6b9ac691cb
Adds three foundation lemmas about `tokenize`:
· tokenize_lparen_cons : tokenize ('(' :: rest) = lparen :: tokenize rest
· tokenize_rparen_cons : tokenize (')' :: rest) = rparen :: tokenize rest
· tokenize_space_cons : tokenize (' ' :: rest) = tokenize rest
These are the trivial cases — pure unfolding of `tokenizeAux` on
single-char-token branches.
The full Phase 3 (`tokenize (toLeanSource v).toList = toTokens v`)
requires four further substantial lemmas:
· readIdent_split : reading an ident sequence followed by a
non-ident-rest char (or end of input) yields
exactly the accumulated string.
· readStrLit_split : reading an escapeStrLit-encoded body until
the closing `"` recovers the original string.
· tokenize_app_clean: tokenize distributes over a concatenation
where the prefix ends "cleanly" (rparen,
whitespace, or strLit close).
· tokenize_render_X: induction over each meta-mirror type using
the above plus IH on sub-values.
Each is multi-page Lean reasoning about `String`/`List Char`/
`readIdent`/`readStrLit` distribution. The proof sketches are
documented inline.
The token-level universal (already proven) plus closed-instance
`decide` tests cover the round-trip operationally. Adding the
Phase 3 universal would let us state
∀ t, fromLeanSource? (toLeanSource t) = some t
without any closed-instance restrictions.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
924 lines
40 KiB
Text
924 lines
40 KiB
Text
/-
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Infoductor.Foundation.MetaParse — the inverse of `toLeanSource`
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=================================================================
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A hand-written tokenizer + recursive-descent parser that reads
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the Lean source emitted by the `toLeanSource` family of renderers
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and reconstructs the original `MetaCTerm` / `MetaClassifier` /
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`MetaArtifact` / `Lean.Name`.
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The bridge's loop closes at the *string* level, in Lean itself:
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no external elaborator needed.
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Implementation strategy:
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· `Token` is a four-arm inductive (parens, ident chains, string
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literals, num literals).
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· `tokenize` is fuel-based, so it's structurally recursive on
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the fuel parameter (no `partial` needed) — fuel is the input
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list length, which is always sufficient.
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· Parsers per type are likewise fuel-based. Each successful
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parse consumes ≥ 1 token, so fuel = `tokens.length + 1` is
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always enough for any well-formed input.
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· String escape: only `"` and `\` are escaped (renderer-side
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`escapeStrLit` mirrors this exactly).
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-/
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import Infoductor.Foundation.Meta
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namespace Infoductor
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-- ── Tokens ──────────────────────────────────────────────────────────────────
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inductive Token where
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| lparen : Token
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| rparen : Token
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| ident : String → Token
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| strLit : String → Token
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| numLit : Nat → Token
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deriving Repr, DecidableEq
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-- ── Character predicates ───────────────────────────────────────────────────
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def isIdentStartChar (c : Char) : Bool :=
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c.isAlpha || c == '_'
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def isIdentRestChar (c : Char) : Bool :=
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c.isAlpha || c.isDigit || c == '_' || c == '.'
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def isWhitespace (c : Char) : Bool :=
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c == ' ' || c == '\n' || c == '\t' || c == '\r'
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-- ── Tokenizer helpers (fuel-based for kernel termination) ──────────────────
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/-- Read identifier chars until a non-identifier char. Returns
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(read string, remaining chars). Fuel-based for kernel
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termination; the tokenizer feeds in `chars.length` fuel
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which is always sufficient. -/
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def readIdent : Nat → List Char → String → String × List Char
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| 0, chars, acc => (acc, chars)
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| _+1, [], acc => (acc, [])
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| n+1, c :: rest, acc =>
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if isIdentRestChar c then readIdent n rest (acc.push c)
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else (acc, c :: rest)
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/-- Read a decimal number. Fuel-based. -/
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def readNum : Nat → List Char → Nat → Nat × List Char
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| 0, chars, acc => (acc, chars)
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| _+1, [], acc => (acc, [])
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| n+1, c :: rest, acc =>
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if c.isDigit then
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readNum n rest (acc * 10 + (c.toNat - '0'.toNat))
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else (acc, c :: rest)
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/-- Read characters of a string literal until the closing `"`,
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handling `\"` and `\\` escapes. Fuel-based. -/
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def readStrLit : Nat → List Char → String → Option (String × List Char)
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| 0, _, _ => none
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| _+1, [], _ => none
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| _+1, '"' :: rest, acc => some (acc, rest)
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| n+1, '\\' :: '"' :: rest, acc => readStrLit n rest (acc.push '"')
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| n+1, '\\' :: '\\' :: rest, acc => readStrLit n rest (acc.push '\\')
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| n+1, c :: rest, acc => readStrLit n rest (acc.push c)
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-- `escapeStrLit` lives in Foundation.Meta now (used by both
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-- the renderer and the parser); see Meta.lean for the definition.
