we keep running into examples where working with well-founded recursion is slow because defeq checks (which are all over the place, including failing ones that are back-tracked) unfold well-founded definitions. The definition of a function defined by well-founded recursion should be an implementation detail that should only be peeked inside by the equation generator and the functional induction generator. We now mark the mutual recursive function as irreducible (if the user did not set a flag explicitly), and use `withAtLeastTransparency .all` when producing the equations. Proofs can be fixed by using rewriting, or – a bit blunt, but nice for adjusting existing proofs – using `unseal` (a.k.a. `attribute [local semireducible]`). Mathlib performance does not change a whole lot: http://speed.lean-fro.org/mathlib4/compare/08b82265-75db-4a28-b12b-08751b9ad04a/to/16f46d5e-28b1-41c4-a107-a6f6594841f8 Build instructions -0.126 %, four modules with significant instructions decrease. To reduce impact, these definitions were changed: * `Nat.mod`, to make `1 % n` reduce definitionally, so that `1` as a `Fin 2` literal works nicely. Theorems with larger `Fin` literals tend to need a `unseal Nat.modCore` https://github.com/leanprover/lean4/pull/4098 * `List.ofFn` rewritten to be structurally recursive and not go via `Array.ofFn`: https://github.com/leanprover-community/batteries/pull/784 Alternative designs explored were * Making `WellFounded.fix` irreducible. One benefit is that recursive functions with equal definitions (possibly after instantiating fixed parameters) are defeq; this is used in mathlib to relate [`OrdinalApprox.gfpApprox`](https://leanprover-community.github.io/mathlib4_docs/Mathlib/SetTheory/Ordinal/FixedPointApproximants.html#OrdinalApprox.gfpApprox) with `.lfpApprox`. But the downside is that one cannot use `unseal` in a targeted way, being explicit in which recursive function needs to be reducible here. And in cases where Lean does unwanted unfolding, we’d still unfold the recursive definition once to expose `WellFounded.fix`, leading to large terms for often no good reason. * Defining `WellFounded.fix` to unroll defintionally once before hitting a irreducible `WellFounded.fixF`. This was explored in #4002. It shares most of the ups and downs with the previous variant, with the additional neat benefit that function calls that do not lead to recursive cases (e.g. a `[]` base case) reduce nicely. This means that the majority of existing `rfl` proofs continue to work. Issue #4051, which demonstrates how badly things can go if wf recursive functions can be unrolled, showed that making the recursive function irreducible there leads to noticeably faster elaboration than making `WellFounded.fix` irreducible; this is good evidence that the present PR is the way to go. This fixes https://github.com/leanprover/lean4/issues/3988 --------- Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
192 lines
8.4 KiB
Text
192 lines
8.4 KiB
Text
/-
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Copyright (c) 2019 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import Lean.Attributes
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import Lean.ScopedEnvExtension
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namespace Lean
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/--
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Reducibility status for a definition.
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-/
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inductive ReducibilityStatus where
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| reducible | semireducible | irreducible
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deriving Inhabited, Repr, BEq
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def ReducibilityStatus.toAttrString : ReducibilityStatus → String
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| .reducible => "[reducible]"
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| .irreducible => "[irreducible]"
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| .semireducible => "[semireducible]"
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builtin_initialize reducibilityCoreExt : PersistentEnvExtension (Name × ReducibilityStatus) (Name × ReducibilityStatus) (NameMap ReducibilityStatus) ←
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registerPersistentEnvExtension {
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name := `reducibilityCore
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mkInitial := pure {}
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addImportedFn := fun _ _ => pure {}
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addEntryFn := fun (s : NameMap ReducibilityStatus) (p : Name × ReducibilityStatus) => s.insert p.1 p.2
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exportEntriesFn := fun m =>
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let r : Array (Name × ReducibilityStatus) := m.fold (fun a n p => a.push (n, p)) #[]
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r.qsort (fun a b => Name.quickLt a.1 b.1)
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statsFn := fun s => "reducibility attribute core extension" ++ Format.line ++ "number of local entries: " ++ format s.size
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}
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builtin_initialize reducibilityExtraExt : SimpleScopedEnvExtension (Name × ReducibilityStatus) (SMap Name ReducibilityStatus) ←
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registerSimpleScopedEnvExtension {
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name := `reducibilityExtra
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initial := {}
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addEntry := fun d (declName, status) => d.insert declName status
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finalizeImport := fun d => d.switch
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}
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@[export lean_get_reducibility_status]
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def getReducibilityStatusCore (env : Environment) (declName : Name) : ReducibilityStatus :=
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let m := reducibilityExtraExt.getState env
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if let some status := m.find? declName then
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status
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else match env.getModuleIdxFor? declName with
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| some modIdx =>
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match (reducibilityCoreExt.getModuleEntries env modIdx).binSearch (declName, .semireducible) (fun a b => Name.quickLt a.1 b.1) with
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| some (_, status) => status
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| none => .semireducible
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| none => (reducibilityCoreExt.getState env).find? declName |>.getD .semireducible
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private def setReducibilityStatusCore (env : Environment) (declName : Name) (status : ReducibilityStatus) (attrKind : AttributeKind) (currNamespace : Name) : Environment :=
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if attrKind matches .global then
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match env.getModuleIdxFor? declName with
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| some _ =>
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-- Trying to set the attribute of a declaration defined in an imported module.
