diff --git a/src/Pure/Proof/proof_syntax.ML b/src/Pure/Proof/proof_syntax.ML --- a/src/Pure/Proof/proof_syntax.ML +++ b/src/Pure/Proof/proof_syntax.ML @@ -1,280 +1,283 @@ (* Title: Pure/Proof/proof_syntax.ML Author: Stefan Berghofer, TU Muenchen Function for parsing and printing proof terms. *) signature PROOF_SYNTAX = sig val add_proof_syntax: theory -> theory val term_of_proof: proof -> term val proof_of_term: theory -> bool -> term -> Proofterm.proof val read_term: theory -> bool -> typ -> string -> term val read_proof: theory -> bool -> bool -> string -> Proofterm.proof val proof_syntax: Proofterm.proof -> theory -> theory val proof_of: bool -> thm -> Proofterm.proof val pretty_proof: Proof.context -> Proofterm.proof -> Pretty.T val pretty_standard_proof_of: Proof.context -> bool -> thm -> Pretty.T - val pretty_proof_boxes_of: Proof.context -> bool -> thm -> Pretty.T + val pretty_proof_boxes_of: Proof.context -> + {full: bool, preproc: theory -> proof -> proof} -> thm -> Pretty.T end; structure Proof_Syntax : PROOF_SYNTAX = struct (**** add special syntax for embedding proof terms ****) val proofT = Type ("Pure.proof", []); local val paramT = Type ("param", []); val paramsT = Type ("params", []); val idtT = Type ("idt", []); val aT = Term.aT []; fun mixfix (sy, ps, p) = Mixfix (Input.string sy, ps, p, Position.no_range); in fun add_proof_syntax thy = thy |> Sign.root_path |> Sign.set_defsort [] |> Sign.add_nonterminals_global [Binding.make ("param", \<^here>), Binding.make ("params", \<^here>)] |> Sign.add_syntax Syntax.mode_default [("_Lam", [paramsT, proofT] ---> proofT, mixfix ("(1\<^bold>\_./ _)", [0, 3], 3)), ("_Lam0", [paramT, paramsT] ---> paramsT, mixfix ("_/ _", [1, 0], 0)), ("_Lam0", [idtT, paramsT] ---> paramsT, mixfix ("_/ _", [1, 0], 0)), ("_Lam1", [idtT, propT] ---> paramT, mixfix ("_: _", [0, 0], 0)), ("", paramT --> paramT, Mixfix.mixfix "'(_')"), ("", idtT --> paramsT, Mixfix.mixfix "_"), ("", paramT --> paramsT, Mixfix.mixfix "_"), (Lexicon.mark_const "Pure.Appt", [proofT, aT] ---> proofT, mixfix ("(1_ \/ _)", [4, 5], 4)), (Lexicon.mark_const "Pure.AppP", [proofT, proofT] ---> proofT, mixfix ("(1_ \/ _)", [4, 5], 4)), (Lexicon.mark_const "Pure.MinProof", proofT, Mixfix.mixfix "\<^bold>?")] |> Sign.add_trrules (map Syntax.Parse_Print_Rule [(Ast.mk_appl (Ast.Constant "_Lam") [Ast.mk_appl (Ast.Constant "_Lam0") [Ast.Variable "l", Ast.Variable "m"], Ast.Variable "A"], Ast.mk_appl (Ast.Constant "_Lam") [Ast.Variable "l", Ast.mk_appl (Ast.Constant "_Lam") [Ast.Variable "m", Ast.Variable "A"]]), (Ast.mk_appl (Ast.Constant "_Lam") [Ast.mk_appl (Ast.Constant "_Lam1") [Ast.Variable "x", Ast.Variable "A"], Ast.Variable "B"], Ast.mk_appl (Ast.Constant (Lexicon.mark_const "Pure.AbsP")) [Ast.Variable "A", (Ast.mk_appl (Ast.Constant "_abs") [Ast.Variable "x", Ast.Variable "B"])]), (Ast.mk_appl (Ast.Constant "_Lam") [Ast.Variable "x", Ast.Variable "A"], Ast.mk_appl (Ast.Constant (Lexicon.mark_const "Pure.Abst")) [(Ast.mk_appl (Ast.Constant "_abs") [Ast.Variable "x", Ast.Variable "A"])])]); end; (** constants for theorems and axioms **) fun add_proof_atom_consts names thy = thy |> Sign.root_path |> Sign.add_consts (map (fn name => (Binding.qualified_name name, proofT, NoSyn)) names); (** proof terms as pure terms **) (* term_of_proof *) local val AbsPt = Const ("Pure.AbsP", propT --> (proofT --> proofT) --> proofT); val AppPt = Const ("Pure.AppP", proofT --> proofT --> proofT); val Hypt = Const ("Pure.Hyp", propT --> proofT); val Oraclet = Const ("Pure.Oracle", propT --> proofT); val MinProoft = Const ("Pure.MinProof", proofT); fun AppT T prf = Const ("Pure.Appt", proofT --> Term.itselfT T --> proofT) $ prf $ Logic.mk_type T; fun OfClasst (T, c) = let val U = Term.itselfT T --> propT in Const ("Pure.OfClass", U --> proofT) $ Const (Logic.const_of_class c, U) end; fun term_of _ (PThm ({serial = i, name, types = Ts, ...}, _)) = fold AppT (these Ts) (Const (Long_Name.append "thm" (if name = "" then string_of_int i else name), proofT)) | term_of _ (PAxm (name, _, Ts)) = fold AppT (these Ts) (Const (Long_Name.append "axm" name, proofT)) | term_of _ (OfClass (T, c)) = AppT T (OfClasst (T, c)) | term_of _ (PBound i) = Bound i | term_of Ts (Abst (s, opT, prf)) = let val T = the_default dummyT opT in Const ("Pure.Abst", (T --> proofT) --> proofT) $ Abs (s, T, term_of (T::Ts) (Proofterm.incr_pboundvars 1 0 prf)) end | term_of Ts (AbsP (s, t, prf)) = AbsPt $ the_default Term.dummy_prop t $ Abs (s, proofT, term_of (proofT::Ts) (Proofterm.incr_pboundvars 0 1 prf)) | term_of Ts (prf1 %% prf2) = AppPt $ term_of Ts prf1 $ term_of Ts prf2 | term_of Ts (prf % opt) = let val t = the_default Term.dummy opt; val T = fastype_of1 (Ts, t) handle TERM _ => dummyT; in Const ("Pure.Appt", proofT --> T --> proofT) $ term_of Ts prf $ t end | term_of _ (Hyp t) = Hypt $ t | term_of _ (Oracle (_, t, _)) = Oraclet $ t | term_of _ MinProof = MinProoft; in val term_of_proof = term_of []; end; (* proof_of_term *) fun proof_of_term thy ty = let val thms = Global_Theory.all_thms_of thy true; val axms = Theory.all_axioms_of thy; fun mk_term t = (if ty then I else map_types (K dummyT)) (Term.no_dummy_patterns t); fun prf_of [] (Bound i) = PBound i | prf_of Ts (Const (s, Type ("Pure.proof", _))) = Proofterm.change_types (if ty then SOME Ts else NONE) (case Long_Name.explode s of "axm" :: xs => let val name = Long_Name.implode xs; val prop = (case AList.lookup (op =) axms name of SOME prop => prop | NONE => error ("Unknown axiom " ^ quote name)) in PAxm (name, prop, NONE) end | "thm" :: xs => let val name = Long_Name.implode xs; in (case AList.lookup (op =) thms name of SOME thm => fst (Proofterm.strip_combt (fst (Proofterm.strip_combP (Thm.proof_of thm)))) | NONE => error ("Unknown theorem " ^ quote name)) end | _ => error ("Illegal proof constant name: " ^ quote s)) | prf_of Ts (Const ("Pure.OfClass", _) $ Const (c_class, _)) = (case try Logic.class_of_const c_class of SOME c => Proofterm.change_types (if ty then SOME Ts else NONE) (OfClass (TVar ((Name.aT, 0), []), c)) | NONE => error ("Bad class constant: " ^ quote c_class)) | prf_of Ts (Const ("Pure.Hyp", _) $ prop) = Hyp prop | prf_of Ts (v as Var ((_, Type ("Pure.proof", _)))) = Hyp v | prf_of [] (Const ("Pure.Abst", _) $ Abs (s, T, prf)) = if T = proofT then error ("Term variable abstraction may not bind proof variable " ^ quote s) else Abst (s, if ty then SOME T else NONE, Proofterm.incr_pboundvars (~1) 0 (prf_of [] prf)) | prf_of [] (Const ("Pure.AbsP", _) $ t $ Abs (s, _, prf)) = AbsP (s, case t of Const ("Pure.dummy_pattern", _) => NONE | _ $ Const ("Pure.dummy_pattern", _) => NONE | _ => SOME (mk_term t), Proofterm.incr_pboundvars 0 (~1) (prf_of [] prf)) | prf_of [] (Const ("Pure.AppP", _) $ prf1 $ prf2) = prf_of [] prf1 %% prf_of [] prf2 | prf_of Ts (Const ("Pure.Appt", _) $ prf $ Const ("Pure.type", Type ("itself", [T]))) = prf_of (T::Ts) prf | prf_of [] (Const ("Pure.Appt", _) $ prf $ t) = prf_of [] prf % (case t of Const ("Pure.dummy_pattern", _) => NONE | _ => SOME (mk_term t)) | prf_of _ t = error ("Not a proof term:\n" ^ Syntax.string_of_term_global thy t) in prf_of [] end; fun read_term thy topsort = let val thm_names = filter_out (fn s => s = "") (map fst (Global_Theory.all_thms_of thy true)); val axm_names = map fst (Theory.all_axioms_of thy); val ctxt = thy |> add_proof_syntax |> add_proof_atom_consts (map (Long_Name.append "axm") axm_names @ map (Long_Name.append "thm") thm_names) |> Proof_Context.init_global |> Proof_Context.allow_dummies |> Proof_Context.set_mode Proof_Context.mode_schematic |> topsort ? (Proof_Context.set_defsort [] #> Config.put Type_Infer.object_logic false #> Config.put Type_Infer_Context.const_sorts false); in fn ty => fn s => (if ty = propT then Syntax.parse_prop else Syntax.parse_term) ctxt s |> Type.constraint ty |> Syntax.check_term ctxt end; fun read_proof thy topsort = let val rd = read_term thy topsort proofT in fn ty => fn s => proof_of_term thy ty (Logic.varify_global (rd s)) end; fun proof_syntax prf = let val thm_names = Symtab.keys (Proofterm.fold_proof_atoms true (fn PThm ({name, ...}, _) => if name <> "" then Symtab.update (name, ()) else I | _ => I) [prf] Symtab.empty); val axm_names = Symtab.keys (Proofterm.fold_proof_atoms true (fn PAxm (name, _, _) => Symtab.update (name, ()) | _ => I) [prf] Symtab.empty); in add_proof_syntax #> add_proof_atom_consts (map (Long_Name.append "thm") thm_names @ map (Long_Name.append "axm") axm_names) end; fun proof_of full thm = let val thy = Thm.theory_of_thm thm; val prop = Thm.full_prop_of thm; val prf = Thm.proof_of thm; in (case fst (Proofterm.strip_combt (fst (Proofterm.strip_combP prf))) of PThm ({prop = prop', ...}, thm_body) => if prop = prop' then Proofterm.thm_body_proof_raw thm_body else prf | _ => prf) |> full ? Proofterm.reconstruct_proof thy prop end; fun pretty_proof ctxt prf = Proof_Context.pretty_term_abbrev (Proof_Context.transfer (proof_syntax prf (Proof_Context.theory_of ctxt)) ctxt) (term_of_proof prf); fun pretty_standard_proof_of ctxt full thm = pretty_proof ctxt (Thm.standard_proof_of {full = full, expand_name = Thm.expand_name thm} thm); -fun pretty_proof_boxes_of ctxt full thm = +fun pretty_proof_boxes_of ctxt {full, preproc} thm = let val thy = Proof_Context.theory_of ctxt; val selection = {included = Proofterm.this_id (Thm.derivation_id thm), excluded = is_some o Global_Theory.lookup_thm_id thy} in Proofterm.proof_boxes selection [Thm.proof_of thm] |> map (fn ({serial = i, pos, prop, ...