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-- ── Tokenizer ──────────────────────────────────────────────────────────────
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/-- Tokenize a `List Char` into `List Token`. Fuel-based for
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kernel termination; the top-level `tokenize` provides
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`chars.length + 1` fuel, which is always sufficient. -/
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def tokenizeAux : Nat → List Char → List Token
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| 0, _ => []
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| _+1, [] => []
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| n+1, '(' :: rest => Token.lparen :: tokenizeAux n rest
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| n+1, ')' :: rest => Token.rparen :: tokenizeAux n rest
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| n+1, '"' :: rest =>
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match readStrLit (n+1) rest "" with
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| some (s, rest') => Token.strLit s :: tokenizeAux n rest'
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| none => []
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| n+1, c :: rest =>
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if isWhitespace c then tokenizeAux n rest
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else if c.isDigit then
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let (num, rest') := readNum (n+1) (c :: rest) 0
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Token.numLit num :: tokenizeAux n rest'
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else if isIdentStartChar c then
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let (ident, rest') := readIdent (n+1) (c :: rest) ""
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Token.ident ident :: tokenizeAux n rest'
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else
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[]
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/-- Top-level tokenizer. Fuel = `chars.length + 1` is always
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sufficient since each token-emitting branch peels ≥ 1 char. -/
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def tokenize (chars : List Char) : List Token :=
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tokenizeAux (chars.length + 1) chars
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/-- Tokenize a `String` directly. -/
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def tokenizeStr (s : String) : List Token :=
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tokenize s.toList
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-- ── Parsers ────────────────────────────────────────────────────────────────
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-- All parsers fuel-based. Recursion structurally on the Nat
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-- parameter, so they're total without `partial`.
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/-- Parse a `Lean.Name`. Recognises:
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· `Lean.Name.anonymous` (atomic)
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· `(Lean.Name.str <name> "<str>")` (recursive)
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· `(Lean.Name.num <name> <nat>)` (recursive)
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The renderer no longer wraps recursive sub-name calls in
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extra parens (post-fix), so the parser handles only the
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canonical bare-atomic + constructor-app forms. -/
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def parseName?Aux : Nat → List Token → Option (Lean.Name × List Token)
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| 0, _ => none
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| _+1, Token.ident "Lean.Name.anonymous" :: rest =>
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some (Lean.Name.anonymous, rest)
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| n+1, Token.lparen :: Token.ident "Lean.Name.str" :: rest =>
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match parseName?Aux n rest with
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| some (p, Token.strLit s :: Token.rparen :: rest') =>
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some (Lean.Name.str p s, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Lean.Name.num" :: rest =>
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match parseName?Aux n rest with
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| some (p, Token.numLit k :: Token.rparen :: rest') =>
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some (Lean.Name.num p k, rest')
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| _ => none
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| _, _ => none
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/-- Parse a `MetaClassifier`. -/
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def parseClassifier?Aux : Nat → List Token → Option (MetaClassifier × List Token)
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| 0, _ => none
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| _+1, Token.ident "Infoductor.MetaClassifier.always" :: rest =>
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some (MetaClassifier.always, rest)
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| _+1, Token.ident "Infoductor.MetaClassifier.never" :: rest =>
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some (MetaClassifier.never, rest)
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.atDecl" :: rest =>
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match parseName?Aux n rest with
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| some (nm, Token.rparen :: rest') => some (MetaClassifier.atDecl nm, rest')
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| _ => none
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| _+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.inFile" :: rest =>
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match rest with
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| Token.strLit s :: Token.rparen :: rest' =>
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some (MetaClassifier.inFile s, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.underAttribute" :: rest =>
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match parseName?Aux n rest with
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| some (nm, Token.rparen :: rest') =>
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some (MetaClassifier.underAttribute nm, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.dependencyOf" :: rest =>
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match parseName?Aux n rest with
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| some (nm, Token.rparen :: rest') =>
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some (MetaClassifier.dependencyOf nm, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.inNamespace" :: rest =>
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match parseName?Aux n rest with
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| some (nm, Token.rparen :: rest') =>
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some (MetaClassifier.inNamespace nm, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.meet" :: rest =>
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match parseClassifier?Aux n rest with
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| some (a, rest') =>
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match parseClassifier?Aux n rest' with
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| some (b, Token.rparen :: rest'') =>
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some (MetaClassifier.meet a b, rest'')
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| _ => none
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaClassifier.join" :: rest =>
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match parseClassifier?Aux n rest with
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| some (a, rest') =>
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match parseClassifier?Aux n rest' with
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| some (b, Token.rparen :: rest'') =>
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some (MetaClassifier.join a b, rest'')
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| _ => none
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| _ => none
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| _, _ => none
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/-- Parse a `MetaCTerm`. -/
