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namespace OAI
section
open Lean in
private def polyCostNames : Array Name := #[
`OAI.ThreeMachine.StackCompiler.Costs.matrixGet,
`OAI.ThreeMachine.StackCompiler.Costs.finEq,
`OAI.ThreeMachine.StackCompiler.Costs.setMem,
`OAI.ThreeMachine.StackCompiler.Costs.setSubset,
`OAI.ThreeMachine.StackCompiler.Costs.setEq,
`OAI.ThreeMachine.StackCompiler.Costs.setInter,
`OAI.ThreeMachine.StackCompiler.Costs.setDiff,
`OAI.ThreeMachine.StackCompiler.Costs.setDisjoint,
`OAI.ThreeMachine.StackCompiler.Costs.noEdgeTest,
`OAI.ThreeMachine.StackCompiler.Costs.noEdgeRow,
`OAI.ThreeMachine.StackCompiler.Costs.noEdges,
`OAI.ThreeMachine.StackCompiler.Costs.stateEqL,
`OAI.ThreeMachine.StackCompiler.Costs.stateEqM,
`OAI.ThreeMachine.StackCompiler.Costs.stateEqR,
`OAI.ThreeMachine.StackCompiler.Costs.stateEqMR,
`OAI.ThreeMachine.StackCompiler.Costs.stateEqLMR,
`OAI.ThreeMachine.StackCompiler.Costs.stateEq,
`OAI.ThreeMachine.StackCompiler.Costs.setCard,
`OAI.ThreeMachine.StackCompiler.Costs.setUnion,
`OAI.ThreeMachine.StackCompiler.Costs.stateCandidate,
`OAI.ThreeMachine.StackCompiler.Costs.stateUpto,
`OAI.ThreeMachine.StackCompiler.Costs.scLZ,
`OAI.ThreeMachine.StackCompiler.Costs.scLZR,
`OAI.ThreeMachine.StackCompiler.Costs.scA,
`OAI.ThreeMachine.StackCompiler.Costs.scB,
`OAI.ThreeMachine.StackCompiler.Costs.scC,
`OAI.ThreeMachine.StackCompiler.Costs.scD,
`OAI.ThreeMachine.StackCompiler.Costs.scE,
`OAI.ThreeMachine.StackCompiler.Costs.scF,
`OAI.ThreeMachine.StackCompiler.Costs.scH,
`OAI.ThreeMachine.StackCompiler.Costs.scI,
`OAI.ThreeMachine.StackCompiler.Costs.scJ,
`OAI.ThreeMachine.StackCompiler.Costs.scIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scHIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scFHIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scEFHIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scDEFHIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scCDEFHIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scBCDEFHIJ,
`OAI.ThreeMachine.StackCompiler.Costs.scAll,
`OAI.ThreeMachine.StackCompiler.Costs.stateCompatible,
`OAI.ThreeMachine.StackCompiler.Costs.blockEmpty,
`OAI.ThreeMachine.StackCompiler.Costs.blockTriple,
`OAI.ThreeMachine.StackCompiler.Costs.statesC,
`OAI.ThreeMachine.StackCompiler.Costs.statesP,
`OAI.ThreeMachine.StackCompiler.Costs.paddedCell,
`OAI.ThreeMachine.StackCompiler.Costs.paddedMatrix,
`OAI.ThreeMachine.StackCompiler.Costs.restrictTimeBound,
`OAI.ThreeMachine.StackCompiler.Costs.predecessorCell,
`OAI.ThreeMachine.StackCompiler.Costs.predecessorCount,
`OAI.ThreeMachine.StackCompiler.Costs.predecessorsBody,
`OAI.ThreeMachine.StackCompiler.Costs.predecessors,
`OAI.ThreeMachine.StackCompiler.Costs.rank,
`OAI.ThreeMachine.StackCompiler.Costs.ranks,
`OAI.ThreeMachine.StackCompiler.Costs.matrixGetFrame,
`OAI.ThreeMachine.StackCompiler.Costs.conePred,
`OAI.ThreeMachine.StackCompiler.Costs.cone,
`OAI.ThreeMachine.StackCompiler.Costs.triplesE,
`OAI.ThreeMachine.StackCompiler.Costs.triplesA,
`OAI.ThreeMachine.StackCompiler.Costs.triplesP,
`OAI.ThreeMachine.StackCompiler.Costs.triples,
`OAI.ThreeMachine.StackCompiler.Costs.conesF,
`OAI.ThreeMachine.StackCompiler.Costs.conesOne,
`OAI.ThreeMachine.StackCompiler.Costs.cones,
`OAI.ThreeMachine.StackCompiler.Costs.thresholds,
`OAI.ThreeMachine.StackCompiler.Costs.atomSetsC,
`OAI.ThreeMachine.StackCompiler.Costs.atomSetsT,
`OAI.ThreeMachine.StackCompiler.Costs.atomSetsD,
`OAI.ThreeMachine.StackCompiler.Costs.atomSets,
`OAI.ThreeMachine.StackCompiler.Costs.evalTemplatesCanonical,
`OAI.ThreeMachine.StackCompiler.Costs.familyAssignments,
`OAI.ThreeMachine.StackCompiler.Costs.familyEval,
