| import OAI.Computability.RationalHitting.OutputComputation |
|
|
| namespace OAI |
|
|
| namespace RationalHitting.ExecutableGenerator |
| open StackLanguage |
|
|
| /-- One fixed finite stack program computes the exact canonical list on literal |
| unary inputs, with a fixed polynomial bound on all actual stack steps. -/ |
| theorem stack_implementation : StackImplementation := by |
| obtain ⟨p⟩ := Runtime.raw_feasible |
| let f : p.Registers → Fin (Fintype.card p.Registers+1) := |
| fun a => (Fintype.equivFin p.Registers a).castSucc |
| have hf : Function.Injective f := by |
| intro a b h |
| apply (Fintype.equivFin p.Registers).injective |
| exact Fin.castSucc_inj.mp h |
| obtain ⟨C,k,hC,hk,hbound⟩ := (p.bound.comp (TimeBound.variable+1)).growth |
| refine ⟨Fintype.card p.Registers,p.program.rename f,f p.input,f p.output,C,k,hC,hk,?_⟩ |
| intro n s hn hs |
| obtain ⟨t,ht,he⟩ := p.correct (n,s) |
| refine ⟨t,?_,?_⟩ |
| · have hb := hbound (n+s+1) (by omega) |
| simp only [TimeBound.eval_comp,TimeBound.eval_add,TimeBound.eval_variable, |
| TimeBound.eval_numeral] at hb |
| have hlen : (unaryWord n s).length+1=n+s+1+1 := by simp [unaryWord];omega |
| have ht' : t≤p.bound.eval ((unaryWord n s).length+1) := ht |
| rw [hlen] at ht' |
| exact ht'.trans hb |
| · have hh := he.rename_single f hf |
| simpa only [single,Function.comp_apply,id_eq] using hh |
|
|
| /-- The finite-state compilation of the uniform stack implementation. -/ |
|
|
| theorem implementation : Implementation := implementation_of_stack stack_implementation |
|
|
| end RationalHitting.ExecutableGenerator |
|
|
| namespace RationalHitting |
|
|
| /-- A rational hitting list preserving every inverse domain, with invertible |
| values, canonical rational binary output, and polynomial deterministic |
| finite-state Turing time. -/ |
| theorem main : MainStatement := |
| ExecutableGenerator.main_of_implementation ExecutableGenerator.implementation |
|
|
| end RationalHitting |
|
|
| end OAI |
|
|
