File size: 16,393 Bytes
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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 | import OAI.Computability.Scheduling.CostBounds
namespace OAI
universe u1 u2
section
namespace ThreeMachine.StackCompiler
def Poly {I : Type u1} (size f : I → ℕ) (d : ℕ) : Prop :=
Majorized f (fun i => (size i+2)^d)
namespace Poly
variable {I : Type u2} {s f g : I → ℕ} {d e : ℕ}
theorem lift (h : Poly s f d) (hde : d ≤ e) : Poly s f e :=
h.trans (Majorized.pow_mono (fun _ => by omega) hde)
theorem of_le (h : ∀ i, f i ≤ g i) (hg : Poly s g d) : Poly s f d :=
(Majorized.of_le h).trans hg
theorem const (s : I → ℕ) (C : ℕ) : Poly s (fun _ => C) 0 :=
Majorized.const C (fun _ => by simp)
theorem base (s : I → ℕ) : Poly s (fun i => s i+2) 1 := by
simpa only [Poly,Nat.pow_one] using Majorized.refl (fun i => s i+2)
theorem size (s : I → ℕ) : Poly s s 1 :=
of_le (fun _ => by omega) (base s)
theorem add (hf : Poly s f d) (hg : Poly s g e) : Poly s (fun i => f i+g i) (max d e) :=
Majorized.add (hf.lift (le_max_left _ _)) (hg.lift (le_max_right _ _))
theorem mul (hf : Poly s f d) (hg : Poly s g e) : Poly s (fun i => f i*g i) (d+e) := by
simpa only [Poly,Nat.pow_add] using Majorized.mul hf hg
theorem pow (hf : Poly s f d) (k : ℕ) : Poly s (fun i => (f i)^k) (d*k) := by
simpa only [Poly,Nat.pow_mul] using Majorized.pow hf k
theorem sub (hf : Poly s f d) (g : I → ℕ) : Poly s (fun i => f i-g i) d :=
of_le (fun _ => Nat.sub_le _ _) hf
theorem max (hf : Poly s f d) (hg : Poly s g e) : Poly s (fun i => max (f i) (g i)) (max d e) :=
of_le (fun _ => by omega) (add hf hg)
end Poly
end ThreeMachine.StackCompiler
open Lean in
def polyRuleNames : Array Name := #[
`OAI.ThreeMachine.StackCompiler.Uniform.time_comp,
`OAI.ThreeMachine.StackCompiler.Uniform.time_pair,
`OAI.ThreeMachine.StackCompiler.Uniform.time_congr,
`OAI.ThreeMachine.StackCompiler.Uniform.time_id,
`OAI.ThreeMachine.StackCompiler.Uniform.time_fst,
`OAI.ThreeMachine.StackCompiler.Uniform.time_snd,
`OAI.ThreeMachine.StackCompiler.Uniform.time_nil,
`OAI.ThreeMachine.StackCompiler.Uniform.time_unit,
`OAI.ThreeMachine.StackCompiler.Uniform.time_zero,
`OAI.ThreeMachine.StackCompiler.Uniform.time_false,
`OAI.ThreeMachine.StackCompiler.Uniform.time_reinterpret,
`OAI.ThreeMachine.StackCompiler.Uniform.time_cons,
`OAI.ThreeMachine.StackCompiler.Uniform.time_choose,
`OAI.ThreeMachine.StackCompiler.Uniform.time_constant,
`OAI.ThreeMachine.StackCompiler.Uniform.time_uniform,
`OAI.ThreeMachine.StackCompiler.Uniform.time_tail,
`OAI.ThreeMachine.StackCompiler.Uniform.time_none,
`OAI.ThreeMachine.StackCompiler.Uniform.time_some_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_ite_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_head?_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_length_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_drop_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_getElem?_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_functionGet_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_functionGetAny_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_functionGetOptionAny_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_reindex,
`OAI.ThreeMachine.StackCompiler.Uniform.time_test_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_reverse,
`OAI.ThreeMachine.StackCompiler.Realizer.time_comp,
`OAI.ThreeMachine.StackCompiler.Realizer.time_pair,
`OAI.ThreeMachine.StackCompiler.Realizer.time_congr,
`OAI.ThreeMachine.StackCompiler.Realizer.time_id,
`OAI.ThreeMachine.StackCompiler.Realizer.time_fst,
`OAI.ThreeMachine.StackCompiler.Realizer.time_snd,
`OAI.ThreeMachine.StackCompiler.Realizer.time_reinterpret,
`OAI.ThreeMachine.StackCompiler.Realizer.time_choose,