`OAI.ThreeMachine.StackCompiler.Costs.family,
`OAI.ThreeMachine.StackCompiler.Costs.fullSolve,
`OAI.ThreeMachine.StackCompiler.Costs.paddedSolve,
`OAI.ThreeMachine.StackCompiler.Costs.scheduleRestriction,
`OAI.ThreeMachine.StackCompiler.Costs.scheduleCandidate,
`OAI.ThreeMachine.StackCompiler.Costs.scheduleMatrixFixed,
`OAI.ThreeMachine.StackCompiler.Costs.scheduleMatrix,
`OAI.ThreeMachine.StackCompiler.Costs.edgePairEq,
`OAI.ThreeMachine.StackCompiler.Costs.edgeAt,
`OAI.ThreeMachine.StackCompiler.Costs.edgeMatrix,
`OAI.ThreeMachine.StackCompiler.Costs.nextMatrixCell,
`OAI.ThreeMachine.StackCompiler.Costs.nextMatrix,
`OAI.ThreeMachine.StackCompiler.Costs.closureMatrixStep,
`OAI.ThreeMachine.StackCompiler.Costs.reachMatrix
]
open Lean Meta Elab Tactic in
private def polyAutoCostHead (e : Expr) : Option Name :=
let e := e.consumeMData
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 polyAutoExprName (e : Expr) (n : Name) : Bool := e.consumeMData.getAppFn.isConstOf n
open Lean Meta Elab Tactic in
private def withPolyFacts (hs : List Expr) (k : TacticM (Expr × Expr)) : TacticM (Expr × Expr) := do
match hs with
| [] => k
| h::hs =>
withLetDecl `polyFact (← instantiateMVars (← inferType h)) h fun v => do
let (a,b) ← withPolyFacts hs k
return (a.replaceFVar v h,b.replaceFVar v h)
open Lean Meta Elab Tactic in
private def polyAutoRule (e : Expr) : TacticM (Option (Expr × Expr)) := do
let some rh := polyAutoCostHead e | return none
let es := e.getAppArgs
for nm in polyRuleNames do
if !(← getEnv).contains nm then continue
let saved ← saveState
try
let mut raw := (← getConstInfo nm).type
while raw.isForall do raw := raw.bindingBody!
let rargs := raw.getAppArgs
if rargs.size < 2 then throwError "not a bound"
unless polyAutoCostHead rargs[rargs.size-2]! == some rh do throwError "different routine"
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 polyAutoCostHead lhs == some rh do throwError "different routine"
let lhsArgs := lhs.getAppArgs
let rpos := if lhs.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Uniform.time then lhsArgs.size-3 else lhsArgs.size-2
let lr := lhsArgs[rpos]!
let rr := es[if e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Uniform.time then es.size-3 else es.size-2]!
if lr.getAppArgs.size == rr.getAppArgs.size then
for (a,b) in lr.getAppArgs.zip rr.getAppArgs do
unless ← isDefEq a b do throwError "routine argument does not match"
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 p ← if tp.getAppFn.isConstOf ``Eq then mkAppM ``le_of_eq #[p] else pure p
return some (rhs,p)
catch _ => saved.restore
return none
open Lean Meta Elab Tactic in
private def polyAutoEstimate (e x : Expr) : TacticM (Option (Expr × Expr × Expr)) := do
let some rh := polyAutoCostHead e | return none
let es := e.getAppArgs
unless e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Uniform.time do return none
for nm in polyCostNames do
if !(← getEnv).contains nm then continue
let saved ← saveState
try
let c ← mkConstWithFreshMVarLevels nm
let (xs,bs,tp) ← forallMetaTelescope (← inferType c)
let tp := tp.consumeMData
unless tp.isAppOf ``ThreeMachine.StackCompiler.Poly do throwError "not polynomial"
let args := tp.getAppArgs
let domain := args[0]!
let sigmaArgs := domain.getAppArgs
unless domain.isAppOf ``Sigma do throwError "not sigma domain"
let fn := args[2]!
withLocalDeclD `p domain fun p => do
let body := (mkApp fn p).headBeta
unless polyAutoCostHead body == some rh do throwError "different routine"
let bs := body.getAppArgs
unless ← isDefEq bs[bs.size-3]! es[es.size-3]! do throwError "different routine args"
let v ← mkAppOptM ``Sigma.mk #[some sigmaArgs[0]!,some sigmaArgs[1]!,some es[es.size-2]!,some es.back!]