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def parseMetaCTerm?Aux : Nat → List Token → Option (MetaCTerm × List Token)
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| 0, _ => none
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| _+1, Token.ident "Infoductor.MetaCTerm.empty" :: rest =>
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some (MetaCTerm.empty, rest)
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.ident" :: rest =>
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match parseName?Aux n rest with
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| some (nm, Token.rparen :: rest') => some (MetaCTerm.ident nm, rest')
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| _ => none
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| _+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.sym" :: rest =>
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match rest with
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| Token.strLit s :: Token.rparen :: rest' =>
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some (MetaCTerm.sym s, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.app" :: rest =>
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match parseMetaCTerm?Aux n rest with
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| some (f, rest') =>
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match parseMetaCTerm?Aux n rest' with
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| some (a, Token.rparen :: rest'') =>
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some (MetaCTerm.app f a, rest'')
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| _ => none
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.lam" :: rest =>
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match rest with
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| Token.strLit x :: rest' =>
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match parseMetaCTerm?Aux n rest' with
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| some (t, Token.rparen :: rest'') => some (MetaCTerm.lam x t, rest'')
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| _ => none
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.plam" :: rest =>
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match rest with
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| Token.strLit i :: rest' =>
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match parseMetaCTerm?Aux n rest' with
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| some (t, Token.rparen :: rest'') => some (MetaCTerm.plam i t, rest'')
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| _ => none
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.comp" :: rest =>
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match rest with
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| Token.strLit s :: rest1 =>
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match parseMetaCTerm?Aux n rest1 with
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| some (A, rest2) =>
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match parseClassifier?Aux n rest2 with
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| some (φ, rest3) =>
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match parseMetaCTerm?Aux n rest3 with
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| some (u, rest4) =>
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match parseMetaCTerm?Aux n rest4 with
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| some (t, Token.rparen :: rest5) =>
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some (MetaCTerm.comp s A φ u t, rest5)
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| _ => none
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| _ => none
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| _ => none
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| _ => none
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaCTerm.transp" :: rest =>
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match rest with
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| Token.strLit s :: rest1 =>
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match parseMetaCTerm?Aux n rest1 with
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| some (A, rest2) =>
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match parseClassifier?Aux n rest2 with
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| some (φ, rest3) =>
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match parseMetaCTerm?Aux n rest3 with
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| some (t, Token.rparen :: rest4) =>
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some (MetaCTerm.transp s A φ t, rest4)
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| _ => none
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| _ => none
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| _ => none
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| _ => none
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| _, _ => none
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/-- Parse a `MetaArtifact`. -/
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def parseArtifact?Aux : Nat → List Token → Option (MetaArtifact × List Token)
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| 0, _ => none
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| _+1, Token.ident "Infoductor.MetaArtifact.empty" :: rest =>
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some (MetaArtifact.empty, rest)
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| _+1, Token.lparen :: Token.ident "Infoductor.MetaArtifact.source" :: rest =>
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match rest with
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| Token.strLit s :: Token.rparen :: rest' =>
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some (MetaArtifact.source s, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaArtifact.refTo" :: rest =>
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match parseName?Aux n rest with
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| some (nm, Token.rparen :: rest') =>
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some (MetaArtifact.refTo nm, rest')
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| _ => none
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| n+1, Token.lparen :: Token.ident "Infoductor.MetaArtifact.cterm" :: rest =>
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match parseMetaCTerm?Aux n rest with
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| some (m, Token.rparen :: rest') =>
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some (MetaArtifact.cterm m, rest')
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| _ => none
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| _, _ => none
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-- ── Top-level wrappers ─────────────────────────────────────────────────────
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-- Fuel = `tokens.length + 1` is always sufficient: every successful
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-- parse arm consumes ≥ 1 token, so depth is bounded by length.
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def parseName? (tokens : List Token) : Option (Lean.Name × List Token) :=
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parseName?Aux (tokens.length + 1) tokens
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def parseClassifier? (tokens : List Token) : Option (MetaClassifier × List Token) :=
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parseClassifier?Aux (tokens.length + 1) tokens
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def parseMetaCTerm? (tokens : List Token) : Option (MetaCTerm × List Token) :=
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parseMetaCTerm?Aux (tokens.length + 1) tokens
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def parseArtifact? (tokens : List Token) : Option (MetaArtifact × List Token) :=
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parseArtifact?Aux (tokens.length + 1) tokens
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def MetaCTerm.fromLeanSource? (s : String) : Option MetaCTerm :=
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match parseMetaCTerm? (tokenizeStr s) with
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| some (t, []) => some t
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| _ => none
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def MetaClassifier.fromLeanSource? (s : String) : Option MetaClassifier :=
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match parseClassifier? (tokenizeStr s) with
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| some (φ, []) => some φ
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| _ => none
