Simproc and Discharger DSLs for Sym.simp

Simproc DSL (sym_simproc)

A syntax category for specifying pre and post simproc chains in Sym.simp variants.

Primitives

• ground — evaluates ground (fully concrete) terms
• telescope — simplifies telescope binders (have-values, arrow hypotheses) but not the final body
• rewrite setName [with discharger] — rewrites using a named theorem set
• rewrite [thm₁, thm₂, ...] [with discharger] — rewrites using inline theorems
• self — recursive simplification (calls the full simplifier)
• none — identity (no simplification)

Combinators

• a >> b — apply a, then apply b to the result (andThen)
• a <|> b — try a, if no progress try b (orElse)

Discharger DSL (sym_discharger)

A syntax category for specifying dischargers used in the with clause of rewrite. Dischargers attempt to prove side conditions of conditional rewrite rules.

Primitives

• self — recursive simplifier discharge (dischargeSimpSelf)
• none — no discharge, only unconditional rewrites apply (dischargeNone)

def Lean.Parser.Sym.Simp.sym_simproc.quot : ParserDescr

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def Lean.Parser.Category.sym_simproc : Category

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• Lean.Parser.Category.sym_simproc = { }

def Lean.Parser.Sym.Simp.sym_discharger.quot : ParserDescr

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def Lean.Parser.Category.sym_discharger : Category

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• Lean.Parser.Category.sym_discharger = { }

def Lean.Parser.Sym.Simp.ground : ParserDescr

Evaluate ground (fully concrete) terms.

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• Lean.Parser.Sym.Simp.ground = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.ground 1024 (Lean.ParserDescr.nonReservedSymbol "ground" false)

def Lean.Parser.Sym.Simp.telescope : ParserDescr

Simplify telescope binders but not the final body.

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• Lean.Parser.Sym.Simp.telescope = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.telescope 1024 (Lean.ParserDescr.nonReservedSymbol "telescope" false)

def Lean.Parser.Sym.Simp.control : ParserDescr

Simplify control-flow expressions (if-then-else, match, cond, dite). Visits only conditions and discriminants. Intended as a pre simproc.

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• Lean.Parser.Sym.Simp.control = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.control 1024 (Lean.ParserDescr.nonReservedSymbol "control" false)

def Lean.Parser.Sym.Simp.arrowTelescope : ParserDescr

Simplify arrow telescopes (p₁ → p₂ → ... → q) without entering binders. Simplifies each pᵢ and q individually. Intended as a pre simproc.

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• Lean.Parser.Sym.Simp.arrowTelescope = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.arrowTelescope 1024 (Lean.ParserDescr.nonReservedSymbol "arrow_telescope" false)

def Lean.Parser.Sym.Simp.rewriteSet : ParserDescr

Rewrite using a named theorem set. Optionally specify a discharger for conditional rewrites.

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def Lean.Parser.Sym.Simp.rewriteInline : ParserDescr

Rewrite using inline theorems. Optionally specify a discharger for conditional rewrites.

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def Lean.Parser.Sym.Simp.self : ParserDescr

Recursive simplification (calls the full simplifier).

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• Lean.Parser.Sym.Simp.self = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.self 1024 (Lean.ParserDescr.nonReservedSymbol "self" false)

def Lean.Parser.Sym.Simp.none : ParserDescr

Identity simproc (no simplification).

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• Lean.Parser.Sym.Simp.none = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.none 1024 (Lean.ParserDescr.nonReservedSymbol "none" false)

def Lean.Parser.Sym.Simp.andThen : TrailingParserDescr

Apply a, then apply b to the result.

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def Lean.Parser.Sym.Simp.orElse : TrailingParserDescr

Try a, if no progress try b.

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def Lean.Parser.Sym.Simp.simprocParen : ParserDescr

Parenthesized simproc expression.

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def Lean.Parser.Sym.Simp.dischSelf : ParserDescr

Recursive simplifier discharge. Calls the full simplifier to prove side conditions.

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• Lean.Parser.Sym.Simp.dischSelf = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.dischSelf 1024 (Lean.ParserDescr.nonReservedSymbol "self" false)

def Lean.Parser.Sym.Simp.dischNone : ParserDescr

No discharge. Only unconditional rewrites will apply.

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• Lean.Parser.Sym.Simp.dischNone = Lean.ParserDescr.node `Lean.Parser.Sym.Simp.dischNone 1024 (Lean.ParserDescr.nonReservedSymbol "none" false)

def Lean.Parser.Sym.Simp.dischParen : ParserDescr

Parenthesized discharger expression.

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register_sym_simp command

Declares a named Sym.simp variant with pre/post simproc chains and optional config overrides.

register_sym_simp myVariant where
  pre  := telescope
  post := ground >> rewrite mySet with self

def Lean.Parser.Category.sym_simp_field : Category

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• Lean.Parser.Category.sym_simp_field = { }

def Lean.Parser.Command.sym_simp_field.quot : ParserDescr

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def Lean.Parser.Command.symSimpFieldPre : ParserDescr

Pre-processing simproc chain.

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def Lean.Parser.Command.symSimpFieldPost : ParserDescr

Post-processing simproc chain.

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def Lean.Parser.Command.symSimpFieldMaxSteps : ParserDescr

Maximum number of simplification steps.

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def Lean.Parser.Command.symSimpFieldMaxDischargeDepth : ParserDescr

Maximum depth of recursive discharge attempts.

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def Lean.Parser.Command.registerSymSimp : ParserDescr

Register a named Sym.simp variant.

register_sym_simp myVariant where
  pre  := telescope
  post := ground >> rewrite [thm1, thm2] with self
  maxSteps := 50000

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