for k in [:xs.size] do
if ← xs[k]!.mvarId!.isAssigned then pure ()
else if bs[k]! == BinderInfo.instImplicit then
xs[k]!.mvarId!.assign (← synthInstance (← inferType xs[k]!))
let h ← instantiateMVars (mkAppN c xs)
if h.hasMVar then throwError "bound has unresolved hypotheses"
let g ← mkLambdaFVars #[x] v
return some (h,g,← instantiateMVars (mkApp args[1]! v))
catch _ => saved.restore
return none
open Lean Meta Elab Tactic in
private def polyAutoDegree (p : Expr) : TacticM Expr := do
let tp := (← instantiateMVars (← inferType p)).consumeMData
let tp ← withReducible <| whnf tp
if tp.isAppOfArity ``ThreeMachine.StackCompiler.Poly 4 then
return tp.getAppArgs[3]!
throwError "poly_auto: unexpected result type {tp} of {p}"
open Lean Meta Elab Tactic in
private def synthPolyAuto (cache : IO.Ref (Std.HashMap (Expr × Expr × Expr) (Expr × Expr))) (fuel : ℕ) (sz x e : Expr) : TacticM (Expr × Expr) := do
let key := (sz,x,e)
if let some r := (← cache.get)[key]? then return r
let result ← (do
match fuel with
| 0 => throwError "poly_auto: expression depth exhausted"
| fuel+1 =>
let e ← withReducible <| whnf (← deltaExpand e (fun n =>
[``Function.comp,``ThreeMachine.Algorithm.Block.append,``ThreeMachine.Algorithm.State.advance,
``ThreeMachine.Algorithm.State.finish,``ThreeMachine.Algorithm.Block.empty,
``ThreeMachine.Algorithm.Block.triple].contains n)).headBeta
let fn ← mkLambdaFVars #[x] e
for decl in (← getLCtx) do
unless decl.isImplementationDetail do
let tp := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName tp ``ThreeMachine.StackCompiler.Poly then
let as := tp.getAppArgs
if as.size == 4 then
if ← withReducible <| isDefEq (← deltaExpand as[1]! (· == ``Function.comp)) sz then
let factFn ← deltaExpand as[2]! (fun n =>
[``Function.comp,``ThreeMachine.Algorithm.Block.append,``ThreeMachine.Algorithm.State.advance,
``ThreeMachine.Algorithm.State.finish,``ThreeMachine.Algorithm.Block.empty,
``ThreeMachine.Algorithm.Block.triple].contains n)
let same ← withReducible <| isDefEq factFn fn
let factBody ← withReducible <| whnf (mkApp factFn x).headBeta
let same ← if same then pure true else if
e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.volume &&
factBody.getAppFn.isConstOf ``ThreeMachine.StackCompiler.volume then
if ← withReducible <| isDefEq factBody.getAppArgs.back! e.getAppArgs.back! then
withTransparency .all <| isDefEq factFn fn
else pure false
else pure false
if same 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 ← withReducible <| isDefEq e se then
return (mkNatLit 1, ← mkAppM ``ThreeMachine.StackCompiler.Poly.size #[sz])
let be ← mkAppM ``Nat.add #[se,mkNatLit 2]
if ← withReducible <| isDefEq e be then
return (mkNatLit 1, ← mkAppM ``ThreeMachine.StackCompiler.Poly.base #[sz])
let es := e.getAppArgs
let isadd := polyAutoExprName e ``Nat.add || polyAutoExprName e ``HAdd.hAdd
let ismul := polyAutoExprName e ``Nat.mul || polyAutoExprName e ``HMul.hMul
let issub := polyAutoExprName e ``Nat.sub || polyAutoExprName e ``HSub.hSub
let ismax := polyAutoExprName e ``Nat.max || polyAutoExprName 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) ← synthPolyAuto cache fuel sz x a
if issub then
let g ← mkLambdaFVars #[x] b
return (d, ← mkAppM ``ThreeMachine.StackCompiler.Poly.sub #[h,g])
let (_,h') ← synthPolyAuto cache 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']
return (← polyAutoDegree proof,proof)
if e.isAppOfArity ``ite 5 then
let pf ← mkLambdaFVars #[x] es[1]!
let (_,h) ← synthPolyAuto cache fuel sz x es[3]!
let (_,h') ← synthPolyAuto cache fuel sz x es[4]!
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.iteNat #[pf,h,h']
return (← polyAutoDegree proof,proof)
if es.size ≥ 2 && (polyAutoExprName e ``Nat.pow || polyAutoExprName e ``HPow.hPow) &&
!(es[es.size-1]!.containsFVar x.fvarId!) then
let (_,h) ← synthPolyAuto cache fuel sz x es[es.size-2]!