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def MetaArtifact.fromLeanSource? (s : String) : Option MetaArtifact :=
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match parseArtifact? (tokenizeStr s) with
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| some (a, []) => some a
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| _ => none
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-- ── Canonical token forms — direct meta-mirror → List Token ────────────────
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-- Each function mirrors the corresponding `toLeanSource` renderer
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-- but produces tokens directly, bypassing the String layer. These
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-- are the canonical token forms against which parser correctness
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-- is proven. The relationship `tokenize ∘ toLeanSource = toTokens`
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-- is established separately as a String-level lemma.
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def nameToTokens : Lean.Name → List Token
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| .anonymous => [Token.ident "Lean.Name.anonymous"]
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| .str p s =>
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[Token.lparen, Token.ident "Lean.Name.str"] ++ nameToTokens p ++
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[Token.strLit s, Token.rparen]
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| .num p k =>
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[Token.lparen, Token.ident "Lean.Name.num"] ++ nameToTokens p ++
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[Token.numLit k, Token.rparen]
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def MetaClassifier.toTokens : MetaClassifier → List Token
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| .always => [Token.ident "Infoductor.MetaClassifier.always"]
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| .never => [Token.ident "Infoductor.MetaClassifier.never"]
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| .atDecl n =>
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.atDecl"] ++
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nameToTokens n ++ [Token.rparen]
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| .inFile s =>
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.inFile",
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Token.strLit s, Token.rparen]
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| .underAttribute n =>
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.underAttribute"] ++
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nameToTokens n ++ [Token.rparen]
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| .dependencyOf n =>
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.dependencyOf"] ++
|
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nameToTokens n ++ [Token.rparen]
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| .inNamespace n =>
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.inNamespace"] ++
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nameToTokens n ++ [Token.rparen]
|
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| .meet a b =>
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.meet"] ++
|
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toTokens a ++ toTokens b ++ [Token.rparen]
|
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| .join a b =>
|
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[Token.lparen, Token.ident "Infoductor.MetaClassifier.join"] ++
|
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toTokens a ++ toTokens b ++ [Token.rparen]
|
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|
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def MetaCTerm.toTokens : MetaCTerm → List Token
|
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| .ident n =>
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[Token.lparen, Token.ident "Infoductor.MetaCTerm.ident"] ++
|
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nameToTokens n ++ [Token.rparen]
|
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| .sym s =>
|
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[Token.lparen, Token.ident "Infoductor.MetaCTerm.sym",
|
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Token.strLit s, Token.rparen]
|
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| .app f a =>
|
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[Token.lparen, Token.ident "Infoductor.MetaCTerm.app"] ++
|
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toTokens f ++ toTokens a ++ [Token.rparen]
|
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| .lam x t =>
|
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[Token.lparen, Token.ident "Infoductor.MetaCTerm.lam",
|
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Token.strLit x] ++ toTokens t ++ [Token.rparen]
|
||
| .plam i t =>
|
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[Token.lparen, Token.ident "Infoductor.MetaCTerm.plam",
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Token.strLit i] ++ toTokens t ++ [Token.rparen]
|
||
| .comp s A φ u t =>
|
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[Token.lparen, Token.ident "Infoductor.MetaCTerm.comp",
|
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Token.strLit s] ++ toTokens A ++ φ.toTokens ++
|
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toTokens u ++ toTokens t ++ [Token.rparen]
|
||
| .transp s A φ t =>
|
||
[Token.lparen, Token.ident "Infoductor.MetaCTerm.transp",
|
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Token.strLit s] ++ toTokens A ++ φ.toTokens ++
|
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toTokens t ++ [Token.rparen]
|
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| .empty => [Token.ident "Infoductor.MetaCTerm.empty"]
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|
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def MetaArtifact.toTokens : MetaArtifact → List Token
|
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| .source s => [Token.lparen, Token.ident "Infoductor.MetaArtifact.source",
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Token.strLit s, Token.rparen]
|
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| .declAt _ => [] -- not source-renderable; toTokens undefined for this arm
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| .cterm m => [Token.lparen, Token.ident "Infoductor.MetaArtifact.cterm"] ++
|
||
m.toTokens ++ [Token.rparen]
|
||
| .refTo n => [Token.lparen, Token.ident "Infoductor.MetaArtifact.refTo"] ++
|
||
nameToTokens n ++ [Token.rparen]
|
||
| .empty => [Token.ident "Infoductor.MetaArtifact.empty"]
|
||
|
||
-- ── Size measures (for fuel bookkeeping in proofs) ─────────────────────────
|
||
|
||
def nameDepth : Lean.Name → Nat
|
||
| .anonymous => 1
|
||
| .str p _ => nameDepth p + 1
|
||
| .num p _ => nameDepth p + 1
|
||
|
||
def classifierDepth : MetaClassifier → Nat
|
||
| .always | .never => 1
|
||
| .atDecl n => nameDepth n + 1
|
||
| .inFile _ => 2
|
||
| .underAttribute n => nameDepth n + 1
|
||
| .dependencyOf n => nameDepth n + 1
|
||
| .inNamespace n => nameDepth n + 1
|
||
| .meet a b => max (classifierDepth a) (classifierDepth b) + 1
|
||
| .join a b => max (classifierDepth a) (classifierDepth b) + 1
|
||
|
||
def cTermDepth : MetaCTerm → Nat
|
||
| .ident n => nameDepth n + 1
|
||
| .sym _ => 2
|
||
| .empty => 1
|
||
| .lam _ t | .plam _ t => cTermDepth t + 1
|
||
| .app f a => max (cTermDepth f) (cTermDepth a) + 1
|
||
| .comp _ A φ u t =>
|
||
max (max (cTermDepth A) (classifierDepth φ))
|
||
(max (cTermDepth u) (cTermDepth t)) + 1
|
||
| .transp _ A φ t =>
|
||
max (max (cTermDepth A) (classifierDepth φ)) (cTermDepth t) + 1
|
||
|
||
def artifactDepth : MetaArtifact → Nat
|
||
| .source _ => 2
|
||
| .declAt _ => 0 -- not source-encodable; round-trip excluded
|
||
| .cterm m => cTermDepth m + 1
|
||
| .refTo n => nameDepth n + 1
|
||
| .empty => 1
|
||
|
||
/-- A `MetaArtifact` is *supported* by the round-trip iff it does
|
||
not carry a `Lean.Syntax` (which cannot be source-rendered).
|
||
All other arms are supported. -/
|
||
def MetaArtifact.supported : MetaArtifact → Bool
|
||
| .declAt _ => false
|
||
| _ => true
|
||
|
||
-- ── Parser correctness on toTokens (Phase 2) ──────────────────────────────
|
||
-- Universal theorems witnessing that each parser, when fed the
|
||
-- canonical token form of a value plus arbitrary trailing tokens,
|
||
-- reconstructs the value exactly and leaves the trailing tokens
|
||
-- untouched. Provided fuel is at least the depth of the value.
|
||
-- Proofs are by structural induction on the meta-mirror; no
|
||
-- String reasoning is needed.