}, proof) => let val proof' = proof - |> full ? Proofterm.reconstruct_proof thy prop + |> Proofterm.reconstruct_proof thy prop + |> preproc thy + |> not full ? Proofterm.shrink_proof |> Proofterm.forall_intr_variables prop; val prop' = prop |> Proofterm.forall_intr_variables_term; val name = Long_Name.append "thm" (string_of_int i); in Pretty.item [Pretty.str (name ^ Position.here_list pos ^ ":"), Pretty.brk 1, Syntax.pretty_term ctxt prop', Pretty.fbrk, pretty_proof ctxt proof'] end) |> Pretty.chunks end; end; diff --git a/src/Pure/proofterm.ML b/src/Pure/proofterm.ML --- a/src/Pure/proofterm.ML +++ b/src/Pure/proofterm.ML @@ -1,2318 +1,2319 @@ (* Title: Pure/proofterm.ML Author: Stefan Berghofer, TU Muenchen LF style proof terms. *) infix 8 % %% %>; signature PROOFTERM = sig type thm_header = {serial: serial, pos: Position.T list, theory_name: string, name: string, prop: term, types: typ list option} type thm_body type thm_node datatype proof = MinProof | PBound of int | Abst of string * typ option * proof | AbsP of string * term option * proof | % of proof * term option | %% of proof * proof | Hyp of term | PAxm of string * term * typ list option | OfClass of typ * class | Oracle of string * term * typ list option | PThm of thm_header * thm_body and proof_body = PBody of {oracles: (string * term option) Ord_List.T, thms: (serial * thm_node) Ord_List.T, proof: proof} type oracle = string * term option type thm = serial * thm_node exception MIN_PROOF of unit val proof_of: proof_body -> proof val join_proof: proof_body future -> proof val map_proof_of: (proof -> proof) -> proof_body -> proof_body val thm_header: serial -> Position.T list -> string -> string -> term -> typ list option -> thm_header val thm_body: proof_body -> thm_body val thm_body_proof_raw: thm_body -> proof val thm_body_proof_open: thm_body -> proof val thm_node_theory_name: thm_node -> string val thm_node_name: thm_node -> string val thm_node_prop: thm_node -> term val thm_node_body: thm_node -> proof_body future val thm_node_thms: thm_node -> thm list val join_thms: thm list -> proof_body list val consolidate: proof_body list -> unit val make_thm: thm_header -> thm_body -> thm val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a val fold_body_thms: ({serial: serial, name: string, prop: term, body: proof_body} -> 'a -> 'a) -> proof_body list -> 'a -> 'a val oracle_ord: oracle ord val thm_ord: thm ord val unions_oracles: oracle Ord_List.T list -> oracle Ord_List.T val unions_thms: thm Ord_List.T list -> thm Ord_List.T val no_proof_body: proof -> proof_body val no_thm_names: proof -> proof val no_thm_proofs: proof -> proof val no_body_proofs: proof -> proof val encode: Consts.T -> proof XML.Encode.T val encode_body: Consts.T -> proof_body XML.Encode.T val encode_standard_term: Consts.T -> term XML.Encode.T val encode_standard_proof: Consts.T -> proof XML.Encode.T val decode: Consts.T -> proof XML.Decode.T val decode_body: Consts.T -> proof_body XML.Decode.T val %> : proof * term -> proof (*primitive operations*) val proofs: int Unsynchronized.ref val proofs_enabled: unit -> bool val atomic_proof: proof -> bool val compact_proof: proof -> bool val proof_combt: proof * term list -> proof val proof_combt': proof * term option list -> proof val proof_combP: proof * proof list -> proof val strip_combt: proof -> proof * term option list val strip_combP: proof -> proof * proof list val strip_thm_body: proof_body -> proof_body val map_proof_same: term Same.operation -> typ Same.operation -> (typ * class -> proof) -> proof Same.operation val map_proof_terms_same: term Same.operation -> typ Same.operation -> proof Same.operation val map_proof_types_same: typ Same.operation -> proof Same.operation val map_proof_terms: (term -> term) -> (typ -> typ) -> proof -> proof val map_proof_types: (typ -> typ) -> proof -> proof val fold_proof_terms: (term -> 'a -> 'a) -> proof -> 'a -> 'a val fold_proof_terms_types: (term -> 'a -> 'a) -> (typ -> 'a -> 'a) -> proof -> 'a -> 'a val maxidx_proof: proof -> int -> int val size_of_proof: proof -> int val change_types: typ list option -> proof -> proof val prf_abstract_over: term -> proof -> proof val prf_incr_bv: int -> int -> int -> int -> proof -> proof val incr_pboundvars: int -> int -> proof -> proof val prf_loose_bvar1: proof -> int -> bool val prf_loose_Pbvar1: proof -> int -> bool val prf_add_loose_bnos: int -> int -> proof -> int list * int list -> int list * int list val norm_proof: Envir.env -> proof -> proof val norm_proof': Envir.env -> proof -> proof val prf_subst_bounds: term list -> proof -> proof val prf_subst_pbounds: proof list -> proof -> proof val freeze_thaw_prf: proof -> proof * (proof -> proof) (*proof terms for specific inference rules*) val trivial_proof: proof val implies_intr_proof: term -> proof -> proof val implies_intr_proof': term -> proof -> proof val forall_intr_proof: string * term -> typ option -> proof -> proof val forall_intr_proof': term -> proof -> proof val varify_proof: term -> (string * sort) list -> proof -> proof val legacy_freezeT: term -> proof -> proof val rotate_proof: term list -> term -> (string * typ) list -> term list -> int -> proof -> proof val permute_prems_proof: term list -> int -> int -> proof -> proof val generalize_proof: string list * string list -> int -> term -> proof -> proof val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list -> proof -> proof val lift_proof: term -> int -> term -> proof -> proof val incr_indexes: int -> proof -> proof val assumption_proof: term list -> term -> int -> proof -> proof val bicompose_proof: bool -> term list -> term list -> term option -> term list -> int -> int -> proof -> proof -> proof val equality_axms: (string * term) list val reflexive_axm: proof val symmetric_axm: proof val transitive_axm: proof val equal_intr_axm: proof val equal_elim_axm: proof val abstract_rule_axm: proof val combination_axm: proof val reflexive_proof: proof val symmetric_proof: proof -> proof val transitive_proof: typ -> term -> proof -> proof -> proof val equal_intr_proof: term -> term -> proof -> proof -> proof val equal_elim_proof: term -> term -> proof -> proof -> proof val abstract_rule_proof: string * term -> proof -> proof val combination_proof: term -> term -> term -> term -> proof -> proof -> proof val strip_shyps_proof: Sorts.algebra -> (typ * sort) list -> (typ * sort) list -> sort list -> proof -> proof val of_sort_proof: Sorts.algebra -> (class * class -> proof) -> (string * class list list * class -> proof) -> (typ * class -> proof) -> typ * sort -> proof list val axm_proof: string -> term -> proof val oracle_proof: string -> term -> proof val shrink_proof: proof -> proof (*rewriting on proof terms*) val add_prf_rrule: proof * proof -> theory -> theory val add_prf_rproc: (typ list -> term option list -> proof -> (proof * proof) option) -> theory -> theory val set_preproc: (theory -> proof -> proof) -> theory -> theory + val apply_preproc: theory -> proof -> proof val forall_intr_variables_term: term -> term val forall_intr_variables: term -> proof -> proof val no_skel: proof val normal_skel: proof val rewrite_proof: theory -> (proof * proof) list * (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof val rewrite_proof_notypes: (proof * proof) list * (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof val rew_proof: theory -> proof -> proof val reconstruct_proof: theory -> term -> proof -> proof val prop_of': term list -> proof -> term val prop_of: proof -> term val expand_name_empty: thm_header -> string option val expand_proof: theory -> (thm_header -> string option) -> proof -> proof val standard_vars: Name.context -> term * proof option -> term * proof option val standard_vars_term: Name.context -> term -> term val add_standard_vars: proof -> (string * typ) list -> (string * typ) list val add_standard_vars_term: term -> (string * typ) list -> (string * typ) list val export_enabled: unit -> bool val export_standard_enabled: unit -> bool val export_proof_boxes_required: theory -> bool val export_proof_boxes: proof list -> unit val fulfill_norm_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body val thm_proof: theory -> (class * class -> proof) -> (string * class list list * class -> proof) -> string * Position.T -> sort list -> term list -> term -> (serial * proof_body future) list -> proof_body -> thm * proof val unconstrain_thm_proof: theory -> (class * class -> proof) -> (string * class list list * class -> proof) -> sort list -> term -> (serial * proof_body future) list -> proof_body -> thm * proof val get_identity: sort list -> term list -> term -> proof -> {serial: serial, theory_name: string, name: string} option val get_approximative_name: sort list -> term list -> term -> proof -> string type thm_id = {serial: serial, theory_name: string} val make_thm_id: serial * string -> thm_id val thm_header_id: thm_header -> thm_id val thm_id: thm -> thm_id val get_id: sort list -> term list -> term -> proof -> thm_id option val this_id: thm_id option -> thm_id -> bool val proof_boxes: {excluded: thm_id -> bool, included: thm_id -> bool} -> proof list -> (thm_header * proof) list (*exception MIN_PROOF*) end structure Proofterm : PROOFTERM = struct (** datatype proof **) type thm_header = {serial: serial, pos: Position.T list, theory_name: string, name: string, prop: term, types: typ list option}; datatype proof = MinProof | PBound of int | Abst of string * typ option * proof | AbsP of string * term option * proof | op % of proof * term option | op %% of proof * proof | Hyp of term | PAxm of string * term * typ list option | OfClass of typ * class | Oracle of string * term * typ list option | PThm of thm_header * thm_body and proof_body = PBody of {oracles: (string * term option) Ord_List.T, thms: (serial * thm_node) Ord_List.T, proof: proof} and thm_body = Thm_Body of {export_proof: unit lazy, open_proof: proof -> proof, body: proof_body future} and thm_node = Thm_Node of {theory_name: string, name: string, prop: term, body: proof_body future, consolidate: unit lazy}; type oracle = string * term option; val oracle_ord = prod_ord fast_string_ord (option_ord Term_Ord.fast_term_ord); type thm = serial * thm_node; val thm_ord: thm ord = fn ((i, _), (j, _)) => int_ord (j, i); exception MIN_PROOF of unit; fun proof_of (PBody {proof, ...}) = proof; val join_proof = Future.join #> proof_of; fun map_proof_of f (PBody {oracles, thms, proof}) = PBody {oracles = oracles, thms = thms, proof = f proof}; fun thm_header serial pos theory_name name prop types : thm_header = {serial = serial, pos = pos, theory_name = theory_name, name = name, prop = prop, types = types}; val no_export_proof = Lazy.value (); fun thm_body body = Thm_Body {export_proof = no_export_proof, open_proof = I, body = Future.value body}; fun thm_body_export_proof (Thm_Body {export_proof, ...}) = export_proof; fun thm_body_proof_raw (Thm_Body {body, ...}) = join_proof body; fun thm_body_proof_open (Thm_Body {open_proof, body, ...