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.pow #[h,es[es.size-1]!]
return (← polyAutoDegree proof,proof)
if es.size == 1 && polyAutoExprName e ``Nat.succ then
let (_,h) ← synthPolyAuto cache fuel sz x es[0]!
let hc ← mkAppM ``ThreeMachine.StackCompiler.Poly.const #[sz,mkNatLit 1]
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.add #[h,hc]
return (← polyAutoDegree proof,proof)
if let .proj ``Fin 0 v := e then
let tp ← inferType v
let n := tp.getAppArgs[0]!
let (_,h) ← synthPolyAuto cache fuel sz x n
let vf ← mkLambdaFVars #[x] v
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.finVal #[h,vf]
return (← polyAutoDegree proof,proof)
if e.isAppOfArity ``Fin.val 2 then
let (_,h) ← synthPolyAuto cache fuel sz x es[0]!
let vf ← mkLambdaFVars #[x] es[1]!
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.finVal #[h,vf]
return (← polyAutoDegree proof,proof)
let block? := match e with
| .proj ``ThreeMachine.Algorithm.Block 0 b => some b
| _ => if polyAutoExprName e ``ThreeMachine.Algorithm.Block.length then some es.back! else none
if let some b := block? then
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[b])
let bf ← mkLambdaFVars #[x] b
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.blockLength #[bf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName e ``Finset.card then
let v ← withReducible <| whnf (← deltaExpand es[es.size-1]! (· == ``Function.comp)).headBeta
let tp ← withReducible <| whnf (← inferType v)
let elem ← withReducible <| whnf tp.getAppArgs[0]!
if polyAutoExprName elem ``Fin then
let (_,h) ← synthPolyAuto cache fuel sz x elem.getAppArgs[0]!
let vf ← mkLambdaFVars #[x] v
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.finsetCard #[h,vf]
return (← polyAutoDegree proof,proof)
if polyAutoExprName e ``List.length then
let v ← withReducible <| whnf (← deltaExpand es[es.size-1]! (· == ``Function.comp)).headBeta
if polyAutoExprName v ``List.nil then
return (mkNatLit 0, ← mkAppM ``ThreeMachine.StackCompiler.Poly.const #[sz,mkNatLit 0])
if polyAutoExprName v ``List.cons then
let va := v.getAppArgs
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[va.back!])
let af ← mkLambdaFVars #[x] va[va.size-2]!
let xf ← mkLambdaFVars #[x] va.back!
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthCons #[af,xf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.tail || polyAutoExprName v ``List.reverse then
let xs := v.getAppArgs.back!
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[xs])
let xf ← mkLambdaFVars #[x] xs
let nm := if polyAutoExprName v ``List.tail then
``ThreeMachine.StackCompiler.Poly.lengthTail else ``ThreeMachine.StackCompiler.Poly.lengthReverse
let pr ← mkAppM nm #[xf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.take || polyAutoExprName v ``List.drop then
let va := v.getAppArgs
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[va.back!])
let kf ← mkLambdaFVars #[x] va[va.size-2]!
let xf ← mkLambdaFVars #[x] va.back!
let nm := if polyAutoExprName v ``List.take then
``ThreeMachine.StackCompiler.Poly.lengthTake else ``ThreeMachine.StackCompiler.Poly.lengthDrop
let pr ← mkAppM nm #[kf,xf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.append || polyAutoExprName v ``HAppend.hAppend || polyAutoExprName v ``Append.append then
let va := v.getAppArgs
let a := va[va.size-2]!
let b := va.back!
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[a])
let (_,h') ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[b])
let af ← mkLambdaFVars #[x] a
let bf ← mkLambdaFVars #[x] b
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthAppend #[af,bf,h,h']
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.range then
let (_,h) ← synthPolyAuto cache fuel sz x v.getAppArgs.back!
let kf ← mkLambdaFVars #[x] v.getAppArgs.back!
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthRange #[kf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.replicate then
let va := v.getAppArgs
let (_,h) ← synthPolyAuto cache fuel sz x va[va.size-2]!
let kf ← mkLambdaFVars #[x] va[va.size-2]!
let af ← mkLambdaFVars #[x] va.back!
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthReplicate #[kf,af,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``Option.toList then
let ofn ← mkLambdaFVars #[x] v.getAppArgs.back!
let pr ← mkAppOptM ``ThreeMachine.StackCompiler.Poly.lengthOption #[none,some sz,none,some ofn]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.map then
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[v.getAppArgs.back!])
let ff ← mkLambdaFVars #[x] v.getAppArgs[v.getAppArgs.size-2]!
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthMap #[ff,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.product then
let vs := v.getAppArgs
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[vs[vs.size-2]!])
let (_,h') ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[vs.back!])
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthProduct #[h,h']
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.filter then
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[v.getAppArgs.back!])
let pf ← mkLambdaFVars #[x] v.getAppArgs[v.getAppArgs.size-2]!
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthFilter #[pf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.finRange then
let (_,h) ← synthPolyAuto cache fuel sz x v.getAppArgs[0]!
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthFinRange #[h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``Finset.sort then
let set := v.getAppArgs[1]!