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reducibilityExtraExt.addEntry env (declName, status)
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| none =>
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--
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reducibilityCoreExt.addEntry env (declName, status)
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else
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-- `scoped` and `local` must be handled by `reducibilityExtraExt`
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reducibilityExtraExt.addCore env (declName, status) attrKind currNamespace
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@[export lean_set_reducibility_status]
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private def setReducibilityStatusImp (env : Environment) (declName : Name) (status : ReducibilityStatus) : Environment :=
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setReducibilityStatusCore env declName status .global .anonymous
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/-
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TODO: it would be great if we could distinguish between the following two situations
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1-
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```
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@[reducible] def foo := ...
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```
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2-
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```
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def foo := ...
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...
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attribute [reducible] foo
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```
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Reason: the second one is problematic if user has add simp theorems or TC instances that include `foo`.
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Recall that the discrimination trees unfold `[reducible]` declarations while indexing new entries.
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-/
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register_builtin_option allowUnsafeReducibility : Bool := {
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defValue := false
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descr := "enables users to modify the reducibility settings for declarations even when such changes are deemed potentially hazardous. For example, `simp` and type class resolution maintain term indices where reducible declarations are expanded."
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}
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private def validate (declName : Name) (status : ReducibilityStatus) (attrKind : AttributeKind) : CoreM Unit := do
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let suffix := "use `set_option allowUnsafeReducibility true` to override reducibility status validation"
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unless allowUnsafeReducibility.get (← getOptions) do
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match (← getConstInfo declName) with
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| .defnInfo _ =>
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let statusOld := getReducibilityStatusCore (← getEnv) declName
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match attrKind with
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| .scoped =>
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throwError "failed to set reducibility status for `{declName}`, the `scoped` modifier is not recommended for this kind of attribute\n{suffix}"
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| .global =>
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if (← getEnv).getModuleIdxFor? declName matches some _ then
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throwError "failed to set reducibility status, `{declName}` has not been defined in this file, consider using the `local` modifier\n{suffix}"
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match status with
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| .reducible =>
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unless statusOld matches .semireducible do
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throwError "failed to set `[reducible]`, `{declName}` is not currently `[semireducible]`, but `{statusOld.toAttrString}`\n{suffix}"
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| .irreducible =>
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unless statusOld matches .semireducible do
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throwError "failed to set `[irreducible]`, `{declName}` is not currently `[semireducible]`, but `{statusOld.toAttrString}`\n{suffix}"
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| .semireducible =>
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throwError "failed to set `[semireducible]` for `{declName}`, declarations are `[semireducible]` by default\n{suffix}"
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| .local =>
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match status with
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| .reducible =>
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throwError "failed to set `[local reducible]` for `{declName}`, recall that `[reducible]` affects the term indexing datastructures used by `simp` and type class resolution\n{suffix}"
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| .irreducible =>
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unless statusOld matches .semireducible do
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throwError "failed to set `[local irreducible]`, `{declName}` is currently `{statusOld.toAttrString}`, `[semireducible]` expected\n{suffix}"
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| .semireducible =>
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unless statusOld matches .irreducible do
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throwError "failed to set `[local semireducible]`, `{declName}` is currently `{statusOld.toAttrString}`, `[irreducible]` expected\n{suffix}"
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| _ => throwError "failed to set reducibility status, `{declName}` is not a definition\n{suffix}"
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private def addAttr (status : ReducibilityStatus) (declName : Name) (stx : Syntax) (attrKind : AttributeKind) : AttrM Unit := do
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Attribute.Builtin.ensureNoArgs stx
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validate declName status attrKind
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let ns ← getCurrNamespace
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modifyEnv fun env => setReducibilityStatusCore env declName status attrKind ns
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builtin_initialize
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registerBuiltinAttribute {
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ref := by exact decl_name%
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name := `irreducible
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descr := "irreducible declaration"
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add := addAttr .irreducible
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applicationTime := .afterTypeChecking
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}
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builtin_initialize
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registerBuiltinAttribute {
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ref := by exact decl_name%
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name := `reducible
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descr := "reducible declaration"
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add := addAttr .reducible
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applicationTime := .afterTypeChecking
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}
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builtin_initialize
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registerBuiltinAttribute {
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ref := by exact decl_name%
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name := `semireducible
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descr := "semireducible declaration"
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add := addAttr .semireducible
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applicationTime := .afterTypeChecking
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}
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/-- Return the reducibility attribute for the given declaration. -/
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def getReducibilityStatus [Monad m] [MonadEnv m] (declName : Name) : m ReducibilityStatus := do
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return getReducibilityStatusCore (← getEnv) declName
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/-- Set the reducibility attribute for the given declaration. -/
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def setReducibilityStatus [Monad m] [MonadEnv m] (declName : Name) (s : ReducibilityStatus) : m Unit := do
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modifyEnv fun env => setReducibilityStatusCore env declName s .global .anonymous
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/-- Set the given declaration as `[reducible]` -/
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def setReducibleAttribute [Monad m] [MonadEnv m] (declName : Name) : m Unit := do
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setReducibilityStatus declName ReducibilityStatus.reducible
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/-- Return `true` if the given declaration has been marked as `[reducible]`. -/
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def isReducible [Monad m] [MonadEnv m] (declName : Name) : m Bool := do
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match (← getReducibilityStatus declName) with
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| .reducible => return true
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| _ => return false
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/-- Return `true` if the given declaration has been marked as `[irreducible]` -/
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def isIrreducible [Monad m] [MonadEnv m] (declName : Name) : m Bool := do
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match (← getReducibilityStatus declName) with
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| .irreducible => return true
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| _ => return false
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/-- Set the given declaration as `[irreducible]` -/
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def setIrreducibleAttribute [Monad m] [MonadEnv m] (declName : Name) : m Unit := do
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setReducibilityStatus declName ReducibilityStatus.irreducible
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end Lean
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