}) = open_proof (join_proof body); fun rep_thm_node (Thm_Node args) = args; val thm_node_theory_name = #theory_name o rep_thm_node; val thm_node_name = #name o rep_thm_node; val thm_node_prop = #prop o rep_thm_node; val thm_node_body = #body o rep_thm_node; val thm_node_thms = thm_node_body #> Future.join #> (fn PBody {thms, ...} => thms); val thm_node_consolidate = #consolidate o rep_thm_node; fun join_thms (thms: thm list) = Future.joins (map (thm_node_body o #2) thms); val consolidate = maps (fn PBody {thms, ...} => map (thm_node_consolidate o #2) thms) #> Lazy.consolidate #> map Lazy.force #> ignore; fun make_thm_node theory_name name prop body = Thm_Node {theory_name = theory_name, name = name, prop = prop, body = body, consolidate = Lazy.lazy_name "Proofterm.make_thm_node" (fn () => let val PBody {thms, ...} = Future.join body in consolidate (join_thms thms) end)}; fun make_thm ({serial, theory_name, name, prop, ...}: thm_header) (Thm_Body {body, ...}) = (serial, make_thm_node theory_name name prop body); (* proof atoms *) fun fold_proof_atoms all f = let fun app (Abst (_, _, prf)) = app prf | app (AbsP (_, _, prf)) = app prf | app (prf % _) = app prf | app (prf1 %% prf2) = app prf1 #> app prf2 | app (prf as PThm ({serial = i, ...}, Thm_Body {body, ...})) = (fn (x, seen) => if Inttab.defined seen i then (x, seen) else let val (x', seen') = (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen) in (f prf x', seen') end) | app prf = (fn (x, seen) => (f prf x, seen)); in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end; fun fold_body_thms f = let fun app (PBody {thms, ...}) = tap join_thms thms |> fold (fn (i, thm_node) => fn (x, seen) => if Inttab.defined seen i then (x, seen) else let val name = thm_node_name thm_node; val prop = thm_node_prop thm_node; val body = Future.join (thm_node_body thm_node); val (x', seen') = app body (x, Inttab.update (i, ()) seen); in (f {serial = i, name = name, prop = prop, body = body} x', seen') end); in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end; (* proof body *) val unions_oracles = Ord_List.unions oracle_ord; val unions_thms = Ord_List.unions thm_ord; fun no_proof_body proof = PBody {oracles = [], thms = [], proof = proof}; val no_thm_body = thm_body (no_proof_body MinProof); fun no_thm_names (Abst (x, T, prf)) = Abst (x, T, no_thm_names prf) | no_thm_names (AbsP (x, t, prf)) = AbsP (x, t, no_thm_names prf) | no_thm_names (prf % t) = no_thm_names prf % t | no_thm_names (prf1 %% prf2) = no_thm_names prf1 %% no_thm_names prf2 | no_thm_names (PThm ({serial, pos, theory_name, name = _, prop, types}, thm_body)) = PThm (thm_header serial pos theory_name "" prop types, thm_body) | no_thm_names a = a; fun no_thm_proofs (Abst (x, T, prf)) = Abst (x, T, no_thm_proofs prf) | no_thm_proofs (AbsP (x, t, prf)) = AbsP (x, t, no_thm_proofs prf) | no_thm_proofs (prf % t) = no_thm_proofs prf % t | no_thm_proofs (prf1 %% prf2) = no_thm_proofs prf1 %% no_thm_proofs prf2 | no_thm_proofs (PThm (header, _)) = PThm (header, no_thm_body) | no_thm_proofs a = a; fun no_body_proofs (Abst (x, T, prf)) = Abst (x, T, no_body_proofs prf) | no_body_proofs (AbsP (x, t, prf)) = AbsP (x, t, no_body_proofs prf) | no_body_proofs (prf % t) = no_body_proofs prf % t | no_body_proofs (prf1 %% prf2) = no_body_proofs prf1 %% no_body_proofs prf2 | no_body_proofs (PThm (header, Thm_Body {export_proof, open_proof, body})) = let val body' = Future.value (no_proof_body (join_proof body)); val thm_body' = Thm_Body {export_proof = export_proof, open_proof = open_proof, body = body'}; in PThm (header, thm_body') end | no_body_proofs a = a; (** XML data representation **) (* encode *) local open XML.Encode Term_XML.Encode; fun proof consts prf = prf |> variant [fn MinProof => ([], []), fn PBound a => ([], int a), fn Abst (a, b, c) => ([a], pair (option typ) (proof consts) (b, c)), fn AbsP (a, b, c) => ([a], pair (option (term consts)) (proof consts) (b, c)), fn a % b => ([], pair (proof consts) (option (term consts)) (a, b)), fn a %% b => ([], pair (proof consts) (proof consts) (a, b)), fn Hyp a => ([], term consts a), fn PAxm (a, b, c) => ([a], pair (term consts) (option (list typ)) (b, c)), fn OfClass (a, b) => ([b], typ a), fn Oracle (a, b, c) => ([a], pair (term consts) (option (list typ)) (b, c)), fn PThm ({serial, pos, theory_name, name, prop, types}, Thm_Body {open_proof, body, ...}) => ([int_atom serial, theory_name, name], pair (list properties) (pair (term consts) (pair (option (list typ)) (proof_body consts))) (map Position.properties_of pos, (prop, (types, map_proof_of open_proof (Future.join body)))))] and proof_body consts (PBody {oracles, thms, proof = prf}) = triple (list (pair string (option (term consts)))) (list (thm consts)) (proof consts) (oracles, thms, prf) and thm consts (a, thm_node) = pair int (pair string (pair string (pair (term consts) (proof_body consts)))) (a, (thm_node_theory_name thm_node, (thm_node_name thm_node, (thm_node_prop thm_node, (Future.join (thm_node_body thm_node)))))); fun standard_term consts t = t |> variant [fn Const (a, b) => ([a], list typ (Consts.typargs consts (a, b))), fn Free (a, _) => ([a], []), fn Var (a, _) => (indexname a, []), fn Bound a => ([], int a), fn Abs (a, b, c) => ([a], pair typ (standard_term consts) (b, c)), fn op $ a => ([], pair (standard_term consts) (standard_term consts) a)]; fun standard_proof consts prf = prf |> variant [fn MinProof => ([], []), fn PBound a => ([], int a), fn Abst (a, SOME b, c) => ([a], pair typ (standard_proof consts) (b, c)), fn AbsP (a, SOME b, c) => ([a], pair (standard_term consts) (standard_proof consts) (b, c)), fn a % SOME b => ([], pair (standard_proof consts) (standard_term consts) (a, b)), fn a %% b => ([], pair (standard_proof consts) (standard_proof consts) (a, b)), fn Hyp a => ([], standard_term consts a), fn PAxm (name, _, SOME Ts) => ([name], list typ Ts), fn OfClass (T, c) => ([c], typ T), fn Oracle (name, prop, SOME Ts) => ([name], pair (standard_term consts) (list typ) (prop, Ts)), fn PThm ({serial, theory_name, name, types = SOME Ts, ...}, _) => ([int_atom serial, theory_name, name], list typ Ts)]; in val encode = proof; val encode_body = proof_body; val encode_standard_term = standard_term; val encode_standard_proof = standard_proof; end; (* decode *) local open XML.Decode Term_XML.Decode; fun proof consts prf = prf |> variant [fn ([], []) => MinProof, fn ([], a) => PBound (int a), fn ([a], b) => let val (c, d) = pair (option typ) (proof consts) b in Abst (a, c, d) end, fn ([a], b) => let val (c, d) = pair (option (term consts)) (proof consts) b in AbsP (a, c, d) end, fn ([], a) => op % (pair (proof consts) (option (term consts)) a), fn ([], a) => op %% (pair (proof consts) (proof consts) a), fn ([], a) => Hyp (term consts a), fn ([a], b) => let val (c, d) = pair (term consts) (option (list typ)) b in PAxm (a, c, d) end, fn ([b], a) => OfClass (typ a, b), fn ([a], b) => let val (c, d) = pair (term consts) (option (list typ)) b in Oracle (a, c, d) end, fn ([a, b, c], d) => let val ((e, (f, (g, h)))) = pair (list properties) (pair (term consts) (pair (option (list typ)) (proof_body consts))) d; val header = thm_header (int_atom a) (map Position.of_properties e) b c f g; in PThm (header, thm_body h) end] and proof_body consts x = let val (a, b, c) = triple (list (pair string (option (term consts)))) (list (thm consts)) (proof consts) x; in PBody {oracles = a, thms = b, proof = c} end and thm consts x = let val (a, (b, (c, (d, e)))) = pair int (pair string (pair string (pair (term consts) (proof_body consts)))) x in (a, make_thm_node b c d (Future.value e)) end; in val decode = proof; val decode_body = proof_body; end; (** proof objects with different levels of detail **) val proofs = Unsynchronized.ref 2; fun proofs_enabled () = ! proofs >= 2; fun atomic_proof prf = (case prf of Abst _ => false | AbsP _ => false | op % _ => false | op %% _ => false | MinProof => false | _ => true); fun compact_proof (prf % _) = compact_proof prf | compact_proof (prf1 %% prf2) = atomic_proof prf2 andalso compact_proof prf1 | compact_proof prf = atomic_proof prf; fun (prf %> t) = prf % SOME t; val proof_combt = Library.foldl (op %>); val proof_combt' = Library.foldl (op %); val proof_combP = Library.foldl (op %%); fun strip_combt prf = let fun stripc (prf % t, ts) = stripc (prf, t::ts) | stripc x = x in stripc (prf, []) end; fun strip_combP prf = let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs) | stripc x = x in stripc (prf, []) end; fun strip_thm_body (body as PBody {proof, ...}) = (case fst (strip_combt (fst (strip_combP proof))) of PThm (_, Thm_Body {body = body', ...}) => Future.join body' | _ => body); val mk_Abst = fold_rev (fn (x, _: typ) => fn prf => Abst (x, NONE, prf)); val mk_AbsP = fold_rev (fn _: term => fn prf => AbsP ("H", NONE, prf)); fun map_proof_same term typ ofclass = let val typs = Same.map typ; fun proof (Abst (s, T, prf)) = (Abst (s, Same.map_option typ T, Same.commit proof prf) handle Same.SAME => Abst (s, T, proof prf)) | proof (AbsP (s, t, prf)) = (AbsP (s, Same.map_option term t, Same.commit proof prf) handle Same.SAME => AbsP (s, t, proof prf)) | proof (prf % t) = (proof prf % Same.commit (Same.map_option term) t handle Same.SAME => prf % Same.map_option term t) | proof (prf1 %% prf2) = (proof prf1 %% Same.commit proof prf2 handle Same.SAME => prf1 %% proof prf2) | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts)) | proof (OfClass T_c) = ofclass T_c | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts)) | proof (PThm ({serial, pos, theory_name, name, prop, types = SOME Ts}, thm_body)) = PThm (thm_header serial pos theory_name name prop (SOME (typs Ts)), thm_body) | proof _ = raise Same.SAME; in proof end; fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c)); fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ; fun same eq f x = let val x' = f x in if eq (x, x') then raise Same.SAME else x' end; fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g)); fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f)); fun fold_proof_terms f (Abst (_, _, prf)) = fold_proof_terms f prf | fold_proof_terms f (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f prf | fold_proof_terms f (AbsP (_, NONE, prf)) = fold_proof_terms f prf | fold_proof_terms f (prf % SOME t) = fold_proof_terms f prf #> f t | fold_proof_terms f (prf % NONE) = fold_proof_terms f prf | fold_proof_terms f (prf1 %% prf2) = fold_proof_terms f prf1 #> fold_proof_terms f prf2 | fold_proof_terms _ _ = I; fun fold_proof_terms_types f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms_types f g prf | fold_proof_terms_types f g (Abst (_, NONE, prf)) = fold_proof_terms_types f g prf | fold_proof_terms_types f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms_types f g prf | fold_proof_terms_types f g (AbsP (_, NONE, prf)) = fold_proof_terms_types f g prf | fold_proof_terms_types f g (prf % SOME t) = fold_proof_terms_types f g prf #> f t | fold_proof_terms_types f g (prf % NONE) = fold_proof_terms_types f g prf | fold_proof_terms_types f g (prf1 %% prf2) = fold_proof_terms_types f g prf1 #> fold_proof_terms_types f g prf2 | fold_proof_terms_types _ g (PAxm (_, _, SOME Ts)) = fold g Ts | fold_proof_terms_types _ g (OfClass (T, _)) = g T | fold_proof_terms_types _ g (Oracle (_, _, SOME Ts)) = fold g Ts | fold_proof_terms_types _ g (PThm ({types = SOME Ts, ...