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``Finset.card #[set])
let sf ← mkLambdaFVars #[x] set
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthSort #[sf,h]
return (← polyAutoDegree pr,pr)
if polyAutoExprName v ``List.ofFn then
let fn := v.getAppArgs.back!
let (_,h) ← synthPolyAuto cache fuel sz x v.getAppArgs[1]!
let ff ← mkLambdaFVars #[x] fn
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthOfFn #[ff,h]
return (← polyAutoDegree pr,pr)
let vfn ← mkLambdaFVars #[x] (← mkAppM ``ThreeMachine.StackCompiler.volume #[v])
for decl in (← getLCtx) do
let dt := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName dt ``ThreeMachine.StackCompiler.Poly then
let da := dt.getAppArgs
if (← withReducible <| isDefEq da[1]! sz) && (← withReducible <| isDefEq da[2]! vfn) then
let vf ← mkLambdaFVars #[x] v
let pr ← mkAppM ``ThreeMachine.StackCompiler.Poly.lengthVolume #[vf,decl.toExpr]
return (← polyAutoDegree pr,pr)
throwError "poly_auto: no length bound for {v}"
if polyAutoExprName e ``ThreeMachine.StackCompiler.volume then
let val ← withReducible <| whnf (← deltaExpand es[es.size-1]! (· == ``Function.comp)).headBeta
let vf ← mkLambdaFVars #[x] val
let tp ← withReducible <| whnf (← inferType val)
let ts := tp.getAppArgs
let finish (pr : Expr) : TacticM (Expr × Expr) := do
return (← polyAutoDegree pr,pr)
if polyAutoExprName val ``List.nil then
return (mkNatLit 0, ← mkAppM ``ThreeMachine.StackCompiler.Poly.const #[sz,mkNatLit 1])
if val.isAppOfArity ``ite 5 then
let vs := val.getAppArgs
let pf ← mkLambdaFVars #[x] vs[1]!
let af ← mkLambdaFVars #[x] vs[3]!
let bf ← mkLambdaFVars #[x] vs[4]!
let (_,ha) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[vs[3]!])
let (_,hb) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[vs[4]!])
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeIte #[pf,af,bf,ha,hb])
if polyAutoExprName val ``ThreeMachine.Algorithm.lookup then
let vs := val.getAppArgs
let xs := vs[vs.size-2]!
let k := vs.back!
let xf ← mkLambdaFVars #[x] xs
let kf ← mkLambdaFVars #[x] k
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[xs])
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeLookup #[xf,kf,h])
if polyAutoExprName val ``Option.toList then
let o := val.getAppArgs.back!
let ofn ← mkLambdaFVars #[x] o
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[o])
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeOptionToList #[ofn,h])
if polyAutoExprName val ``Option.some then
let a := val.getAppArgs.back!
let af ← mkLambdaFVars #[x] a
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[a])
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeOptionSome #[af,h])
if polyAutoExprName val ``Option.map then
let vs := val.getAppArgs
let f := vs[vs.size-2]!
let o := vs.back!
let ofn ← mkLambdaFVars #[x] o
let ff ← mkLambdaFVars #[x] f
let listFn ← mkLambdaFVars #[x] (← mkAppM ``Option.toList #[o])
let pool ← mkAppM ``ThreeMachine.StackCompiler.Poly.ListPool #[listFn]
let (_,ho) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[o])
let locals := (← getLCtx).decls.toArray.filterMap (fun d => d)
let xd ← inferType x
let hf ← withLocalDeclD `q pool fun q => do
let root ← mkAppM ``Sigma.fst #[q]
let item ← mkAppM ``Subtype.val #[← mkAppM ``Sigma.snd #[q]]
let szNew ← mkLambdaFVars #[q] (mkApp sz root)
let rootFn ← mkLambdaFVars #[q] root
let mut hs : Array Expr := #[]
for decl in locals do
let dt := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName dt ``ThreeMachine.StackCompiler.Poly then
if (← withReducible <| isDefEq dt.getAppArgs[0]! xd) then
hs := hs.push (← mkAppM ``ThreeMachine.StackCompiler.Poly.precomp #[decl.toExpr,rootFn])
let hlist ← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeOptionToList #[ofn,ho]
hs := hs.push (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumePool #[listFn,hlist])
let (_,pr) ← withPolyFacts hs.toList do
synthPolyAuto cache fuel szNew q (← mkAppM ``ThreeMachine.StackCompiler.volume #[mkApp (f.replaceFVar x root) item])
return pr
return ← finish (← mkAppOptM ``ThreeMachine.StackCompiler.Poly.volumeOptionMap #[none,some sz,none,none,none,none,some ff,some ofn,some hf])
if polyAutoExprName val ``Option.none then
let h ← mkAppM ``ThreeMachine.StackCompiler.Poly.const #[sz,mkNatLit 1]
return ← finish h
let blockTime? := match val with
| .proj ``ThreeMachine.Algorithm.Block 1 b => some b
| _ => if polyAutoExprName val ``ThreeMachine.Algorithm.Block.time then some val.getAppArgs.back! else none
if let some b := blockTime? then
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[b])
let bf ← mkLambdaFVars #[x] b
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.blockTime #[bf,h])
let proj? := match val with
| .proj ``Prod k p => some (k,p)
| _ => if polyAutoExprName val ``Prod.fst then some (0,val.getAppArgs.back!)