|
||
|
||
theorem parseName?Aux_correct :
|
||
∀ (n : Lean.Name) (rest : List Token) (fuel : Nat),
|
||
fuel ≥ nameDepth n →
|
||
parseName?Aux fuel (nameToTokens n ++ rest) = some (n, rest)
|
||
| .anonymous, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [nameDepth] at h
|
||
· simp [nameToTokens, parseName?Aux]
|
||
| .str p s, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [nameDepth] at h
|
||
· simp only [nameToTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseName?Aux]
|
||
have hp : f ≥ nameDepth p := by simp [nameDepth] at h; omega
|
||
have ih := parseName?Aux_correct p
|
||
(Token.strLit s :: Token.rparen :: rest) f hp
|
||
rw [ih]
|
||
| .num p k, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [nameDepth] at h
|
||
· simp only [nameToTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseName?Aux]
|
||
have hp : f ≥ nameDepth p := by simp [nameDepth] at h; omega
|
||
have ih := parseName?Aux_correct p
|
||
(Token.numLit k :: Token.rparen :: rest) f hp
|
||
rw [ih]
|
||
|
||
theorem parseClassifier?Aux_correct :
|
||
∀ (φ : MetaClassifier) (rest : List Token) (fuel : Nat),
|
||
fuel ≥ classifierDepth φ →
|
||
parseClassifier?Aux fuel (φ.toTokens ++ rest) = some (φ, rest)
|
||
| .always, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp [MetaClassifier.toTokens, parseClassifier?Aux]
|
||
| .never, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp [MetaClassifier.toTokens, parseClassifier?Aux]
|
||
| .atDecl n, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp only [MetaClassifier.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseClassifier?Aux]
|
||
have hn : f ≥ nameDepth n := by simp [classifierDepth] at h; omega
|
||
rw [parseName?Aux_correct n (Token.rparen :: rest) f hn]
|
||
| .inFile s, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp [MetaClassifier.toTokens, parseClassifier?Aux]
|
||
| .underAttribute n, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp only [MetaClassifier.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseClassifier?Aux]
|
||
have hn : f ≥ nameDepth n := by
|
||
simp [classifierDepth] at h; omega
|
||
rw [parseName?Aux_correct n (Token.rparen :: rest) f hn]
|
||
| .dependencyOf n, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp only [MetaClassifier.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseClassifier?Aux]
|
||
have hn : f ≥ nameDepth n := by
|
||
simp [classifierDepth] at h; omega
|
||
rw [parseName?Aux_correct n (Token.rparen :: rest) f hn]
|
||
| .inNamespace n, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp only [MetaClassifier.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseClassifier?Aux]
|
||
have hn : f ≥ nameDepth n := by
|
||
simp [classifierDepth] at h; omega
|
||
rw [parseName?Aux_correct n (Token.rparen :: rest) f hn]
|
||
| .meet a b, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp only [MetaClassifier.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseClassifier?Aux]
|
||
have ha : f ≥ classifierDepth a := by
|
||
simp [classifierDepth] at h; omega
|
||
have hb : f ≥ classifierDepth b := by
|
||
simp [classifierDepth] at h; omega
|
||
simp only [parseClassifier?Aux_correct a _ f ha,
|
||
parseClassifier?Aux_correct b _ f hb]
|
||
| .join a b, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [classifierDepth] at h
|
||
· simp only [MetaClassifier.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseClassifier?Aux]
|
||
have ha : f ≥ classifierDepth a := by
|
||
simp [classifierDepth] at h; omega
|
||
have hb : f ≥ classifierDepth b := by
|
||
simp [classifierDepth] at h; omega
|
||
simp only [parseClassifier?Aux_correct a _ f ha,
|
||
parseClassifier?Aux_correct b _ f hb]
|
||
|
||
theorem parseMetaCTerm?Aux_correct :
|
||
∀ (t : MetaCTerm) (rest : List Token) (fuel : Nat),
|
||
fuel ≥ cTermDepth t →
|
||
parseMetaCTerm?Aux fuel (t.toTokens ++ rest) = some (t, rest)
|
||
| .empty, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp [MetaCTerm.toTokens, parseMetaCTerm?Aux]
|
||
| .ident n, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp only [MetaCTerm.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseMetaCTerm?Aux]
|
||
have hn : f ≥ nameDepth n := by simp [cTermDepth] at h; omega
|
||
rw [parseName?Aux_correct n (Token.rparen :: rest) f hn]
|
||
| .sym s, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp [MetaCTerm.toTokens, parseMetaCTerm?Aux]
|
||
| .app fa aa, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp only [MetaCTerm.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseMetaCTerm?Aux]
|
||
have hf : f ≥ cTermDepth fa := by simp [cTermDepth] at h; omega
|
||
have ha : f ≥ cTermDepth aa := by simp [cTermDepth] at h; omega
|
||
simp only [parseMetaCTerm?Aux_correct fa _ f hf,
|
||
parseMetaCTerm?Aux_correct aa _ f ha]
|
||
| .lam x t, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp only [MetaCTerm.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseMetaCTerm?Aux]
|
||
have ht : f ≥ cTermDepth t := by simp [cTermDepth] at h; omega
|
||
simp only [parseMetaCTerm?Aux_correct t _ f ht]
|
||
| .plam i t, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp only [MetaCTerm.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseMetaCTerm?Aux]
|
||
have ht : f ≥ cTermDepth t := by simp [cTermDepth] at h; omega
|
||
simp only [parseMetaCTerm?Aux_correct t _ f ht]
|
||
| .comp s A φ u t, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp only [MetaCTerm.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseMetaCTerm?Aux]
|
||
have hA : f ≥ cTermDepth A := by simp [cTermDepth] at h; omega
|
||
have hφ : f ≥ classifierDepth φ := by simp [cTermDepth] at h; omega
|
||
have hu : f ≥ cTermDepth u := by simp [cTermDepth] at h; omega
|
||
have ht : f ≥ cTermDepth t := by simp [cTermDepth] at h; omega
|
||
simp only [parseMetaCTerm?Aux_correct A _ f hA,
|
||
parseClassifier?Aux_correct φ _ f hφ,
|
||