}, _)) = fold g Ts | fold_proof_terms_types _ _ _ = I; fun maxidx_proof prf = fold_proof_terms_types Term.maxidx_term Term.maxidx_typ prf; fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf | size_of_proof (AbsP (_, _, prf)) = 1 + size_of_proof prf | size_of_proof (prf % _) = 1 + size_of_proof prf | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2 | size_of_proof _ = 1; fun change_types types (PAxm (name, prop, _)) = PAxm (name, prop, types) | change_types (SOME [T]) (OfClass (_, c)) = OfClass (T, c) | change_types types (Oracle (name, prop, _)) = Oracle (name, prop, types) | change_types types (PThm ({serial, pos, theory_name, name, prop, types = _}, thm_body)) = PThm (thm_header serial pos theory_name name prop types, thm_body) | change_types _ prf = prf; (* utilities *) fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t | strip_abs _ t = t; fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts); (*Abstraction of a proof term over its occurrences of v, which must contain no loose bound variables. The resulting proof term is ready to become the body of an Abst.*) fun prf_abstract_over v = let fun abst' lev u = if v aconv u then Bound lev else (case u of Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t) | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t) | _ => raise Same.SAME) and absth' lev t = (abst' lev t handle Same.SAME => t); fun abst lev (AbsP (a, t, prf)) = (AbsP (a, Same.map_option (abst' lev) t, absth lev prf) handle Same.SAME => AbsP (a, t, abst lev prf)) | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf) | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2 handle Same.SAME => prf1 %% abst lev prf2) | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t handle Same.SAME => prf % Same.map_option (abst' lev) t) | abst _ _ = raise Same.SAME and absth lev prf = (abst lev prf handle Same.SAME => prf); in absth 0 end; (*increments a proof term's non-local bound variables required when moving a proof term within abstractions inc is increment for bound variables lev is level at which a bound variable is considered 'loose'*) fun incr_bv' inct tlev t = incr_bv (inct, tlev, t); fun prf_incr_bv' incP _ Plev _ (PBound i) = if i >= Plev then PBound (i+incP) else raise Same.SAME | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) = (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t, prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME => AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body)) | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) = Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body) | prf_incr_bv' incP inct Plev tlev (prf %% prf') = (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf' handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf') | prf_incr_bv' incP inct Plev tlev (prf % t) = (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t) | prf_incr_bv' _ _ _ _ _ = raise Same.SAME and prf_incr_bv incP inct Plev tlev prf = (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf); fun incr_pboundvars 0 0 prf = prf | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf; fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k) | prf_loose_bvar1 (_ % NONE) _ = true | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k | prf_loose_bvar1 (AbsP (_, NONE, _)) _ = true | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1) | prf_loose_bvar1 _ _ = false; fun prf_loose_Pbvar1 (PBound i) k = i = k | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1) | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k | prf_loose_Pbvar1 _ _ = false; fun prf_add_loose_bnos plev _ (PBound i) (is, js) = if i < plev then (is, js) else (insert (op =) (i-plev) is, js) | prf_add_loose_bnos plev tlev (prf1 %% prf2) p = prf_add_loose_bnos plev tlev prf2 (prf_add_loose_bnos plev tlev prf1 p) | prf_add_loose_bnos plev tlev (prf % opt) (is, js) = prf_add_loose_bnos plev tlev prf (case opt of NONE => (is, insert (op =) ~1 js) | SOME t => (is, add_loose_bnos (t, tlev, js))) | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) = prf_add_loose_bnos (plev+1) tlev prf (case opt of NONE => (is, insert (op =) ~1 js) | SOME t => (is, add_loose_bnos (t, tlev, js))) | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p = prf_add_loose_bnos plev (tlev+1) prf p | prf_add_loose_bnos _ _ _ _ = ([], []); (* substitutions *) fun del_conflicting_tvars envT T = Term_Subst.instantiateT (map_filter (fn ixnS as (_, S) => (Type.lookup envT ixnS; NONE) handle TYPE _ => SOME (ixnS, Logic.dummy_tfree S)) (Term.add_tvarsT T [])) T; fun del_conflicting_vars env t = Term_Subst.instantiate (map_filter (fn ixnS as (_, S) => (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ => SOME (ixnS, Logic.dummy_tfree S)) (Term.add_tvars t []), map_filter (fn (ixnT as (_, T)) => (Envir.lookup env ixnT; NONE) handle TYPE _ => SOME (ixnT, Free ("dummy", T))) (Term.add_vars t [])) t; fun norm_proof env = let val envT = Envir.type_env env; fun msg s = warning ("type conflict in norm_proof:\n" ^ s); fun htype f t = f env t handle TYPE (s, _, _) => (msg s; f env (del_conflicting_vars env t)); fun htypeT f T = f envT T handle TYPE (s, _, _) => (msg s; f envT (del_conflicting_tvars envT T)); fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) => (msg s; f envT (map (del_conflicting_tvars envT) Ts)); fun norm (Abst (s, T, prf)) = (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf) handle Same.SAME => Abst (s, T, norm prf)) | norm (AbsP (s, t, prf)) = (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf) handle Same.SAME => AbsP (s, t, norm prf)) | norm (prf % t) = (norm prf % Option.map (htype Envir.norm_term) t handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t) | norm (prf1 %% prf2) = (norm prf1 %% Same.commit norm prf2 handle Same.SAME => prf1 %% norm prf2) | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts) | norm (OfClass (T, c)) = OfClass (htypeT Envir.norm_type_same T, c) | norm (Oracle (s, prop, Ts)) = Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts) | norm (PThm ({serial = i, pos = p, theory_name, name = a, prop = t, types = Ts}, thm_body)) = PThm (thm_header i p theory_name a t (Same.map_option (htypeTs Envir.norm_types_same) Ts), thm_body) | norm _ = raise Same.SAME; in Same.commit norm end; (* remove some types in proof term (to save space) *) fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t) | remove_types (t $ u) = remove_types t $ remove_types u | remove_types (Const (s, _)) = Const (s, dummyT) | remove_types t = t; fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) = Envir.Envir {maxidx = maxidx, tenv = Vartab.map (K (apsnd remove_types)) tenv, tyenv = tyenv}; fun norm_proof' env prf = norm_proof (remove_types_env env) prf; (* substitution of bound variables *) fun prf_subst_bounds args prf = let val n = length args; fun subst' lev (Bound i) = (if i Bound (i-n)) (*loose: change it*) | subst' lev (Abs (a, T, body)) = Abs (a, T, subst' (lev+1) body) | subst' lev (f $ t) = (subst' lev f $ substh' lev t handle Same.SAME => f $ subst' lev t) | subst' _ _ = raise Same.SAME and substh' lev t = (subst' lev t handle Same.SAME => t); fun subst lev (AbsP (a, t, body)) = (AbsP (a, Same.map_option (subst' lev) t, substh lev body) handle Same.SAME => AbsP (a, t, subst lev body)) | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body) | subst lev (prf %% prf') = (subst lev prf %% substh lev prf' handle Same.SAME => prf %% subst lev prf') | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t handle Same.SAME => prf % Same.map_option (subst' lev) t) | subst _ _ = raise Same.SAME and substh lev prf = (subst lev prf handle Same.SAME => prf); in (case args of [] => prf | _ => substh 0 prf) end; fun prf_subst_pbounds args prf = let val n = length args; fun subst (PBound i) Plev tlev = (if i < Plev then raise Same.SAME (*var is locally bound*) else incr_pboundvars Plev tlev (nth args (i-Plev)) handle General.Subscript => PBound (i-n) (*loose: change it*)) | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev) | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1)) | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev handle Same.SAME => prf %% subst prf' Plev tlev) | subst (prf % t) Plev tlev = subst prf Plev tlev % t | subst _ _ _ = raise Same.SAME and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf) in (case args of [] => prf | _ => substh prf 0 0) end; (* freezing and thawing of variables in proof terms *) local fun frzT names = map_type_tvar (fn (ixn, S) => TFree (the (AList.lookup (op =) names ixn), S)); fun thawT names = map_type_tfree (fn (a, S) => (case AList.lookup (op =) names a of NONE => TFree (a, S) | SOME ixn => TVar (ixn, S))); fun freeze names names' (t $ u) = freeze names names' t $ freeze names names' u | freeze names names' (Abs (s, T, t)) = Abs (s, frzT names' T, freeze names names' t) | freeze _ names' (Const (s, T)) = Const (s, frzT names' T) | freeze _ names' (Free (s, T)) = Free (s, frzT names' T) | freeze names names' (Var (ixn, T)) = Free (the (AList.lookup (op =) names ixn), frzT names' T) | freeze _ _ t = t; fun thaw names names' (t $ u) = thaw names names' t $ thaw names names' u | thaw names names' (Abs (s, T, t)) = Abs (s, thawT names' T, thaw names names' t) | thaw _ names' (Const (s, T)) = Const (s, thawT names' T) | thaw names names' (Free (s, T)) = let val T' = thawT names' T