| import Mathlib |
| import OAI.Computability.QuantumFactoring.BitStackWords |
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| namespace OAI |
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| section |
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| namespace ExactQuantumFactoring.BitStackProgram.Procedure |
| variable {β : Type} |
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|
| /-- A truth table on one Boolean has two literal finite output words. This |
| performs no run-time computation in its Boolean branch labels. -/ |
| noncomputable def ofBool (eb : β→List Bool) (f : Bool→β) : |
| Procedure boolCode eb f := by |
| let p:=constant (fun _ : Unit=>[]) eb (f false) |
| let q:=constant (fun _ : Unit=>[]) eb (f true) |
| exact ((chooseBit p q).precompose (fun b=>(b,()))).congrFun |
| (by intro b;cases b <;> rfl) |
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| noncomputable def ofBool₂ (eb : β→List Bool) (f : Bool→Bool→β) : |
| Procedure (prodCode boolCode boolCode) eb (fun x=>f x.1 x.2) := |
| (choose (ofBool eb (f false)) (ofBool eb (f true))).congrFun |
| (by rintro ⟨b,c⟩;cases b <;> rfl) |
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| noncomputable def ofBool₃ (eb : β→List Bool) (f : Bool→Bool→Bool→β) : |
| Procedure (prodCode boolCode (prodCode boolCode boolCode)) eb |
| (fun x=>f x.1 x.2.1 x.2.2) := |
| (choose (ofBool₂ eb (f false)) (ofBool₂ eb (f true))).congrFun |
| (by rintro ⟨b,c,d⟩;cases b <;> rfl) |
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| noncomputable def boolNot : Procedure boolCode boolCode not := ofBool boolCode not |
| noncomputable def boolAnd : Procedure (prodCode boolCode boolCode) boolCode |
| (fun x=>x.1 && x.2) := ofBool₂ boolCode and |
| noncomputable def boolOr : Procedure (prodCode boolCode boolCode) boolCode |
| (fun x=>x.1 || x.2) := ofBool₂ boolCode or |
| noncomputable def boolXor : Procedure (prodCode boolCode boolCode) boolCode |
| (fun x=>xor x.1 x.2) := ofBool₂ boolCode xor |
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| noncomputable def cons : Procedure (prodCode boolCode (id : List Bool→List Bool)) id |
| (fun x=>x.1::x.2) := by |
| let pp : Procedure (id : List Bool→List Bool) id (fun xs=>false::xs):= |
| (prepend id [false]).result (by intro xs;rfl) |
| let qq : Procedure (id : List Bool→List Bool) id (fun xs=>true::xs):= |
| (prepend id [true]).result (by intro xs;rfl) |
| exact (choose pp qq).congrFun (by rintro ⟨b,xs⟩;cases b <;> rfl) |
| end ExactQuantumFactoring.BitStackProgram.Procedure |
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| end |
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| end OAI |
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