`OAI.ThreeMachine.StackCompiler.Realizer.time_not_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_and_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_or_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_succ_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_test_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_add_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_sub_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_le_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_eqNat_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_setFilter,
`OAI.ThreeMachine.StackCompiler.Uniform.time_setEmpty,
`OAI.ThreeMachine.StackCompiler.Uniform.time_vectorMap,
`OAI.ThreeMachine.StackCompiler.Uniform.time_vectorMapAny,
`OAI.ThreeMachine.StackCompiler.Uniform.time_andD_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_noEdges,
`OAI.ThreeMachine.StackCompiler.Uniform.time_stateEq,
`OAI.ThreeMachine.StackCompiler.Uniform.time_stateCompatible,
`OAI.ThreeMachine.StackCompiler.Uniform.time_append_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_getD_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_zero,
`OAI.ThreeMachine.StackCompiler.Realizer.time_nil,
`OAI.ThreeMachine.StackCompiler.Realizer.time_cons,
`OAI.ThreeMachine.StackCompiler.Realizer.time_reverse_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_range_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_orD_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_states,
`OAI.ThreeMachine.StackCompiler.Uniform.time_blockAppend,
`OAI.ThreeMachine.StackCompiler.Uniform.time_blockAppendNamed,
`OAI.ThreeMachine.StackCompiler.Uniform.time_stateAdvance,
`OAI.ThreeMachine.StackCompiler.Uniform.time_lookup_setEq_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_lookup_stateEq_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_tryAdvance,
`OAI.ThreeMachine.StackCompiler.Uniform.time_solve,
`OAI.ThreeMachine.StackCompiler.Uniform.time_initialMarks,
`OAI.ThreeMachine.StackCompiler.Uniform.time_markings,
`OAI.ThreeMachine.StackCompiler.Uniform.time_layerStep,
`OAI.ThreeMachine.StackCompiler.Uniform.time_getElemD_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_matrixRows,
`OAI.ThreeMachine.StackCompiler.Uniform.time_paddedMatrix,
`OAI.ThreeMachine.StackCompiler.Realizer.time_triple_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_cardinalMap,
`OAI.ThreeMachine.StackCompiler.Uniform.time_cardinalValue,
`OAI.ThreeMachine.StackCompiler.Uniform.time_makeUniverse,
`OAI.ThreeMachine.StackCompiler.Uniform.time_restrictTime,
`OAI.ThreeMachine.StackCompiler.Uniform.time_scheduleMatrix,
`OAI.ThreeMachine.StackCompiler.Uniform.time_predecessorCount,
`OAI.ThreeMachine.StackCompiler.Uniform.time_predecessors,
`OAI.ThreeMachine.StackCompiler.Uniform.time_rankFromCounts,
`OAI.ThreeMachine.StackCompiler.Uniform.time_natLT_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_finVal,
`OAI.ThreeMachine.StackCompiler.Uniform.time_thresholdSets,
`OAI.ThreeMachine.StackCompiler.Uniform.time_triples,
`OAI.ThreeMachine.StackCompiler.Uniform.time_cones_cons,
`OAI.ThreeMachine.StackCompiler.Uniform.time_finEmpty,
`OAI.ThreeMachine.StackCompiler.Uniform.time_finCons,
`OAI.ThreeMachine.StackCompiler.Uniform.time_assignments_succ,
`OAI.ThreeMachine.StackCompiler.Uniform.time_atomSets,
`OAI.ThreeMachine.StackCompiler.Uniform.time_family,
`OAI.ThreeMachine.StackCompiler.Uniform.time_fullSolveK,
`OAI.ThreeMachine.StackCompiler.Uniform.time_scheduleMatrixFixed,
`OAI.ThreeMachine.StackCompiler.Uniform.time_bestMatrixStep,
`OAI.ThreeMachine.StackCompiler.Uniform.time_functionListOption_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_sndFunctionListOption_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_binaryValueStep_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_binaryLeadingStep_le,
`OAI.ThreeMachine.StackCompiler.Uniform.time_binaryTakeStep_le,
`OAI.ThreeMachine.StackCompiler.Realizer.time_pred,
`OAI.ThreeMachine.StackCompiler.Uniform.time_binaryParse
]
open Lean Meta Elab Tactic in
private def polyCostHead (e : Expr) : Option Name :=
let as := e.getAppArgs
if e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Uniform.time && as.size ≥ 3 then
as[as.size-3]!.getAppFn.constName?
