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760f90e | 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 | 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
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