parseMetaCTerm?Aux_correct u _ f hu,
|
||
parseMetaCTerm?Aux_correct t _ f ht]
|
||
| .transp s A φ t, rest, fuel, h => by
|
||
rcases fuel with _ | f
|
||
· simp [cTermDepth] at h
|
||
· simp only [MetaCTerm.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseMetaCTerm?Aux]
|
||
have hA : f ≥ cTermDepth A := by simp [cTermDepth] at h; omega
|
||
have hφ : f ≥ classifierDepth φ := by simp [cTermDepth] at h; omega
|
||
have ht : f ≥ cTermDepth t := by simp [cTermDepth] at h; omega
|
||
simp only [parseMetaCTerm?Aux_correct A _ f hA,
|
||
parseClassifier?Aux_correct φ _ f hφ,
|
||
parseMetaCTerm?Aux_correct t _ f ht]
|
||
|
||
theorem parseArtifact?Aux_correct :
|
||
∀ (a : MetaArtifact) (rest : List Token) (fuel : Nat),
|
||
a.supported = true →
|
||
fuel ≥ artifactDepth a →
|
||
parseArtifact?Aux fuel (a.toTokens ++ rest) = some (a, rest)
|
||
| .empty, rest, fuel, _, h => by
|
||
rcases fuel with _ | f
|
||
· simp [artifactDepth] at h
|
||
· simp [MetaArtifact.toTokens, parseArtifact?Aux]
|
||
| .source s, rest, fuel, _, h => by
|
||
rcases fuel with _ | f
|
||
· simp [artifactDepth] at h
|
||
· simp [MetaArtifact.toTokens, parseArtifact?Aux]
|
||
| .refTo n, rest, fuel, _, h => by
|
||
rcases fuel with _ | f
|
||
· simp [artifactDepth] at h
|
||
· simp only [MetaArtifact.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseArtifact?Aux]
|
||
have hn : f ≥ nameDepth n := by simp [artifactDepth] at h; omega
|
||
rw [parseName?Aux_correct n (Token.rparen :: rest) f hn]
|
||
| .cterm m, rest, fuel, _, h => by
|
||
rcases fuel with _ | f
|
||
· simp [artifactDepth] at h
|
||
· simp only [MetaArtifact.toTokens, List.append_assoc, List.cons_append,
|
||
List.nil_append, parseArtifact?Aux]
|
||
have hm : f ≥ cTermDepth m := by simp [artifactDepth] at h; omega
|
||
simp only [parseMetaCTerm?Aux_correct m _ f hm]
|
||
| .declAt _, _, _, hsup, _ => by
|
||
simp [MetaArtifact.supported] at hsup
|
||
|
||
-- ── Token-level round-trip — the canonical universal theorems ─────────────
|
||
-- These follow directly from the `parser?Aux_correct` lemmas above
|
||
-- by setting `rest = []` and `fuel = depth + k` (any sufficient
|
||
-- fuel). They're the cleanest universal statements: the parser,
|
||
-- starting from a value's canonical token form, recovers the
|
||
-- value with no leftover tokens. No String reasoning needed.
|
||
|
||
/-- Top-level token-entry parser. Tokenisation is presentation;
|
||
this is the *algorithmic* round-trip's input. -/
|
||
def MetaCTerm.fromTokens? (tokens : List Token) : Option MetaCTerm :=
|
||
match parseMetaCTerm? tokens with
|
||
| some (t, []) => some t
|
||
| _ => none
|
||
|
||
def MetaClassifier.fromTokens? (tokens : List Token) : Option MetaClassifier :=
|
||
match parseClassifier? tokens with
|
||
| some (φ, []) => some φ
|
||
| _ => none
|
||
|
||
def Infoductor.nameFromTokens? (tokens : List Token) : Option Lean.Name :=
|
||
match parseName? tokens with
|
||
| some (n, []) => some n
|
||
| _ => none
|
||
|
||
def MetaArtifact.fromTokens? (tokens : List Token) : Option MetaArtifact :=
|
||
match parseArtifact? tokens with
|
||
| some (a, []) => some a
|
||
| _ => none
|
||
|
||
-- Length-vs-depth lemmas: each toTokens output is at least as long
|
||
-- as the depth of the value, so `tokens.length + 1` is always
|
||
-- sufficient fuel.
|
||
|
||
theorem nameToTokens_length_bound (n : Lean.Name) :
|
||
(nameToTokens n).length + 1 ≥ nameDepth n := by
|
||
induction n with
|
||
| anonymous => simp [nameToTokens, nameDepth]
|
||
| str p s ih => simp [nameToTokens, nameDepth]; omega
|
||
| num p k ih => simp [nameToTokens, nameDepth]; omega
|
||
|
||
theorem classifierToTokens_length_bound (φ : MetaClassifier) :
|
||
(φ.toTokens).length + 1 ≥ classifierDepth φ := by
|
||
induction φ with
|
||
| always => simp [MetaClassifier.toTokens, classifierDepth]
|
||
| never => simp [MetaClassifier.toTokens, classifierDepth]
|
||
| atDecl n =>
|
||
simp [MetaClassifier.toTokens, classifierDepth]
|
||
have := nameToTokens_length_bound n; omega
|
||
| inFile s => simp [MetaClassifier.toTokens, classifierDepth]
|
||
| underAttribute n =>
|
||
simp [MetaClassifier.toTokens, classifierDepth]
|
||
have := nameToTokens_length_bound n; omega
|
||
| dependencyOf n =>
|
||
simp [MetaClassifier.toTokens, classifierDepth]
|
||
have := nameToTokens_length_bound n; omega
|
||
| inNamespace n =>
|
||
simp [MetaClassifier.toTokens, classifierDepth]
|
||
have := nameToTokens_length_bound n; omega
|
||
| meet a b iha ihb => simp [MetaClassifier.toTokens, classifierDepth]; omega
|
||
| join a b iha ihb => simp [MetaClassifier.toTokens, classifierDepth]; omega
|
||
|
||
theorem cTermToTokens_length_bound (t : MetaCTerm) :
|
||
(t.toTokens).length + 1 ≥ cTermDepth t := by
|
||
induction t with
|
||
| empty => simp [MetaCTerm.toTokens, cTermDepth]
|
||
| ident n =>
|
||
simp [MetaCTerm.toTokens, cTermDepth]
|
||
have := nameToTokens_length_bound n; omega
|
||
| sym s => simp [MetaCTerm.toTokens, cTermDepth]
|
||
| app f a ihf iha => simp [MetaCTerm.toTokens, cTermDepth]; omega
|
||
| lam x t ih => simp [MetaCTerm.toTokens, cTermDepth]; omega
|
||
| plam i t ih => simp [MetaCTerm.toTokens, cTermDepth]; omega
|
||
| comp s A φ u t ihA ihu iht =>
|
||
simp [MetaCTerm.toTokens, cTermDepth]
|
||
have := classifierToTokens_length_bound φ
|
||
omega
|
||
| transp s A φ t ihA iht =>
|
||
simp [MetaCTerm.toTokens, cTermDepth]
|
||
have := classifierToTokens_length_bound φ
|
||
omega
|
||
|
||
/-- Every meta-mirror value's canonical token form parses back to
|
||
the same value. Universal — by structural induction on the
|
||
meta-mirror type, with sufficient fuel guaranteed by the
|
||
length-vs-depth lemma above. -/
|
||
theorem nameFromTokens?_round_trip (n : Lean.Name) :
|
||
Infoductor.nameFromTokens? (nameToTokens n) = some n := by
|
||
unfold Infoductor.nameFromTokens? parseName?
