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2f887db | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 | import Mathlib
import OAI.Computability.QuantumFactoring.BitStackWords
namespace OAI
section
namespace ExactQuantumFactoring.BitStackProgram.Procedure
variable {β : Type}
/-- 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)
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)
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)
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
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
end
end OAI
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