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import Lean
import Base.Utils
import Base.Primitives.Base
import Base.Extensions
namespace Progress
open Lean Elab Term Meta
open Utils Extensions
-- We can't define and use trace classes in the same file
initialize registerTraceClass `Progress
/- # Progress tactic -/
structure PSpecDesc where
-- The universally quantified variables
-- Can be fvars or mvars
fvars : Array Expr
-- The existentially quantified variables
evars : Array Expr
-- The function applied to its arguments
fArgsExpr : Expr
-- ⊤ if the function is a constant (must be if we are registering a theorem,
-- but is not necessarily the case if we are looking at a goal)
fIsConst : Bool
-- The function arguments
fLevels : List Level
args : Array Expr
-- The returned value
ret : Expr
-- The postcondition (if there is)
post : Option Expr
section Methods
variable [MonadLiftT MetaM m] [MonadControlT MetaM m] [Monad m] [MonadOptions m]
variable [MonadTrace m] [MonadLiftT IO m] [MonadRef m] [AddMessageContext m]
variable [MonadError m]
variable {a : Type}
/- Analyze a goal or a pspec theorem to decompose its arguments.
PSpec theorems should be of the following shape:
```
∀ x1 ... xn, H1 → ... Hn → ∃ y1 ... ym. f x1 ... xn = .ret ... ∧ Post1 ∧ ... ∧ Postk
```
The continuation `k` receives the following inputs:
- universally quantified variables
- assumptions
- existentially quantified variables
- function name
- function arguments
- return
- postconditions
TODO: generalize for when we do inductive proofs
-/
partial
def withPSpec [Inhabited (m a)] [Nonempty (m a)]
(isGoal : Bool) (th : Expr) (k : PSpecDesc → m a) :
m a := do
trace[Progress] "Proposition: {th}"
-- Dive into the quantified variables and the assumptions
-- Note that if we analyze a pspec theorem to register it in a database (i.e.
-- a discrimination tree), we need to introduce *meta-variables* for the
-- quantified variables.
let telescope (k : Array Expr → Expr → m a) : m a :=
if isGoal then forallTelescope th.consumeMData (fun fvars th => k fvars th)
else do
let (fvars, _, th) ← forallMetaTelescope th.consumeMData
k fvars th
telescope fun fvars th => do
trace[Progress] "Universally quantified arguments and assumptions: {fvars}"
-- Dive into the existentials
existsTelescope th.consumeMData fun evars th => do
trace[Progress] "Existentials: {evars}"
trace[Progress] "Proposition after stripping the quantifiers: {th}"
-- Take the first conjunct
let (th, post) ← optSplitConj th.consumeMData
trace[Progress] "After splitting the conjunction:\n- eq: {th}\n- post: {post}"
-- Destruct the equality
let (mExpr, ret) ← destEq th.consumeMData
trace[Progress] "After splitting the equality:\n- lhs: {th}\n- rhs: {ret}"
-- Recursively destruct the monadic application to dive into the binds,
-- if necessary (this is for when we use `withPSpec` inside of the `progress` tactic),
-- and destruct the application to get the function name
let rec strip_monad mExpr := do
mExpr.consumeMData.withApp fun mf margs => do
trace[Progress] "After stripping the arguments of the monad expression:\n- mf: {mf}\n- margs: {margs}"
if mf.isConst ∧ mf.constName = ``Bind.bind then do
-- Dive into the bind
let fExpr := (margs.get! 4).consumeMData
-- Recursve
strip_monad fExpr
else
-- No bind
pure (mExpr, mf, margs)
let (fArgsExpr, f, args) ← strip_monad mExpr
trace[Progress] "After stripping the arguments of the function call:\n- f: {f}\n- args: {args}"
let fLevels ← do
-- If we are registering a theorem, then the function must be a constant
if ¬ f.isConst then
if isGoal then pure []
else throwError "Not a constant: {f}"
else pure f.constLevels!
-- *Sanity check* (activated if we are analyzing a theorem to register it in a DB)
-- Check if some existentially quantified variables
let _ := do
-- Collect all the free variables in the arguments
let allArgsFVars ← args.foldlM (fun hs arg => getFVarIds arg hs) HashSet.empty
-- Check if they intersect the fvars we introduced for the existentially quantified variables
let evarsSet : HashSet FVarId := HashSet.empty.insertMany (evars.map (fun (x : Expr) => x.fvarId!))
let filtArgsFVars := allArgsFVars.toArray.filter (fun var => evarsSet.contains var)
if filtArgsFVars.isEmpty then pure ()
else
let filtArgsFVars := filtArgsFVars.map (fun fvarId => Expr.fvar fvarId)
throwError "Some of the function inputs are not universally quantified: {filtArgsFVars}"
-- Return
trace[Progress] "Function with arguments: {fArgsExpr}";
let thDesc := {
fvars := fvars
evars := evars
fArgsExpr
fIsConst := f.isConst
fLevels
args := args
ret := ret
post := post
}
k thDesc
end Methods
def getPSpecFunArgsExpr (isGoal : Bool) (th : Expr) : MetaM Expr :=
withPSpec isGoal th (fun d => do pure d.fArgsExpr)
-- pspec attribute
structure PSpecAttr where
attr : AttributeImpl
ext : DiscrTreeExtension Name
deriving Inhabited
/- The persistent map from expressions to pspec theorems. -/
initialize pspecAttr : PSpecAttr ← do
let ext ← mkDiscrTreeExtention `pspecMap
let attrImpl : AttributeImpl := {
name := `pspec
descr := "Marks theorems to use with the `progress` tactic"
add := fun thName stx attrKind => do
Attribute.Builtin.ensureNoArgs stx
-- TODO: use the attribute kind
unless attrKind == AttributeKind.global do
throwError "invalid attribute 'pspec', must be global"
-- Lookup the theorem
let env ← getEnv
let thDecl := env.constants.find! thName
let fKey ← MetaM.run' (do
let fExpr ← getPSpecFunArgsExpr false thDecl.type
trace[Progress] "Registering spec theorem for {fExpr}"
-- Convert the function expression to a discrimination tree key
-- We use the default configuration
let config : WhnfCoreConfig := {}
DiscrTree.mkPath fExpr config)
let env := ext.addEntry env (fKey, thName)
setEnv env
trace[Progress] "Saved the environment"
pure ()
}
registerBuiltinAttribute attrImpl
pure { attr := attrImpl, ext := ext }
def PSpecAttr.find? (s : PSpecAttr) (e : Expr) : MetaM (Array Name) := do
-- We use the default configuration
let config : WhnfCoreConfig := {}
(s.ext.getState (← getEnv)).getMatch e config
def PSpecAttr.getState (s : PSpecAttr) : MetaM (DiscrTree Name) := do
pure (s.ext.getState (← getEnv))
def showStoredPSpec : MetaM Unit := do
let st ← pspecAttr.getState
-- TODO: how can we iterate over (at least) the values stored in the tree?
--let s := st.toList.foldl (fun s (f, th) => f!"{s}\n{f} → {th}") f!""
let s := f!"{st}"
IO.println s
end Progress
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