|
||
have h := nameToTokens_length_bound n
|
||
have := parseName?Aux_correct n [] ((nameToTokens n).length + 1) h
|
||
rw [List.append_nil] at this
|
||
rw [this]
|
||
|
||
theorem classifierFromTokens?_round_trip (φ : MetaClassifier) :
|
||
MetaClassifier.fromTokens? φ.toTokens = some φ := by
|
||
unfold MetaClassifier.fromTokens? parseClassifier?
|
||
have h := classifierToTokens_length_bound φ
|
||
have := parseClassifier?Aux_correct φ [] ((φ.toTokens).length + 1) h
|
||
rw [List.append_nil] at this
|
||
rw [this]
|
||
|
||
theorem cTermFromTokens?_round_trip (t : MetaCTerm) :
|
||
MetaCTerm.fromTokens? t.toTokens = some t := by
|
||
unfold MetaCTerm.fromTokens? parseMetaCTerm?
|
||
have h := cTermToTokens_length_bound t
|
||
have := parseMetaCTerm?Aux_correct t [] ((t.toTokens).length + 1) h
|
||
rw [List.append_nil] at this
|
||
rw [this]
|
||
|
||
theorem artifactFromTokens?_round_trip (a : MetaArtifact)
|
||
(hsup : a.supported = true) :
|
||
MetaArtifact.fromTokens? a.toTokens = some a := by
|
||
unfold MetaArtifact.fromTokens? parseArtifact?
|
||
-- artifact length bound
|
||
have hlen : (a.toTokens).length + 1 ≥ artifactDepth a := by
|
||
cases a with
|
||
| empty => simp [MetaArtifact.toTokens, artifactDepth]
|
||
| source s => simp [MetaArtifact.toTokens, artifactDepth]
|
||
| declAt _ => simp [MetaArtifact.supported] at hsup
|
||
| cterm m =>
|
||
simp [MetaArtifact.toTokens, artifactDepth]
|
||
have := cTermToTokens_length_bound m; omega
|
||
| refTo n =>
|
||
simp [MetaArtifact.toTokens, artifactDepth]
|
||
have := nameToTokens_length_bound n; omega
|
||
have := parseArtifact?Aux_correct a [] ((a.toTokens).length + 1) hsup hlen
|
||
rw [List.append_nil] at this
|
||
rw [this]
|
||
|
||
-- ── Phase 3: tokenize ∘ render = toTokens ─────────────────────────────────
|
||
-- The String-level half. Foundation lemmas about tokenize's
|
||
-- behaviour, then induction over each meta-mirror type.
|
||
|
||
/-- `tokenize` on `(` :: rest reduces to `lparen :: tokenize rest`. -/
|
||
theorem tokenize_lparen_cons (rest : List Char) :
|
||
tokenize ('(' :: rest) = Token.lparen :: tokenize rest := by
|
||
simp [tokenize, tokenizeAux]
|
||
|
||
/-- `tokenize` on `)` :: rest reduces to `rparen :: tokenize rest`. -/
|
||
theorem tokenize_rparen_cons (rest : List Char) :
|
||
tokenize (')' :: rest) = Token.rparen :: tokenize rest := by
|
||
simp [tokenize, tokenizeAux]
|
||
|
||
/-- `tokenize` skips a leading space. -/
|
||
theorem tokenize_space_cons (rest : List Char) :
|
||
tokenize (' ' :: rest) = tokenize rest := by
|
||
simp [tokenize, tokenizeAux, isWhitespace]
|
||
|
||
-- Phase 3 deferred: the full `tokenize ∘ render = toTokens`
|
||
-- universal theorem requires careful String/List reasoning about
|
||
-- `readIdent` / `readStrLit` distribution. Proof sketch:
|
||
--
|
||
-- readIdent_split : reading an ident sequence followed by a
|
||
-- non-ident-rest char (or end of input) yields
|
||
-- exactly the accumulated string.
|
||
-- readStrLit_split : reading an escapeStrLit-encoded body until
|
||
-- the closing `"` recovers the original string.
|
||
-- tokenize_app_clean: tokenize distributes over a concatenation
|
||
-- where the prefix ends "cleanly" (rparen,
|
||
-- whitespace, or strLit close).
|
||
-- tokenize_render_X: induction over each meta-mirror type using
|
||
-- the above plus IH on sub-values.
|
||
--
|
||
-- These compose to `∀ v, tokenize (toLeanSource v).toList = toTokens v`,
|
||
-- which combined with the Phase 2 token-level universal gives the
|
||
-- String-level universal `∀ v, fromLeanSource? (toLeanSource v) = some v`.
|
||
--
|
||
-- The kernel-rooted `decide`-based tests for closed instances below
|
||
-- (and in `Infoductor/Test.lean`) provide empirical coverage in
|
||
-- the meantime.
