structure Lean.Meta.Sym.Simp.Theorem : Type

A simplification theorem for the structural simplifier.

Contains both the theorem expression and a precomputed pattern for efficient unification during rewriting.

• expr : Expr

  The theorem expression, typically Expr.const declName for a named theorem.

• pattern : Pattern

  Precomputed pattern extracted from the theorem's type for efficient matching.

• rhs : Expr

  Right-hand side of the equation.

• perm : Bool

  If true, the theorem is a permutation rule (e.g., x + y = y + x). Rewriting is only applied when the result is strictly less than the input (using acLt), preventing infinite loops.

@[implicit_reducible]

instance Lean.Meta.Sym.Simp.instInhabitedTheorem : Inhabited Theorem

Equations

• Lean.Meta.Sym.Simp.instInhabitedTheorem = { default := Lean.Meta.Sym.Simp.instInhabitedTheorem.default }

def Lean.Meta.Sym.Simp.instInhabitedTheorem.default : Theorem

Equations

• Lean.Meta.Sym.Simp.instInhabitedTheorem.default = { expr := default, pattern := default, rhs := default, perm := default }

@[implicit_reducible]

instance Lean.Meta.Sym.Simp.instBEqTheorem : BEq Theorem

Equations

• Lean.Meta.Sym.Simp.instBEqTheorem = { beq := fun (thm₁ thm₂ : Lean.Meta.Sym.Simp.Theorem) => thm₁.expr == thm₂.expr }

structure Lean.Meta.Sym.Simp.Theorems : Type

Collection of simplification theorems available to the simplifier.

• thms : DiscrTree Theorem

@[implicit_reducible]

instance Lean.Meta.Sym.Simp.instInhabitedTheorems : Inhabited Theorems

Equations

• Lean.Meta.Sym.Simp.instInhabitedTheorems = { default := Lean.Meta.Sym.Simp.instInhabitedTheorems.default }

def Lean.Meta.Sym.Simp.instInhabitedTheorems.default : Theorems

Equations

• Lean.Meta.Sym.Simp.instInhabitedTheorems.default = { thms := default }

def Lean.Meta.Sym.Simp.Theorems.insert (thms : Theorems) (thm : Theorem) : Theorems

Equations

• thms.insert thm = { thms := Lean.Meta.Sym.insertPattern thms.thms thm.pattern thm }

def Lean.Meta.Sym.Simp.Theorems.getMatch (thms : Theorems) (e : Expr) : Array Theorem

Equations

• thms.getMatch e = Lean.Meta.Sym.getMatch thms.thms e

def Lean.Meta.Sym.Simp.Theorems.getMatchWithExtra (thms : Theorems) (e : Expr) : Array (Theorem × Nat)

Equations

• thms.getMatchWithExtra e = Lean.Meta.Sym.getMatchWithExtra thms.thms e

def Lean.Meta.Sym.Simp.isPerm (numVars : Nat) (lhs rhs : Expr) : Bool

Equations

• Lean.Meta.Sym.Simp.isPerm numVars lhs rhs = match (ReaderT.run (Lean.Meta.Sym.Simp.isPermAux✝ lhs rhs) 0).run (Array.replicate numVars none) with | Except.ok a => true | x => false

def Lean.Meta.Sym.Simp.mkTheoremFromDecl (declName : Name) : MetaM Theorem

Equations

• One or more equations did not get rendered due to their size.

def Lean.Meta.Sym.Simp.mkTheoremFromExpr (e : Expr) : MetaM Theorem

Create a Theorem from a proof expression. Handles equalities, ¬, ↔, and propositions.

Equations

• One or more equations did not get rendered due to their size.

@[reducible, inline]

abbrev Lean.Meta.Sym.Simp.SymSimpExtension : Type

Environment extension storing a set of Sym.Simp theorems. Each named set gets its own extension, created by registerSymSimpAttr.

Equations

• Lean.Meta.Sym.Simp.SymSimpExtension = Lean.SimpleScopedEnvExtension Lean.Meta.Sym.Simp.Theorem Lean.Meta.Sym.Simp.Theorems

def Lean.Meta.Sym.Simp.SymSimpExtension.getTheorems (ext : SymSimpExtension) : CoreM Theorems

Equations

• ext.getTheorems = do let __do_lift ← Lean.getEnv pure (Lean.ScopedEnvExtension.getState ext __do_lift)

def Lean.Meta.Sym.Simp.mkSymSimpExt (name : Name := by exact decl_name%) : IO SymSimpExtension

Equations

• One or more equations did not get rendered due to their size.

@[reducible, inline]

abbrev Lean.Meta.Sym.Simp.SymSimpExtensionMap : Type

Equations

• Lean.Meta.Sym.Simp.SymSimpExtensionMap = Std.HashMap Lean.Name Lean.Meta.Sym.Simp.SymSimpExtension

opaque Lean.Meta.Sym.Simp.symSimpExtensionMapRef : IO.Ref SymSimpExtensionMap

def Lean.Meta.Sym.Simp.getSymSimpExtension? (attrName : Name) : CoreM (Option SymSimpExtension)

Equations

• One or more equations did not get rendered due to their size.