else if e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Realizer.time && as.size ≥ 2 then
as[as.size-2]!.getAppFn.constName?
else none
open Lean Meta Elab Tactic in
private def polyExprName (e : Expr) (n : Name) : Bool := e.getAppFn.isConstOf n
open Lean Meta Elab Tactic in
private def synthPoly (fuel : ℕ) (sz x e : Expr) : TacticM (Expr × Expr) := do
match fuel with
| 0 => throwError "poly_bound: expression depth exhausted"
| fuel+1 =>
let e := e.headBeta
let fn ← mkLambdaFVars #[x] e
for decl in (← getLCtx) do
unless decl.isImplementationDetail do
let tp ← instantiateMVars decl.type
if polyExprName tp ``ThreeMachine.StackCompiler.Poly then
let as := tp.getAppArgs
if as.size == 4 then
if ← isDefEq as[1]! sz then
if ← isDefEq as[2]! fn then
return (as[3]!,decl.toExpr)
if !(e.containsFVar x.fvarId!) then
return (mkNatLit 0, ← mkAppM ``ThreeMachine.StackCompiler.Poly.const #[sz,e])
let se := mkApp sz x
if ← isDefEq e se then
return (mkNatLit 1, ← mkAppM ``ThreeMachine.StackCompiler.Poly.size #[sz])
let be ← mkAppM ``Nat.add #[se,mkNatLit 2]
if ← isDefEq e be then
return (mkNatLit 1, ← mkAppM ``ThreeMachine.StackCompiler.Poly.base #[sz])
let es := e.getAppArgs
let isadd := polyExprName e ``Nat.add || polyExprName e ``HAdd.hAdd
let ismul := polyExprName e ``Nat.mul || polyExprName e ``HMul.hMul
let issub := polyExprName e ``Nat.sub || polyExprName e ``HSub.hSub
let ismax := polyExprName e ``Nat.max || polyExprName e ``Max.max
if es.size ≥ 2 && (isadd || ismul || issub || ismax) then
let a := es[es.size-2]!
let b := es[es.size-1]!
let (d,h) ← synthPoly fuel sz x a
if issub then
let g ← mkLambdaFVars #[x] b
return (d, ← mkAppM ``ThreeMachine.StackCompiler.Poly.sub #[h,g])
let (_,h') ← synthPoly fuel sz x b
let nm := if isadd then ``ThreeMachine.StackCompiler.Poly.add
else if ismul then ``ThreeMachine.StackCompiler.Poly.mul
else ``ThreeMachine.StackCompiler.Poly.max
let proof ← mkAppM nm #[h,h']
let tp ← inferType proof
return (tp.getAppArgs[3]!,proof)
if es.size ≥ 2 && (polyExprName e ``Nat.pow || polyExprName e ``HPow.hPow) &&
!(es[es.size-1]!.containsFVar x.fvarId!) then
let (_,h) ← synthPoly fuel sz x es[es.size-2]!
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.pow #[h,es[es.size-1]!]
let tp ← inferType proof
return (tp.getAppArgs[3]!,proof)
if es.size == 1 && polyExprName e ``Nat.succ then
let (_,h) ← synthPoly fuel sz x es[0]!
let hc ← mkAppM ``ThreeMachine.StackCompiler.Poly.const #[sz,mkNatLit 1]
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.add #[h,hc]
let tp ← inferType proof
return (tp.getAppArgs[3]!,proof)
if polyExprName e ``ThreeMachine.StackCompiler.volume then
let val := es[es.size-1]!