|
||
|
||
-- ── Round-trip — atomic kernel-reducible witnesses ─────────────────────────
|
||
-- For non-recursive shapes the round-trip is closed by `rfl` (or
|
||
-- `decide`) directly: rendering produces a fixed string, tokenising
|
||
-- produces a fixed token list, parsing returns the original. These
|
||
-- closed-form witnesses live here in `Foundation` (no example-level
|
||
-- Decidable instances needed).
|
||
|
||
theorem MetaCTerm.toLeanSource_empty_round_trip :
|
||
MetaCTerm.fromLeanSource? MetaCTerm.empty.toLeanSource = some MetaCTerm.empty := by
|
||
decide
|
||
|
||
theorem MetaClassifier.toLeanSource_always_round_trip :
|
||
MetaClassifier.fromLeanSource? MetaClassifier.always.toLeanSource =
|
||
some MetaClassifier.always := by
|
||
decide
|
||
|
||
theorem MetaClassifier.toLeanSource_never_round_trip :
|
||
MetaClassifier.fromLeanSource? MetaClassifier.never.toLeanSource =
|
||
some MetaClassifier.never := by
|
||
decide
|
||
|
||
theorem MetaArtifact.toLeanSource_empty_round_trip_render :
|
||
(MetaArtifact.fromLeanSource? MetaArtifact.empty.toLeanSource).map
|
||
MetaArtifact.toLeanSource = some MetaArtifact.empty.toLeanSource := by
|
||
decide
|
||
|
||
-- ── Round-trip — compositional shapes via decide (closed inputs) ───────────
|
||
-- These witness round-trip for arbitrary closed `MetaCTerm` values
|
||
-- via the kernel's `decide`. Each case is a closed proposition;
|
||
-- the kernel evaluates the renderer, tokenizer, and parser end-
|
||
-- to-end and checks structural equality.
|
||
|
||
theorem MetaCTerm.toLeanSource_ident_anonymous_round_trip :
|
||
MetaCTerm.fromLeanSource? (MetaCTerm.ident Lean.Name.anonymous).toLeanSource =
|
||
some (MetaCTerm.ident Lean.Name.anonymous) := by
|
||
decide
|
||
|
||
theorem MetaCTerm.toLeanSource_app_empty_round_trip :
|
||
MetaCTerm.fromLeanSource? (MetaCTerm.app .empty .empty).toLeanSource =
|
||
some (MetaCTerm.app .empty .empty) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaCTerm.toLeanSource_lam_x_empty_round_trip :
|
||
MetaCTerm.fromLeanSource? (MetaCTerm.lam "x" .empty).toLeanSource =
|
||
some (MetaCTerm.lam "x" .empty) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaCTerm.toLeanSource_comp_round_trip :
|
||
MetaCTerm.fromLeanSource?
|
||
(MetaCTerm.comp "i" .empty .always .empty .empty).toLeanSource =
|
||
some (MetaCTerm.comp "i" .empty .always .empty .empty) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaCTerm.toLeanSource_transp_round_trip :
|
||
MetaCTerm.fromLeanSource?
|
||
(MetaCTerm.transp "i" .empty .never .empty).toLeanSource =
|
||
some (MetaCTerm.transp "i" .empty .never .empty) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaCTerm.toLeanSource_plam_round_trip :
|
||
MetaCTerm.fromLeanSource? (MetaCTerm.plam "i" .empty).toLeanSource =
|
||
some (MetaCTerm.plam "i" .empty) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaCTerm.toLeanSource_sym_round_trip :
|
||
MetaCTerm.fromLeanSource? (MetaCTerm.sym "x").toLeanSource =
|
||
some (MetaCTerm.sym "x") := by
|
||
decide
|
||
|
||
-- Compositional witness: a `.comp` whose sub-fields are themselves
|
||
-- non-trivial `MetaCTerm`s round-trips through the parser, exercising
|
||
-- the structural recursion of both renderer and parser end-to-end.
|
||
set_option maxRecDepth 16000 in
|
||
theorem MetaCTerm.toLeanSource_nested_round_trip :
|
||
MetaCTerm.fromLeanSource?
|
||
(MetaCTerm.comp "i" (.ident `Univ) .always
|
||
(.lam "x" (.sym "y")) (.sym "z")).toLeanSource =
|
||
some (MetaCTerm.comp "i" (.ident `Univ) .always
|
||
(.lam "x" (.sym "y")) (.sym "z")) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaClassifier.toLeanSource_meet_round_trip :
|
||
MetaClassifier.fromLeanSource?
|
||
(MetaClassifier.meet .always .never).toLeanSource =
|
||
some (MetaClassifier.meet .always .never) := by
|
||
decide
|
||
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaClassifier.toLeanSource_atDecl_round_trip :
|
||
MetaClassifier.fromLeanSource?
|
||
(MetaClassifier.atDecl `Foo).toLeanSource =
|
||
some (MetaClassifier.atDecl `Foo) := by
|
||
decide
|
||
|
||
-- 3-level deep name regression test: `eq0.i` (the FaceFormula
|
||
-- `eq0` encoding) round-trips. Pre-fix this case failed because
|
||
-- the renderer double-parenthesised the recursive sub-name.
|
||
set_option maxRecDepth 4000 in
|
||
theorem MetaClassifier.toLeanSource_atDecl_three_level_round_trip :
|
||
MetaClassifier.fromLeanSource?
|
||
(MetaClassifier.atDecl
|
||
(Lean.Name.mkStr (Lean.Name.mkSimple "eq0") "i")).toLeanSource =
|
||
some (MetaClassifier.atDecl
|
||
(Lean.Name.mkStr (Lean.Name.mkSimple "eq0") "i")) := by
|
||
decide
|
||
|
||
end Infoductor
|