| import Mathlib |
| import OAI.Combinatorics.MatchingCount.Tapes.TreeErasure |
|
|
| namespace OAI |
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|
| namespace MatchingFPRAS.TreeTyped |
| variable {A B C D : Type} [Codec A] [Codec B] [Codec C] [Codec D] |
| lemma program_congr {f g : A→B} (F : Realizer f) (h : ∀ a,f a=g a) : (F.congr h).program=F.program := rfl |
| lemma program_recode {f : C→D} (F : Realizer f) (i : A→C) (g : A→B) (hi : ∀ a,encode (i a)=encode a) (ho : ∀ a,encode (f (i a))=encode (g a)) : (F.recode i g hi ho).program=F.program := rfl |
| lemma program_composition {f : A→B} {g : B→C} (F : Realizer f) (G : Realizer g) : |
| (composition F G).program=RegisterProc.seq F.program G.program := rfl |
| lemma program_pair {f : A→B} {g : A→C} (F : Realizer f) (G : Realizer g) : |
| (pair F G).program=TreeFunction.pair F.program G.program := rfl |
| lemma program_fold {f : A×B→B} (F : Realizer f) : |
| (fold F).program=RegisterControl.compile (Fold.code F.program) := rfl |
| lemma program_choose {f : A→Bool} {g h : A→B} (F : Realizer f) (G : Realizer g) (H : Realizer h) : |
| (choose F G H).program=RegisterProc.seq (TreeFunction.copy 0 1 (by decide)) |
| (RegisterProc.seq (TreeFunction.cons 1 2 (by decide)) (RegisterProc.seq F.program |
| (RegisterStructured.select 0 (RegisterProc.seq (TreeFunction.split 0 2 (by decide)) H.program) |
| (RegisterProc.seq (TreeFunction.split 0 2 (by decide)) G.program)))) := rfl |
| lemma program_constant (a : B) : (constant (A:=A) a).program=(constantData (A:=TreeData.Data) (encode a)).program := constantData_program _ |
| end MatchingFPRAS.TreeTyped |
|
|
| end OAI |
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