
- Defined in
- Mathlib.Computability.Partrec
- Cited by
- 80 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- PrimcodablePrimcodable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Primcodablestatement and proof · cited by 325
- Partrecproof · cited by 48
- PFun.liftproof · cited by 36
Cited by85
Results whose statement or proof uses this declaration.
- Primrec.to_compstatement · cited by 40
- Computable₂proof · cited by 32
- Computable.compstatement and proof · cited by 31
- Computable.sndstatement · cited by 21
- ManyOneReducibleproof · cited by 17
- ComputablePredproof · cited by 17
- Computable.to₂statement and proof · cited by 17
- Computable.conststatement · cited by 16
- OneOneReducibleproof · cited by 15
- Computable.fststatement · cited by 15
- Partrec.compstatement and proof · cited by 12
- Computable₂.compstatement and proof · cited by 9