else if polyAutoExprName val ``Prod.snd then some (1,val.getAppArgs.back!) else none
if let some (k,p) := proj? then
let pf ← mkLambdaFVars #[x] p
let pv ← mkLambdaFVars #[x] (← mkAppM ``ThreeMachine.StackCompiler.volume #[p])
for decl in (← getLCtx) do
let dt := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName dt ``ThreeMachine.StackCompiler.Poly then
let ds := dt.getAppArgs
if (← withReducible <| isDefEq ds[1]! sz) && (← withReducible <| isDefEq ds[2]! pv) then
return ← finish (← mkAppM (if k == 0 then ``ThreeMachine.StackCompiler.Poly.volumeFst else
``ThreeMachine.StackCompiler.Poly.volumeSnd) #[pf,decl.toExpr])
if polyAutoExprName val ``Finset.sort then
let set := val.getAppArgs[1]!
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[set])
return ← finish h
if polyAutoExprName val ``List.ofFn then
let f := val.getAppArgs.back!
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[f])
return ← finish h
if polyAutoExprName val ``List.finRange then
let (_,h) ← synthPolyAuto cache fuel sz x val.getAppArgs[0]!
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeFinRange #[h])
if polyAutoExprName tp ``Nat then
let (_,h) ← synthPolyAuto cache fuel sz x val
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeNat #[h])
if polyAutoExprName tp ``Bool then
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeBool #[sz,vf])
if polyAutoExprName tp ``Unit || polyAutoExprName tp ``PUnit then
return ← finish (← mkAppM `OAI.ThreeMachine.StackCompiler.Poly.volumeUnit #[sz,vf])
if polyAutoExprName tp ``Prod then
let a ← mkAppM ``Prod.fst #[val]
let b ← mkAppM ``Prod.snd #[val]
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[a])
let (_,h') ← synthPolyAuto cache 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 polyAutoExprName tp ``Fin then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeFin
if polyAutoExprName tp ``Finset && polyAutoExprName ts[0]! ``Fin then
dim? := some ts[0]!.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeFinset
if polyAutoExprName tp ``ThreeMachine.StackCompiler.Universe then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeUniverse
if polyAutoExprName tp ``ThreeMachine.StackCompiler.Cardinal then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeCardinal
if polyAutoExprName tp ``ThreeMachine.StackCompiler.Matrix then
dim? := some ts[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeMatrix
if polyAutoExprName tp ``ThreeMachine.Algorithm.State && polyAutoExprName ts[0]! ``Fin then
dim? := some ts[0]!.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeState
if polyAutoExprName tp ``ThreeMachine.Algorithm.Block then
if val.getAppFn.isConstOf ``ThreeMachine.Algorithm.Block.mk then
let bl ← mkAppM ``ThreeMachine.Algorithm.Block.length #[val]
let bt ← mkAppM ``ThreeMachine.Algorithm.Block.time #[val]
let (_,hl) ← synthPolyAuto cache fuel sz x bl
let (_,ht) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[bt])
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeBlock #[vf,hl,ht])
if let .forallE _ dom body _ := (← whnf tp) then
if polyAutoExprName dom ``Fin && polyAutoExprName body ``Bool then
dim? := some dom.getAppArgs[0]!; nm := `OAI.ThreeMachine.StackCompiler.Poly.volumeBoolVector
if polyAutoExprName dom ``Fin then
if let .forallE _ dom₂ body₂ _ := body then
if polyAutoExprName dom₂ ``Fin && polyAutoExprName 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) ← synthPolyAuto cache fuel sz x dim
return ← finish (← mkAppM nm #[h,vf])
if polyAutoExprName tp ``List then
let (_,hl) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[val])
let pool ← mkAppM ``ThreeMachine.StackCompiler.Poly.ListPool #[vf]
let locals := (← getLCtx).decls.toArray.filterMap (fun d => d)
let xd ← inferType x
let hv ← withLocalDeclD `q pool fun q => do
let root ← mkAppM ``Sigma.fst #[q]
let item ← mkAppM ``Subtype.val #[← mkAppM ``Sigma.snd #[q]]
let szNew ← mkLambdaFVars #[q] (mkApp sz root)
let rootFn ← mkLambdaFVars #[q] root
let mut hs : Array Expr := #[]
for decl in locals do
let dt := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName dt ``ThreeMachine.StackCompiler.Poly then
if (← withReducible <| isDefEq dt.getAppArgs[0]! xd) then
hs := hs.push (← mkAppM ``ThreeMachine.StackCompiler.Poly.precomp #[decl.toExpr,rootFn])
let (_,pr) ← withPolyFacts hs.toList do
synthPolyAuto cache fuel szNew q (← mkAppM ``ThreeMachine.StackCompiler.volume #[item])
return pr
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.listVolume #[vf,hl,hv])
if let .forallE _ dom _ _ := (← whnf tp) then
if polyAutoExprName dom ``Fin then
let n := dom.getAppArgs[0]!