in (case AList.lookup (op =) names s of NONE => Free (s, T') | SOME ixn => Var (ixn, T')) end | thaw _ names' (Var (ixn, T)) = Var (ixn, thawT names' T) | thaw _ _ t = t; in fun freeze_thaw_prf prf = let val (fs, Tfs, vs, Tvs) = fold_proof_terms_types (fn t => fn (fs, Tfs, vs, Tvs) => (Term.add_free_names t fs, Term.add_tfree_names t Tfs, Term.add_var_names t vs, Term.add_tvar_names t Tvs)) (fn T => fn (fs, Tfs, vs, Tvs) => (fs, Term.add_tfree_namesT T Tfs, vs, Term.add_tvar_namesT T Tvs)) prf ([], [], [], []); val names = vs ~~ Name.variant_list fs (map fst vs); val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs); val rnames = map swap names; val rnames' = map swap names'; in (map_proof_terms (freeze names names') (frzT names') prf, map_proof_terms (thaw rnames rnames') (thawT rnames')) end; end; (** inference rules **) (* trivial implication *) val trivial_proof = AbsP ("H", NONE, PBound 0); (* implication introduction *) fun gen_implies_intr_proof f h prf = let fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf) | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf) | abshyp i (prf % t) = abshyp i prf % t | abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2 handle Same.SAME => prf1 %% abshyp i prf2) | abshyp _ _ = raise Same.SAME and abshyph i prf = (abshyp i prf handle Same.SAME => prf); in AbsP ("H", f h, abshyph 0 prf) end; val implies_intr_proof = gen_implies_intr_proof (K NONE); val implies_intr_proof' = gen_implies_intr_proof SOME; (* forall introduction *) fun forall_intr_proof (a, v) opt_T prf = Abst (a, opt_T, prf_abstract_over v prf); fun forall_intr_proof' v prf = let val (a, T) = (case v of Var ((a, _), T) => (a, T) | Free (a, T) => (a, T)) in forall_intr_proof (a, v) (SOME T) prf end; (* varify *) fun varify_proof t fixed prf = let val fs = Term.fold_types (Term.fold_atyps (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t []; val used = Name.context |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t; val fmap = fs ~~ #1 (fold_map Name.variant (map fst fs) used); fun thaw (a, S) = (case AList.lookup (op =) fmap (a, S) of NONE => TFree (a, S) | SOME b => TVar ((b, 0), S)); in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end; local fun new_name ix (pairs, used) = let val v = singleton (Name.variant_list used) (string_of_indexname ix) in ((ix, v) :: pairs, v :: used) end; fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of NONE => TVar (ix, sort) | SOME name => TFree (name, sort)); in fun legacy_freezeT t prf = let val used = Term.add_tfree_names t []; val (alist, _) = fold_rev new_name (map #1 (Term.add_tvars t [])) ([], used); in (case alist of [] => prf (*nothing to do!*) | _ => let val frzT = map_type_tvar (freeze_one alist) in map_proof_terms (map_types frzT) frzT prf end) end; end; (* rotate assumptions *) fun rotate_proof Bs Bi' params asms m prf = let val i = length asms; val j = length Bs; in mk_AbsP (Bs @ [Bi']) (proof_combP (prf, map PBound (j downto 1) @ [mk_Abst params (mk_AbsP asms (proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)), map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))])) end; (* permute premises *) fun permute_prems_proof prems' j k prf = let val n = length prems' in mk_AbsP prems' (proof_combP (prf, map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k)))) end; (* generalization *) fun generalize_proof (tfrees, frees) idx prop prf = let val gen = if null frees then [] else fold_aterms (fn Free (x, T) => member (op =) frees x ? insert (op =) (x, T) | _ => I) (Term_Subst.generalize (tfrees, []) idx prop) []; in prf |> Same.commit (map_proof_terms_same (Term_Subst.generalize_same (tfrees, []) idx) (Term_Subst.generalizeT_same tfrees idx)) |> fold (fn (x, T) => forall_intr_proof (x, Free (x, T)) NONE) gen |> fold_rev (fn (x, T) => fn prf' => prf' %> Var (Name.clean_index (x, idx), T)) gen end; (* instantiation *) fun instantiate (instT, inst) = Same.commit (map_proof_terms_same (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst)) (Term_Subst.instantiateT_same instT)); (* lifting *) fun lift_proof Bi inc prop prf = let fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes ([], Us, inc) (mk_abs Ts t)); fun lift' Us Ts (Abst (s, T, prf)) = (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf) handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf)) | lift' Us Ts (AbsP (s, t, prf)) = (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf) handle Same.SAME => AbsP (s, t, lift' Us Ts prf)) | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t) | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2 handle Same.SAME => prf1 %% lift' Us Ts prf2) | lift' _ _ (PAxm (s, prop, Ts)) = PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts) | lift' _ _ (OfClass (T, c)) = OfClass (Logic.incr_tvar_same inc T, c) | lift' _ _ (Oracle (s, prop, Ts)) = Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts) | lift' _ _ (PThm ({serial = i, pos = p, theory_name, name = s, prop, types = Ts}, thm_body)) = PThm (thm_header i p theory_name s prop ((Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), thm_body) | lift' _ _ _ = raise Same.SAME and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf); val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop); val k = length ps; fun mk_app b (i, j, prf) = if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j); fun lift Us bs i j (Const ("Pure.imp", _) $ A $ B) = AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B) | lift Us bs i j (Const ("Pure.all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t) | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf, map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k)))) (i + k - 1 downto i)); in mk_AbsP ps (lift [] [] 0 0 Bi) end; fun incr_indexes i = Same.commit (map_proof_terms_same (Logic.incr_indexes_same ([], [], i)) (Logic.incr_tvar_same i)); (* proof by assumption *) fun mk_asm_prf t i m = let fun imp_prf _ i 0 = PBound i | imp_prf (Const ("Pure.imp", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1)) | imp_prf _ i _ = PBound i; fun all_prf (Const ("Pure.all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t) | all_prf t = imp_prf t (~i) m in all_prf t end; fun assumption_proof Bs Bi n prf = mk_AbsP Bs (proof_combP (prf, map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1])); (* composition of object rule with proof state *) fun flatten_params_proof i j n (Const ("Pure.imp", _) $ A $ B, k) = AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k)) | flatten_params_proof i j n (Const ("Pure.all", _) $ Abs (a, T, t), k) = Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k)) | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i), map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0))); fun bicompose_proof flatten Bs As A oldAs n m rprf sprf = let val lb = length Bs; val la = length As; in mk_AbsP (Bs @ As) (proof_combP (sprf, map PBound (lb + la - 1 downto la)) %% proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @ map (if flatten then flatten_params_proof 0 0 n else PBound o snd) (oldAs ~~ (la - 1 downto 0)))) end; (** type classes **) fun strip_shyps_proof algebra present witnessed extra_sorts prf = let fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE; val extra = map (`Logic.dummy_tfree) extra_sorts; val replacements = present @ extra @ witnessed; fun replace T = if exists (fn (T', _) => T' = T) present then raise Same.SAME else (case get_first (get (Type.sort_of_atyp T)) replacements of SOME T' => T' | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term"); in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end; fun of_sort_proof algebra classrel_proof arity_proof hyps = Sorts.of_sort_derivation algebra {class_relation = fn _ => fn _ => fn (prf, c1) => fn c2 => if c1 = c2 then prf else classrel_proof (c1, c2) %% prf, type_constructor = fn (a, _) => fn dom => fn c => let val Ss = map (map snd) dom and prfs = maps (map fst) dom in proof_combP (arity_proof (a, Ss, c), prfs) end, type_variable = fn typ => map (fn c => (hyps (typ, c), c)) (Type.sort_of_atyp typ)}; (** axioms and theorems **) val add_type_variables = (fold_types o fold_atyps) (insert (op =)); fun type_variables_of t = rev (add_type_variables t []); val add_variables = fold_aterms (fn a => (is_Var a orelse is_Free a) ? insert (op =) a); fun variables_of t = rev (add_variables t []); fun test_args _ [] = true | test_args is (Bound i :: ts) = not (member (op =) is i) andalso test_args (i :: is) ts | test_args _ _ = false; fun is_fun (Type ("fun", _)) = true | is_fun (TVar _) = true | is_fun _ = false; fun vars_of t = map Var (rev (Term.add_vars t [])); fun add_funvars Ts (vs, t) = if is_fun (fastype_of1 (Ts, t)) then union (op =) vs (map_filter (fn Var (ixn, T) => if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t)) else vs; fun add_npvars q p Ts (vs, Const ("Pure.imp", _) $ t $ u) = add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u) | add_npvars q p Ts (vs, Const ("Pure.all", Type (_, [Type (_, [T, _]), _])) $ t) = add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t) | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t) | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t) and add_npvars' Ts (vs, t) = (case strip_comb t of (Var (ixn, _), ts) => if test_args [] ts then vs else Library.foldl (add_npvars' Ts) (AList.update (op =) (ixn, Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts) | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts) | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts)); fun prop_vars (Const ("Pure.imp", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q) | prop_vars (Const ("Pure.all", _) $ Abs (_, _, t)) = prop_vars t | prop_vars t = (case strip_comb t of (Var (ixn, _), _) => [ixn] | _ => []); fun is_proj t = let fun is_p i t = (case strip_comb t of (Bound _, []) => false | (Bound j, ts) => j >= i orelse exists (is_p i) ts | (Abs (_, _, u), _) => is_p (i+1) u | (_, ts) => exists (is_p i) ts) in (case strip_abs_body t of Bound _ => true | t' => is_p 0 t') end; fun prop_args prop = let val needed_vars = union (op =) (Library.foldl (uncurry (union (op =))) ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop)))) (prop_vars prop); in variables_of prop |> map (fn var as Var (ixn, _) => if member (op =) needed_vars ixn then SOME var else NONE | free => SOME free) end; fun const_proof mk name prop = let val args = prop_args prop; val ({outer_constraints, ...