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ea76aac | 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 56 57 58 59 | import Mathlib
import OAI.Computability.MinUncut.Estimates.ExpressionEffectivity
import OAI.Computability.MinUncut.Estimates.ReversePrefixProgram
namespace OAI
section
noncomputable section
namespace MinUncut.Preprocess.Syntax
open MinUncut.Costed MinUncut.CodeEffective Turing.ToPartrec
def prefCode (cs : List Code) : Code :=
cs.foldr (fun c b=>.cons (.comp c Blocks.extractor.code) b) (PolyProgram.drop 2).code
lemma p_prefCode : Primrec prefCode :=
Primrec.list_foldr Primrec.id (Primrec.const _)
(primrec_cons.comp
(primrec_comp.comp (Primrec.fst.comp Primrec.snd) (Primrec.const _))
(Primrec.snd.comp Primrec.snd)).to₂
def stepCode (cs : List Code) : Code :=
.cons PolyProgram.succ.code
(.cons (bin PolyProgram.add.code (PolyProgram.projection 1).code (constCode cs.length)) (prefCode cs))
lemma p_stepCode : Primrec stepCode :=
primrec_cons.comp (Primrec.const _)
(primrec_cons.comp
((p_bin _).comp (Primrec.const _) (p_constCode.comp Primrec.list_length)) p_prefCode)
lemma prefCode_eq (es : List AExpr) : prefCode (es.map (fun e=>e.program.code)) =
(Blocks.stepProgram.go es).code := by
induction es with
| nil => rfl
| cons e es ih => simp only [prefCode,List.map_cons,List.foldr_cons] at *; rw [ih]; rfl
lemma stepCode_eq (es : List AExpr) : stepCode (es.map (fun e=>e.program.code))=(Blocks.stepProgram es).code := by
simp only [stepCode,List.length_map,prefCode_eq]
rfl
lemma p_iterCode : Primrec iterCode := by
exact primrec_fix.comp (primrec_case.comp (Primrec.const _)
(primrec_cons.comp (Primrec.const _)
(primrec_cons.comp (Primrec.const _) (primrec_comp.comp Primrec.id (Primrec.const _)))))
def forwardCode (cs : List Code) (N : Code) : Code :=
.comp reversePrefixProgram.code (.comp PolyProgram.tail.code
(.comp (iterCode (stepCode cs.reverse))
(.cons N (.cons (constCode 0) (.cons (constCode 0) Code.id)))))
lemma p_forwardCode : Primrec₂ forwardCode := by
exact primrec_comp.comp (Primrec.const _)
(primrec_comp.comp (Primrec.const _)
(primrec_comp.comp (p_iterCode.comp (p_stepCode.comp (Primrec.list_reverse.comp Primrec.fst)))
(primrec_cons.comp Primrec.snd (Primrec.const _))))
lemma forwardCode_eq (es : List AExpr) (N : AExpr) :
forwardCode (es.map (fun e=>e.program.code)) N.program.code=(Blocks.forward es N).code := by
unfold forwardCode
rw [←List.map_reverse,stepCode_eq]
rfl
end MinUncut.Preprocess.Syntax
end
end
end OAI
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