let nf ← mkLambdaFVars #[x] n
let (_,hn) ← synthPolyAuto cache fuel sz x n
let pool ← mkAppM ``ThreeMachine.StackCompiler.Poly.FinPool #[nf]
let locals := (← getLCtx).decls.toArray.filterMap (fun d => d)
let xd ← inferType x
let hf ← withLocalDeclD `q pool fun q => do
let root ← mkAppM ``Sigma.fst #[q]
let item ← mkAppM ``Sigma.snd #[q]
let szNew ← mkLambdaFVars #[q] (mkApp sz root)
let rootFn ← mkLambdaFVars #[q] root
let mut hs : Array Expr := #[]
for decl in locals do
let dt := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName dt ``ThreeMachine.StackCompiler.Poly then
if (← withReducible <| isDefEq dt.getAppArgs[0]! xd) then
hs := hs.push (← mkAppM ``ThreeMachine.StackCompiler.Poly.precomp #[decl.toExpr,rootFn])
let (_,pr) ← withPolyFacts hs.toList do
synthPolyAuto cache fuel szNew q (← mkAppM ``ThreeMachine.StackCompiler.volume #[mkApp (val.replaceFVar x root) item])
return pr
return ← finish (← mkAppM ``ThreeMachine.StackCompiler.Poly.volumeFunction #[vf,hn,hf])
if let some (h,g,z) ← polyAutoEstimate e x then
let (_,hs) ← synthPolyAuto cache fuel sz x z
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.reparam #[h,g,hs]
return (← polyAutoDegree proof,proof)
if e.getAppFn.isConstOf ``ThreeMachine.StackCompiler.Uniform.time && es.size ≥ 3 then
let routine := es[es.size-3]!
let rh := routine.getAppFn.constName?
let loopNames := #[``ThreeMachine.StackCompiler.Uniform.map,
``ThreeMachine.StackCompiler.Uniform.filter, ``ThreeMachine.StackCompiler.Uniform.any,
``ThreeMachine.StackCompiler.Uniform.all,
``ThreeMachine.StackCompiler.Uniform.filterMap, ``ThreeMachine.StackCompiler.Uniform.firstResult,
``ThreeMachine.StackCompiler.Uniform.flatMap, ``ThreeMachine.StackCompiler.Uniform.optionMap]
if let some k := loopNames.findIdx? (some · == rh) then
let R := routine.getAppArgs.back!
unless !(R.containsFVar x.fvarId!) do throwError "dynamic routine"
let idx := es[es.size-2]!
let inp := es.back!
let baseValue ← mkAppM ``Prod.fst #[inp]
let list ← if k == 7 then mkAppM ``Option.toList #[baseValue] else pure baseValue
let env ← mkAppM ``Prod.snd #[inp]
let idxFn ← mkLambdaFVars #[x] idx
let listFn ← mkLambdaFVars #[x] list
let envFn ← mkLambdaFVars #[x] env
let (_,hl) ← synthPolyAuto cache fuel sz x (← mkAppM ``List.length #[list])
let (_,hx) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[list])
let (_,he) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[env])
let ra := routine.getAppArgs
let dom ← inferType x
let pool ← mkAppOptM ``ThreeMachine.StackCompiler.Poly.Pool #[some ra[0]!,some dom,some ra[1]!,some idxFn,some listFn]
let locals := (← getLCtx).decls.toArray.filterMap (fun d => d)
let (ht,hv) ← withLocalDeclD `q pool fun q => do
let root ← mkAppM ``Sigma.fst #[q]
let item ← mkAppM ``Subtype.val #[← mkAppM ``Sigma.snd #[q]]
let sub (e : Expr) := e.replaceFVar x root
let sizeNew ← mkLambdaFVars #[q] (mkApp sz root)
let rootFn ← mkLambdaFVars #[q] root
let mut hs : Array Expr := #[]
for decl in locals do
let dt := (← instantiateMVars decl.type).consumeMData
if polyAutoExprName dt ``ThreeMachine.StackCompiler.Poly then
if (← isDefEq dt.getAppArgs[0]! dom) then
let p ← mkAppM ``ThreeMachine.StackCompiler.Poly.precomp #[decl.toExpr,rootFn]
hs := hs.push p
let hp ← mkAppM ``ThreeMachine.StackCompiler.Poly.volumePool #[listFn,hx]
hs := hs.push hp
withPolyFacts hs.toList do
let arg ← mkAppM ``Prod.mk #[item,sub env]
let cost ← mkAppM ``ThreeMachine.StackCompiler.Uniform.time #[R,sub idx,arg]
let (_,ht) ← synthPolyAuto cache fuel sizeNew q cost
if k == 0 || k ≥ 4 then
let f := (← inferType R).getAppArgs.back!