}, prop1) = Logic.unconstrainT [] prop; val head = mk (name, prop1, NONE); in proof_combP (proof_combt' (head, args), map OfClass outer_constraints) end; val axm_proof = const_proof PAxm; val oracle_proof = const_proof Oracle; val shrink_proof = let fun shrink ls lev (prf as Abst (a, T, body)) = let val (b, is, ch, body') = shrink ls (lev+1) body in (b, is, ch, if ch then Abst (a, T, body') else prf) end | shrink ls lev (prf as AbsP (a, t, body)) = let val (b, is, ch, body') = shrink (lev::ls) lev body in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is, ch, if ch then AbsP (a, t, body') else prf) end | shrink ls lev prf = let val (is, ch, _, prf') = shrink' ls lev [] [] prf in (false, is, ch, prf') end and shrink' ls lev ts prfs (prf as prf1 %% prf2) = let val p as (_, is', ch', prf') = shrink ls lev prf2; val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1 in (union (op =) is is', ch orelse ch', ts', if ch orelse ch' then prf'' %% prf' else prf) end | shrink' ls lev ts prfs (prf as prf1 % t) = let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1 in (is, ch orelse ch', ts', if ch orelse ch' then prf' % t' else prf) end | shrink' ls lev ts prfs (prf as PBound i) = (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts orelse has_duplicates (op =) (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts)) orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf) | shrink' _ _ ts _ (Hyp t) = ([], false, map (pair false) ts, Hyp t) | shrink' _ _ ts _ (prf as MinProof) = ([], false, map (pair false) ts, prf) | shrink' _ _ ts _ (prf as OfClass _) = ([], false, map (pair false) ts, prf) | shrink' _ _ ts prfs prf = let val prop = (case prf of PAxm (_, prop, _) => prop | Oracle (_, prop, _) => prop | PThm ({prop, ...}, _) => prop | _ => raise Fail "shrink: proof not in normal form"); val vs = vars_of prop; val (ts', ts'') = chop (length vs) ts; val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts'; val nvs = Library.foldl (fn (ixns', (ixn, ixns)) => insert (op =) ixn (case AList.lookup (op =) insts ixn of SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns' | _ => union (op =) ixns ixns')) (needed prop ts'' prfs, add_npvars false true [] ([], prop)); val insts' = map (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE) | (_, x) => (false, x)) insts in ([], false, insts' @ map (pair false) ts'', prf) end and needed (Const ("Pure.imp", _) $ t $ u) ts ((b, _, _, _)::prfs) = union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs) | needed (Var (ixn, _)) (_::_) _ = [ixn] | needed _ _ _ = []; in fn prf => #4 (shrink [] 0 prf) end; (** axioms for equality **) val aT = TFree ("'a", []); val bT = TFree ("'b", []); val x = Free ("x", aT); val y = Free ("y", aT); val z = Free ("z", aT); val A = Free ("A", propT); val B = Free ("B", propT); val f = Free ("f", aT --> bT); val g = Free ("g", aT --> bT); val equality_axms = [("reflexive", Logic.mk_equals (x, x)), ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))), ("transitive", Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))), ("equal_intr", Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))), ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)), ("abstract_rule", Logic.mk_implies (Logic.all x (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))), ("combination", Logic.list_implies ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))]; val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm, equal_elim_axm, abstract_rule_axm, combination_axm] = map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms; val reflexive_proof = reflexive_axm % NONE; val is_reflexive_proof = fn PAxm ("Pure.reflexive", _, _) % _ => true | _ => false; fun symmetric_proof prf = if is_reflexive_proof prf then prf else symmetric_axm % NONE % NONE %% prf; fun transitive_proof U u prf1 prf2 = if is_reflexive_proof prf1 then prf2 else if is_reflexive_proof prf2 then prf1 else if U = propT then transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2 else transitive_axm % NONE % NONE % NONE %% prf1 %% prf2; fun equal_intr_proof A B prf1 prf2 = equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2; fun equal_elim_proof A B prf1 prf2 = equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2; fun abstract_rule_proof (a, x) prf = abstract_rule_axm % NONE % NONE %% forall_intr_proof (a, x) NONE prf; fun check_comb (PAxm ("Pure.combination", _, _) % f % _ % _ % _ %% prf %% _) = is_some f orelse check_comb prf | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) = check_comb prf1 andalso check_comb prf2 | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf | check_comb _ = false; fun combination_proof f g t u prf1 prf2 = let val f = Envir.beta_norm f; val g = Envir.beta_norm g; val prf = if check_comb prf1 then combination_axm % NONE % NONE else (case prf1 of PAxm ("Pure.reflexive", _, _) % _ => combination_axm %> remove_types f % NONE | _ => combination_axm %> remove_types f %> remove_types g) in prf % (case head_of f of Abs _ => SOME (remove_types t) | Var _ => SOME (remove_types t) | _ => NONE) % (case head_of g of Abs _ => SOME (remove_types u) | Var _ => SOME (remove_types u) | _ => NONE) %% prf1 %% prf2 end; (** rewriting on proof terms **) (* simple first order matching functions for terms and proofs (see pattern.ML) *) exception PMatch; fun flt (i: int) = filter (fn n => n < i); fun fomatch Ts tymatch j instsp p = let fun mtch (instsp as (tyinsts, insts)) = fn (Var (ixn, T), t) => if j>0 andalso not (null (flt j (loose_bnos t))) then raise PMatch else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))), (ixn, t) :: insts) | (Free (a, T), Free (b, U)) => if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch | (Const (a, T), Const (b, U)) => if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u) | (Bound i, Bound j) => if i=j then instsp else raise PMatch | _ => raise PMatch in mtch instsp (apply2 Envir.beta_eta_contract p) end; fun match_proof Ts tymatch = let fun optmatch _ inst (NONE, _) = inst | optmatch _ _ (SOME _, NONE) = raise PMatch | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y) fun matcht Ts j (pinst, tinst) (t, u) = (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u)); fun matchT (pinst, (tyinsts, insts)) p = (pinst, (tymatch (tyinsts, K p), insts)); fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us); fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) = if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst) else (case apfst (flt i) (apsnd (flt j) (prf_add_loose_bnos 0 0 prf ([], []))) of ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst) | ([], _) => if j = 0 then ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst) else raise PMatch | _ => raise PMatch) | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) = optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2) | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') = mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2') | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) = mtch (the_default dummyT opU :: Ts) i (j+1) (optmatch matchT inst (opT, opU)) (prf1, prf2) | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) = mtch (the_default dummyT opU :: Ts) i (j+1) inst (incr_pboundvars 0 1 prf1 %> Bound 0, prf2) | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) = mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2) | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) = mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2) | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) = if s1 = s2 then optmatch matchTs inst (opTs, opUs) else raise PMatch | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) = if c1 = c2 then matchT inst (T1, T2) else raise PMatch | mtch Ts i j inst (PThm ({name = name1, prop = prop1, types = types1, ...}, _), PThm ({name = name2, prop = prop2, types = types2, ...}, _)) = if name1 = name2 andalso prop1 = prop2 then optmatch matchTs inst (types1, types2) else raise PMatch | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch | mtch _ _ _ _ _ = raise PMatch in mtch Ts 0 0 end; fun prf_subst (pinst, (tyinsts, insts)) = let val substT = Envir.subst_type_same tyinsts; val substTs = Same.map substT; fun subst' lev (Var (xi, _)) = (case AList.lookup (op =) insts xi of NONE => raise Same.SAME | SOME u => incr_boundvars lev u) | subst' _ (Const (s, T)) = Const (s, substT T) | subst' _ (Free (s, T)) = Free (s, substT T) | subst' lev (Abs (a, T, body)) = (Abs (a, substT T, Same.commit (subst' (lev + 1)) body) handle Same.SAME => Abs (a, T, subst' (lev + 1) body)) | subst' lev (f $ t) = (subst' lev f $ Same.commit (subst' lev) t handle Same.SAME => f $ subst' lev t) | subst' _ _ = raise Same.SAME; fun subst plev tlev (AbsP (a, t, body)) = (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body) handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body)) | subst plev tlev (Abst (a, T, body)) = (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body) handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body)) | subst plev tlev (prf %% prf') = (subst plev tlev prf %% Same.commit (subst plev tlev) prf' handle Same.SAME => prf %% subst plev tlev prf') | subst plev tlev (prf % t) = (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t handle Same.SAME => prf % Same.map_option (subst' tlev) t) | subst plev tlev (Hyp (Var (xi, _))) = (case AList.lookup (op =) pinst xi of NONE => raise Same.SAME | SOME prf' => incr_pboundvars plev tlev prf') | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts) | subst _ _ (OfClass (T, c)) = OfClass (substT T, c) | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts) | subst _ _ (PThm ({serial = i, pos = p, theory_name, name = id, prop, types}, thm_body)) = PThm (thm_header i p theory_name id prop (Same.map_option substTs types), thm_body) | subst _ _ _ = raise Same.SAME; in fn t => subst 0 0 t handle Same.SAME => t end; (*A fast unification filter: true unless the two terms cannot be unified. Terms must be NORMAL. Treats all Vars as distinct. *) fun could_unify prf1 prf2 = let fun matchrands (prf1 %% prf2) (prf1' %% prf2') = could_unify prf2 prf2' andalso matchrands prf1 prf1' | matchrands (prf % SOME t) (prf' % SOME t') = Term.could_unify (t, t') andalso matchrands prf prf' | matchrands (prf % _) (prf' % _) = matchrands prf prf' | matchrands _ _ = true fun head_of (prf %% _) = head_of prf | head_of (prf % _) = head_of prf | head_of prf = prf in case (head_of prf1, head_of prf2) of (_, Hyp (Var _)) => true | (Hyp (Var _), _) => true | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2 | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2 | (PThm ({name = a, prop = propa, ...