let vf ← mkLambdaFVars #[x] val
let tp ← inferType val
let ts := tp.getAppArgs
let finish (pr : Expr) : TacticM (Expr × Expr) := do
let tp ← inferType pr
return (tp.getAppArgs[3]!,pr)
if polyExprName tp ``Nat then
let (_,h) ← synthPoly fuel sz x val
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeNat #[h])
if polyExprName tp ``Bool then
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeBool #[sz,vf])
if polyExprName tp ``Unit then
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeUnit #[sz,vf])
if polyExprName tp ``Prod then
let a ← mkAppM ``Prod.fst #[val]
let b ← mkAppM ``Prod.snd #[val]
let (_,h) ← synthPoly fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[a])
let (_,h') ← synthPoly fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[b])
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeProd #[vf,h,h'])
let mut dim? : Option Expr := none
let mut nm := Name.anonymous
if polyExprName tp ``Fin then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeFin
if polyExprName tp ``Finset && polyExprName ts[0]! ``Fin then
dim? := some ts[0]!.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeFinset
if polyExprName tp ``ThreeMachine.StackCompiler.Universe then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeUniverse
if polyExprName tp ``ThreeMachine.StackCompiler.Cardinal then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeCardinal
if polyExprName tp ``ThreeMachine.StackCompiler.Matrix then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeMatrix
if polyExprName tp ``ThreeMachine.Algorithm.State && polyExprName ts[0]! ``Fin then
dim? := some ts[0]!.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeState
if let .forallE _ dom body _ := (← whnf tp) then
if polyExprName dom ``Fin && polyExprName body ``Bool then
dim? := some dom.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeBoolVector
if polyExprName dom ``Fin then
if let .forallE _ dom₂ body₂ _ := body then
if polyExprName dom₂ ``Fin && polyExprName body₂ ``Bool then
if ← isDefEq dom dom₂ then
dim? := some dom.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeMatrix
if let some dim := dim? then
let (_,h) ← synthPoly fuel sz x dim
return ← finish (← mkAppM nm #[h,vf])
if let some rh := polyCostHead e then
for nm in polyRuleNames do
let saved ← saveState
try
let c ← mkConstWithFreshMVarLevels nm
let (xs,bs,tp) ← forallMetaTelescope (← inferType c)
let args := tp.getAppArgs
if args.size < 2 then throwError "not a bound"
let lhs := args[args.size-2]!
let rhs := args[args.size-1]!
unless polyCostHead lhs == some rh do throwError "different routine"
unless ← isDefEq lhs e do throwError "bound does not match"
for k in [:xs.size] do
if ← xs[k]!.mvarId!.isAssigned then pure ()
else if bs[k]! == BinderInfo.instImplicit then
let v ← synthInstance (← inferType xs[k]!)
xs[k]!.mvarId!.assign v
let p ← instantiateMVars (mkAppN c xs)
if p.hasMVar then throwError "bound has unresolved hypotheses"
let rhs ← instantiateMVars rhs
let (_,h) ← synthPoly fuel sz x rhs
let p ← if tp.getAppFn.isConstOf ``Eq then mkAppM ``le_of_eq #[p] else pure p
let p ← mkLambdaFVars #[x] p
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.of_le #[p,h]
let tp ← inferType proof
return (tp.getAppArgs[3]!,proof)
catch _ => saved.restore
let pos := if e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Uniform.time then es.size-3 else es.size-2
let r := es[pos]!
if let some r' ← unfoldDefinition? r then
let args := es.set! pos r'.headBeta
return ← synthPoly fuel sz x (mkAppN e.getAppFn args)
throwError "poly_bound: no bound for {e}"
open Lean Meta Elab Tactic in
elab "poly_bound" : tactic => do
let goal ← getMainGoal
goal.withContext do
let tp := (← instantiateMVars (← goal.getType)).consumeMData
unless polyExprName tp ``ThreeMachine.StackCompiler.Poly do
throwError "poly_bound expects Poly"
let args := tp.getAppArgs
let sz := args[1]!
let fn := args[2]!
let wanted := args[3]!
let fty ← inferType fn
forallTelescopeReducing fty fun xs _ => do
unless xs.size == 1 do throwError "poly_bound expects unary function"
let body := (mkApp fn xs[0]!).headBeta
let (d,h) ← synthPoly 1000 sz xs[0]! body
let le ← mkFreshExprMVar (← mkAppM ``LE.le #[d,wanted])
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.lift #[h,le]
goal.assign proof
replaceMainGoal [le.mvarId!]
evalTactic (← `(tactic| omega))
end
end OAI
|