let out := mkAppN f #[sub idx,arg]
let (_,hv) ← synthPolyAuto cache fuel sizeNew q (← mkAppM ``ThreeMachine.StackCompiler.volume #[out])
return (ht,hv)
else return (ht,mkNatLit 0)
let nm := #[``ThreeMachine.StackCompiler.Poly.mapTime,
``ThreeMachine.StackCompiler.Poly.filterTime, ``ThreeMachine.StackCompiler.Poly.anyTime,
``ThreeMachine.StackCompiler.Poly.allTime, ``ThreeMachine.StackCompiler.Poly.filterMapTime,
``ThreeMachine.StackCompiler.Poly.firstResultTime, ``ThreeMachine.StackCompiler.Poly.flatMapTime, ``ThreeMachine.StackCompiler.Poly.optionMapTime][k]!
let optionFn ← mkLambdaFVars #[x] baseValue
let hx' ← if k == 7 then do
let (_,h) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[baseValue])
pure h
else pure hx
let pre := if k == 7 then
#[some ra[0]!,some dom,some sz,some ra[1]!,some ra[2]!,some ra[3]!,some ra[4]!,some ra[5]!,some ra[6]!,
some idxFn,some envFn,some optionFn,some ra[7]!,some R,none,none,none,none]
else if k == 0 || k ≥ 4 then
#[some ra[0]!,some dom,some sz,some ra[1]!,some ra[2]!,some ra[3]!,some ra[4]!,some ra[5]!,some ra[6]!,
some idxFn,some listFn,some envFn,some ra[7]!,some R,none,none,none,none,none]
else
#[some ra[0]!,some dom,some sz,some ra[1]!,some ra[2]!,some ra[3]!,some ra[4]!,
some idxFn,some listFn,some envFn,some ra[5]!,some R,none,none,none,none]
let args := pre ++ (if k == 7 then #[some ht,some hx',some he] else #[some hl,some ht,some hx,some he])
let args := if k == 0 || k ≥ 4 then args.push (some hv) else args
let proof ← mkAppOptM nm args
return (← polyAutoDegree proof,proof)
if e.isApp && (← isDefEq (← inferType e) (mkConst ``Nat)) then
let f := e.appFn!
let a := e.appArg!
let tp ← withReducible <| whnf (← inferType f)
if let .forallE _ dom body _ := tp then
if polyAutoExprName dom ``Fin && polyAutoExprName body ``Nat then
let af ← mkLambdaFVars #[x] a
let (_,hf) ← synthPolyAuto cache fuel sz x (← mkAppM ``ThreeMachine.StackCompiler.volume #[f])
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.natFunctionApply #[af,hf]
return (← polyAutoDegree proof,proof)
if (polyAutoCostHead e).isSome then
if let some (rhs,p) ← polyAutoRule e then
let (_,h) ← synthPolyAuto cache fuel sz x rhs
let p ← mkLambdaFVars #[x] p
let proof ← mkAppM ``ThreeMachine.StackCompiler.Poly.of_le #[p,h]
return (← polyAutoDegree proof,proof)
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 r' ← zetaReduce r' (zetaDelta := false)
let r' ← withReducible <| whnf r'
let args := es.set! pos r'.headBeta
return ← synthPolyAuto cache fuel sz x (mkAppN e.getAppFn args)
throwError "poly_auto: no bound for {e}"
)
let (d,p) := result
let d ← instantiateMVars d
let d ← if d.hasFVar then pure d else whnf d
let p ← instantiateMVars p
let p ← if p.approxDepth > 15 then do
let tp := (← inferType p).consumeMData
let args := tp.getAppArgs
let tp := mkAppN tp.getAppFn (args.set! 3 d)
mkAuxTheorem tp p
else pure p
let result := (d,p)
cache.modify (·.insert key result)
return result
open Lean Meta Elab Tactic in
elab "poly_auto" : tactic => do
let goal ← getMainGoal
goal.withContext do
let tp := (← instantiateMVars (← goal.getType)).consumeMData
unless polyAutoExprName tp ``ThreeMachine.StackCompiler.Poly do
throwError "poly_auto expects Poly, got {tp}"
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_auto expects unary function"
let body := (mkApp fn xs[0]!).headBeta.consumeMData
let cache ← IO.mkRef ({} : Std.HashMap (Expr × Expr × Expr) (Expr × Expr))
let (d,h) ← synthPolyAuto cache 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| first | exact Nat.le_refl _ | assumption | omega | decide))
end
end OAI
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