}, _), PThm ({name = b, prop = propb, ...}, _)) => a = b andalso propa = propb andalso matchrands prf1 prf2 | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2 | (AbsP _, _) => true (*because of possible eta equality*) | (Abst _, _) => true | (_, AbsP _) => true | (_, Abst _) => true | _ => false end; (* rewrite proof *) val no_skel = PBound 0; val normal_skel = Hyp (Var ((Name.uu, 0), propT)); fun rewrite_prf tymatch (rules, procs) prf = let fun rew _ _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel) | rew _ _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel) | rew Ts hs prf = (case get_first (fn r => r Ts hs prf) procs of NONE => get_first (fn (prf1, prf2) => SOME (prf_subst (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2) handle PMatch => NONE) (filter (could_unify prf o fst) rules) | some => some); fun rew0 Ts hs (prf as AbsP (_, _, prf' %% PBound 0)) = if prf_loose_Pbvar1 prf' 0 then rew Ts hs prf else let val prf'' = incr_pboundvars (~1) 0 prf' in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end | rew0 Ts hs (prf as Abst (_, _, prf' % SOME (Bound 0))) = if prf_loose_bvar1 prf' 0 then rew Ts hs prf else let val prf'' = incr_pboundvars 0 (~1) prf' in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end | rew0 Ts hs prf = rew Ts hs prf; fun rew1 _ _ (Hyp (Var _)) _ = NONE | rew1 Ts hs skel prf = (case rew2 Ts hs skel prf of SOME prf1 => (case rew0 Ts hs prf1 of SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts hs skel' prf2)) | NONE => SOME prf1) | NONE => (case rew0 Ts hs prf of SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts hs skel' prf1)) | NONE => NONE)) and rew2 Ts hs skel (prf % SOME t) = (case prf of Abst (_, _, body) => let val prf' = prf_subst_bounds [t] body in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end | _ => (case rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf of SOME prf' => SOME (prf' % SOME t) | NONE => NONE)) | rew2 Ts hs skel (prf % NONE) = Option.map (fn prf' => prf' % NONE) (rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf) | rew2 Ts hs skel (prf1 %% prf2) = (case prf1 of AbsP (_, _, body) => let val prf' = prf_subst_pbounds [prf2] body in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end | _ => let val (skel1, skel2) = (case skel of skel1 %% skel2 => (skel1, skel2) | _ => (no_skel, no_skel)) in (case rew1 Ts hs skel1 prf1 of SOME prf1' => (case rew1 Ts hs skel2 prf2 of SOME prf2' => SOME (prf1' %% prf2') | NONE => SOME (prf1' %% prf2)) | NONE => (case rew1 Ts hs skel2 prf2 of SOME prf2' => SOME (prf1 %% prf2') | NONE => NONE)) end) | rew2 Ts hs skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts) hs (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of SOME prf' => SOME (Abst (s, T, prf')) | NONE => NONE) | rew2 Ts hs skel (AbsP (s, t, prf)) = (case rew1 Ts (t :: hs) (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of SOME prf' => SOME (AbsP (s, t, prf')) | NONE => NONE) | rew2 _ _ _ _ = NONE; in the_default prf (rew1 [] [] no_skel prf) end; fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) => Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch); fun rewrite_proof_notypes rews = rewrite_prf fst rews; (* theory data *) structure Data = Theory_Data ( type T = ((stamp * (proof * proof)) list * (stamp * (typ list -> term option list -> proof -> (proof * proof) option)) list) * (theory -> proof -> proof) option; val empty = (([], []), NONE); val extend = I; fun merge (((rules1, procs1), preproc1), ((rules2, procs2), preproc2)) : T = ((AList.merge (op =) (K true) (rules1, rules2), AList.merge (op =) (K true) (procs1, procs2)), merge_options (preproc1, preproc2)); ); fun get_rew_data thy = let val (rules, procs) = #1 (Data.get thy) in (map #2 rules, map #2 procs) end; fun rew_proof thy = rewrite_prf fst (get_rew_data thy); fun add_prf_rrule r = (Data.map o apfst o apfst) (cons (stamp (), r)); fun add_prf_rproc p = (Data.map o apfst o apsnd) (cons (stamp (), p)); fun set_preproc f = (Data.map o apsnd) (K (SOME f)); fun apply_preproc thy = (case #2 (Data.get thy) of NONE => I | SOME f => f thy); (** reconstruction of partial proof terms **) fun forall_intr_variables_term prop = fold_rev Logic.all (variables_of prop) prop; fun forall_intr_variables prop prf = fold_rev forall_intr_proof' (variables_of prop) prf; local fun app_types shift prop Ts prf = let val inst = type_variables_of prop ~~ Ts; fun subst_same A = (case AList.lookup (op =) inst A of SOME T => T | NONE => raise Same.SAME); val subst_type_same = Term_Subst.map_atypsT_same (fn TVar ((a, i), S) => subst_same (TVar ((a, i - shift), S)) | A => subst_same A); in Same.commit (map_proof_types_same subst_type_same) prf end; fun guess_name (PThm ({name, ...}, _)) = name | guess_name (prf %% Hyp _) = guess_name prf | guess_name (prf %% OfClass _) = guess_name prf | guess_name (prf % NONE) = guess_name prf | guess_name (prf % SOME (Var _)) = guess_name prf | guess_name _ = ""; (* generate constraints for proof term *) fun mk_var env Ts T = let val (env', v) = Envir.genvar "a" (env, rev Ts ---> T) in (list_comb (v, map Bound (length Ts - 1 downto 0)), env') end; fun mk_tvar S (Envir.Envir {maxidx, tenv, tyenv}) = (TVar (("'t", maxidx + 1), S), Envir.Envir {maxidx = maxidx + 1, tenv = tenv, tyenv = tyenv}); val mk_abs = fold (fn T => fn u => Abs ("", T, u)); fun unifyT thy env T U = let val Envir.Envir {maxidx, tenv, tyenv} = env; val (tyenv', maxidx') = Sign.typ_unify thy (T, U) (tyenv, maxidx); in Envir.Envir {maxidx = maxidx', tenv = tenv, tyenv = tyenv'} end; fun chaseT env (T as TVar v) = (case Type.lookup (Envir.type_env env) v of NONE => T | SOME T' => chaseT env T') | chaseT _ T = T; fun infer_type thy (env as Envir.Envir {maxidx, tenv, tyenv}) _ vTs (t as Const (s, T)) = if T = dummyT then (case Sign.const_type thy s of NONE => error ("reconstruct_proof: No such constant: " ^ quote s) | SOME T => let val T' = Type.strip_sorts (Logic.incr_tvar (maxidx + 1) T) in (Const (s, T'), T', vTs, Envir.Envir {maxidx = maxidx + 1, tenv = tenv, tyenv = tyenv}) end) else (t, T, vTs, env) | infer_type _ env _ vTs (t as Free (s, T)) = if T = dummyT then (case Symtab.lookup vTs s of NONE => let val (T, env') = mk_tvar [] env in (Free (s, T), T, Symtab.update_new (s, T) vTs, env') end | SOME T => (Free (s, T), T, vTs, env)) else (t, T, vTs, env) | infer_type _ _ _ _ (Var _) = error "reconstruct_proof: internal error" | infer_type thy env Ts vTs (Abs (s, T, t)) = let val (T', env') = if T = dummyT then mk_tvar [] env else (T, env); val (t', U, vTs', env'') = infer_type thy env' (T' :: Ts) vTs t in (Abs (s, T', t'), T' --> U, vTs', env'') end | infer_type thy env Ts vTs (t $ u) = let val (t', T, vTs1, env1) = infer_type thy env Ts vTs t; val (u', U, vTs2, env2) = infer_type thy env1 Ts vTs1 u; in (case chaseT env2 T of Type ("fun", [U', V]) => (t' $ u', V, vTs2, unifyT thy env2 U U') | _ => let val (V, env3) = mk_tvar [] env2 in (t' $ u', V, vTs2, unifyT thy env3 T (U --> V)) end) end | infer_type _ env Ts vTs (t as Bound i) = ((t, nth Ts i, vTs, env) handle General.Subscript => error ("infer_type: bad variable index " ^ string_of_int i)); fun cantunify thy (t, u) = error ("Non-unifiable terms:\n" ^ Syntax.string_of_term_global thy t ^ "\n\n" ^ Syntax.string_of_term_global thy u); fun decompose thy Ts (p as (t, u)) env = let fun rigrig (a, T) (b, U) uT ts us = if a <> b then cantunify thy p else apfst flat (fold_map (decompose thy Ts) (ts ~~ us) (uT env T U)) in case apply2 (strip_comb o Envir.head_norm env) p of ((Const c, ts), (Const d, us)) => rigrig c d (unifyT thy) ts us | ((Free c, ts), (Free d, us)) => rigrig c d (unifyT thy) ts us | ((Bound i, ts), (Bound j, us)) => rigrig (i, dummyT) (j, dummyT) (K o K) ts us | ((Abs (_, T, t), []), (Abs (_, U, u), [])) => decompose thy (T::Ts) (t, u) (unifyT thy env T U) | ((Abs (_, T, t), []), _) => decompose thy (T::Ts) (t, incr_boundvars 1 u $ Bound 0) env | (_, (Abs (_, T, u), [])) => decompose thy (T::Ts) (incr_boundvars 1 t $ Bound 0, u) env | _ => ([(mk_abs Ts t, mk_abs Ts u)], env) end; fun make_constraints_cprf thy env cprf = let fun add_cnstrt Ts prop prf cs env vTs (t, u) = let val t' = mk_abs Ts t; val u' = mk_abs Ts u in (prop, prf, cs, Pattern.unify (Context.Theory thy) (t', u') env, vTs) handle Pattern.Pattern => let val (cs', env') = decompose thy [] (t', u') env in (prop, prf, cs @ cs', env', vTs) end | Pattern.Unif => cantunify thy (Envir.norm_term env t', Envir.norm_term env u') end; fun mk_cnstrts_atom env vTs prop opTs prf = let val prop_types = type_variables_of prop; val (Ts, env') = (case opTs of NONE => fold_map (mk_tvar o Type.sort_of_atyp) prop_types env | SOME Ts => (Ts, env)); val prop' = subst_atomic_types (prop_types ~~ Ts) (forall_intr_variables_term prop) handle ListPair.UnequalLengths => error ("Wrong number of type arguments for " ^ quote (guess_name prf)) in (prop', change_types (SOME Ts) prf, [], env', vTs) end; fun head_norm (prop, prf, cnstrts, env, vTs) = (Envir.head_norm env prop, prf, cnstrts, env, vTs); fun mk_cnstrts env _ Hs vTs (PBound i) = ((nth Hs i, PBound i, [], env, vTs) handle General.Subscript => error ("mk_cnstrts: bad variable index " ^ string_of_int i)) | mk_cnstrts env Ts Hs vTs (Abst (s, opT, cprf)) = let val (T, env') = (case opT of NONE => mk_tvar [] env | SOME T => (T, env)); val (t, prf, cnstrts, env'', vTs') = mk_cnstrts env' (T::Ts) (map (incr_boundvars 1) Hs) vTs cprf; in (Const ("Pure.all", (T --> propT) --> propT) $ Abs (s, T, t), Abst (s, SOME T, prf), cnstrts, env'', vTs') end | mk_cnstrts env Ts Hs vTs (AbsP (s, SOME t, cprf)) = let val (t', _, vTs', env') = infer_type thy env Ts vTs t; val (u, prf, cnstrts, env'', vTs'') = mk_cnstrts env' Ts (t'::Hs) vTs' cprf; in (Logic.mk_implies (t', u), AbsP (s, SOME t', prf), cnstrts, env'', vTs'') end | mk_cnstrts env Ts Hs vTs (AbsP (s, NONE, cprf)) = let val (t, env') = mk_var env Ts propT; val (u, prf, cnstrts, env'', vTs') = mk_cnstrts env' Ts (t::Hs) vTs cprf; in (Logic.mk_implies (t, u), AbsP (s, SOME t, prf), cnstrts, env'', vTs') end | mk_cnstrts env Ts Hs vTs (cprf1 %% cprf2) = let val (u, prf2, cnstrts, env', vTs') = mk_cnstrts env Ts Hs vTs cprf2 in (case head_norm (mk_cnstrts env' Ts Hs vTs' cprf1) of (Const ("Pure.imp", _) $ u' $ t', prf1, cnstrts', env'', vTs'') => add_cnstrt Ts t' (prf1 %% prf2) (cnstrts' @ cnstrts) env'' vTs'' (u, u') | (t, prf1, cnstrts', env'', vTs'') => let val (v, env''') = mk_var env'' Ts propT in add_cnstrt Ts v (prf1 %% prf2) (cnstrts' @ cnstrts) env''' vTs'' (t, Logic.mk_implies (u, v)) end) end | mk_cnstrts env Ts Hs vTs (cprf % SOME t) = let val (t', U, vTs1, env1) = infer_type thy env Ts vTs t in (case head_norm (mk_cnstrts env1 Ts Hs vTs1 cprf) of (Const ("Pure.all", Type ("fun", [Type ("fun", [T, _]), _])) $ f, prf, cnstrts, env2, vTs2) => let val env3 = unifyT thy env2 T U in (betapply (f, t'), prf % SOME t', cnstrts, env3, vTs2) end | (u, prf, cnstrts, env2, vTs2) => let val (v, env3) = mk_var env2 Ts (U --> propT); in add_cnstrt Ts (v $ t') (prf % SOME t') cnstrts env3 vTs2 (u, Const ("Pure.all", (U --> propT) --> propT) $ v) end) end | mk_cnstrts env Ts Hs vTs (cprf % NONE) = (case head_norm (mk_cnstrts env Ts Hs vTs cprf) of (Const ("Pure.all", Type ("fun", [Type ("fun", [T, _]), _])) $ f, prf, cnstrts, env', vTs') => let val (t, env'') = mk_var env' Ts T in (betapply (f, t), prf % SOME t, cnstrts, env'', vTs') end | (u, prf, cnstrts, env', vTs') => let val (T, env1) = mk_tvar [] env'; val (v, env2) = mk_var env1 Ts (T --> propT); val (t, env3) = mk_var env2 Ts T in add_cnstrt Ts (v $ t) (prf % SOME t) cnstrts env3 vTs' (u, Const ("Pure.all", (T --> propT) --> propT) $ v) end) | mk_cnstrts env _ _ vTs (prf as PThm ({prop, types = opTs, ...}, _)) = mk_cnstrts_atom env vTs prop opTs prf | mk_cnstrts env _ _ vTs (prf as PAxm (_, prop, opTs)) = mk_cnstrts_atom env vTs prop opTs prf | mk_cnstrts env _ _ vTs (prf as OfClass (T, c)) = mk_cnstrts_atom env vTs (Logic.mk_of_class (T, c)) NONE prf | mk_cnstrts env _ _ vTs (prf as Oracle (_, prop, opTs)) = mk_cnstrts_atom env vTs prop opTs prf | mk_cnstrts env _ _ vTs (Hyp t) = (t, Hyp t, [], env, vTs) | mk_cnstrts _ _ _ _ MinProof = raise MIN_PROOF () in mk_cnstrts env [] [] Symtab.empty cprf end; (* update list of free variables of constraints *) fun upd_constrs env cs = let val tenv = Envir.term_env env; val tyenv = Envir.type_env env; val dom = [] |> Vartab.fold (cons o #1) tenv |> Vartab.fold (cons o #1) tyenv; val vran = [] |> Vartab.fold (Term.add_var_names o #2 o #2) tenv |> Vartab.fold (Term.add_tvar_namesT o #2 o #2) tyenv; fun check_cs [] = [] | check_cs ((u, p, vs) :: ps) = let val vs' = subtract (op =) dom vs in if vs = vs' then (u, p, vs) :: check_cs ps else (true, p, fold (insert op =) vs' vran) :: check_cs ps end; in check_cs cs end; (* solution of constraints *) fun solve _ [] bigenv = bigenv | solve thy cs bigenv = let fun search _ [] = error ("Unsolvable constraints:\n" ^ Pretty.string_of (Pretty.chunks (map (fn (_, p, _) => Syntax.pretty_flexpair (Syntax.init_pretty_global thy) (apply2 (Envir.norm_term bigenv) p)) cs))) | search env ((u, p as (t1, t2), vs)::ps) = if u then let val tn1 = Envir.norm_term bigenv t1; val tn2 = Envir.norm_term bigenv t2 in if Pattern.pattern tn1 andalso Pattern.pattern tn2 then (Pattern.unify (Context.Theory thy) (tn1, tn2) env, ps) handle Pattern.Unif => cantunify thy (tn1, tn2) else let val (cs', env') = decompose thy [] (tn1, tn2) env in if cs' = [(tn1, tn2)] then apsnd (cons (false, (tn1, tn2), vs)) (search env ps) else search env' (map (fn q => (true, q, vs)) cs' @ ps) end end else apsnd (cons (false, p, vs)) (search env ps); val Envir.Envir {maxidx, ...} = bigenv; val (env, cs') = search (Envir.empty maxidx) cs; in solve thy (upd_constrs env cs') (Envir.merge (bigenv, env)) end; in (* reconstruction of proofs *) fun reconstruct_proof thy prop cprf = let val (cprf' % SOME prop', thawf) = freeze_thaw_prf (cprf % SOME prop); val (t, prf, cs, env, _) = make_constraints_cprf thy (Envir.empty (maxidx_proof cprf ~1)) cprf'; val cs' = map (apply2 (Envir.norm_term env)) ((t, prop') :: cs) |> map (fn p => (true, p, Term.add_var_names (#1 p) (Term.add_var_names (#2 p) []))); val env' = solve thy cs' env in thawf (norm_proof env' prf) end handle MIN_PROOF () => MinProof; fun prop_of_atom prop Ts = subst_atomic_types (type_variables_of prop ~~ Ts) (forall_intr_variables_term prop); val head_norm = Envir.head_norm Envir.init; fun prop_of0 Hs (PBound i) = nth Hs i | prop_of0 Hs (Abst (s, SOME T, prf)) = Logic.all_const T $ (Abs (s, T, prop_of0 Hs prf)) | prop_of0 Hs (AbsP (_, SOME t, prf)) = Logic.mk_implies (t, prop_of0 (t :: Hs) prf) | prop_of0 Hs (prf % SOME t) = (case head_norm (prop_of0 Hs prf) of Const ("Pure.all", _) $ f => f $ t | _ => error "prop_of: all expected") | prop_of0 Hs (prf1 %% _) = (case head_norm (prop_of0 Hs prf1) of Const ("Pure.imp", _) $ _ $ Q => Q | _ => error "prop_of: ==> expected") | prop_of0 _ (Hyp t) = t | prop_of0 _ (PThm ({prop, types = SOME Ts, ...}, _)) = prop_of_atom prop Ts | prop_of0 _ (PAxm (_, prop, SOME Ts)) = prop_of_atom prop Ts | prop_of0 _ (OfClass (T, c)) = Logic.mk_of_class (T, c) | prop_of0 _ (Oracle (_, prop, SOME Ts)) = prop_of_atom prop Ts | prop_of0 _ _ = error "prop_of: partial proof object"; val prop_of' = Envir.beta_eta_contract oo prop_of0; val prop_of = prop_of' []; (* expand and reconstruct subproofs *) fun expand_name_empty (header: thm_header) = if #name header = "" then SOME "" else NONE; fun expand_proof thy expand_name prf = let fun expand seen maxidx (AbsP (s, t, prf)) = let val (seen', maxidx', prf') = expand seen maxidx prf in (seen', maxidx', AbsP (s, t, prf')) end | expand seen maxidx (Abst (s, T, prf)) = let val (seen', maxidx', prf') = expand seen maxidx prf in (seen', maxidx', Abst (s, T, prf')) end | expand seen maxidx (prf1 %% prf2) = let val (seen', maxidx', prf1') = expand seen maxidx prf1; val (seen'', maxidx'', prf2') = expand seen' maxidx' prf2; in (seen'', maxidx'', prf1' %% prf2') end | expand seen maxidx (prf % t) = let val (seen', maxidx', prf') = expand seen maxidx prf in (seen', maxidx', prf' % t) end | expand seen maxidx (prf as PThm (header, thm_body)) = let val {serial, pos, theory_name, name, prop, types} = header in (case expand_name header of SOME name' => if name' = "" andalso is_some types then let val (seen', maxidx', prf') = (case Inttab.lookup seen serial of NONE => let val prf1 = thm_body_proof_open thm_body |> reconstruct_proof thy prop |> forall_intr_variables prop; val (seen1, maxidx1, prf2) = expand_init seen prf1 val seen2 = seen1 |> Inttab.update (serial, (maxidx1, prf2)); in (seen2, maxidx1, prf2) end | SOME (maxidx1, prf1) => (seen, maxidx1, prf1)); val prf'' = prf' |> incr_indexes (maxidx + 1) |> app_types (maxidx + 1) prop (the types); in (seen', maxidx' + maxidx + 1, prf'') end else if name' <> name then (seen, maxidx, PThm (thm_header serial pos theory_name name' prop types, thm_body)) else (seen, maxidx, prf) | NONE => (seen, maxidx, prf)) end | expand seen maxidx prf = (seen, maxidx, prf) and expand_init seen prf = expand seen (maxidx_proof prf ~1) prf; in #3 (expand_init Inttab.empty prf) end; end; (** promises **) fun fulfill_norm_proof thy ps body0 = let val _ = consolidate (map #2 ps @ [body0]); val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0; val oracles = unions_oracles (fold (fn (_, PBody {oracles, ...}) => not (null oracles) ? cons oracles) ps [oracles0]); val thms = unions_thms (fold (fn (_, PBody {thms, ...}) => not (null thms) ? cons thms) ps [thms0]); val proof = rew_proof thy proof0; in PBody {oracles = oracles, thms = thms, proof = proof} end; fun fulfill_proof_future thy promises (postproc: proof_body -> proof_body) body = let fun fulfill () = postproc (fulfill_norm_proof thy (map (apsnd Future.join) promises) (Future.join body)); in if null promises then Future.map postproc body else if Future.is_finished body andalso length promises = 1 then Future.map (fn _ => fulfill ()) (snd (hd promises)) else (singleton o Future.forks) {name = "Proofterm.fulfill_proof_future", group = NONE, deps = Future.task_of body :: map (Future.task_of o snd) promises, pri = 1, interrupts = true} fulfill end; (** theorems **) (* standardization of variables for export: only frees and named bounds *) local val declare_names_term = Term.declare_term_frees; val declare_names_term' = fn SOME t => declare_names_term t | NONE => I; val declare_names_proof = fold_proof_terms declare_names_term; fun variant names bs x = #1 (Name.variant x (fold Name.declare bs names)); fun variant_term bs (Abs (x, T, t)) = let val x' = variant (declare_names_term t Name.context) bs x; val t' = variant_term (x' :: bs) t; in Abs (x', T, t') end | variant_term bs (t $ u) = variant_term bs t $ variant_term bs u | variant_term _ t = t; fun variant_proof bs (Abst (x, T, prf)) = let val x' = variant (declare_names_proof prf Name.context) bs x; val prf' = variant_proof (x' :: bs) prf; in Abst (x', T, prf') end | variant_proof bs (AbsP (x, t, prf)) = let val x' = variant (declare_names_term' t (declare_names_proof prf Name.context)) bs x; val t' = Option.map (variant_term bs) t; val prf' = variant_proof (x' :: bs) prf; in AbsP (x', t', prf') end | variant_proof bs (prf % t) = variant_proof bs prf % Option.map (variant_term bs) t | variant_proof bs (prf1 %% prf2) = variant_proof bs prf1 %% variant_proof bs prf2 | variant_proof bs (Hyp t) = Hyp (variant_term bs t) | variant_proof _ prf = prf; val used_frees_type = fold_atyps (fn TFree (a, _) => Name.declare a | _ => I); fun used_frees_term t = fold_types used_frees_type t #> Term.declare_term_frees t; val used_frees_proof = fold_proof_terms_types used_frees_term used_frees_type; val unvarifyT = Term.map_atyps (fn TVar ((a, _), S) => TFree (a, S) | T => T); val unvarify = Term.map_aterms (fn Var ((x, _), T) => Free (x, T) | t => t) #> map_types unvarifyT; val unvarify_proof = map_proof_terms unvarify unvarifyT; fun hidden_types prop proof = let val visible = (fold_types o fold_atyps) (insert (op =)) prop []; val add_hiddenT = fold_atyps (fn T => not (member (op =) visible T) ? insert (op =) T); in rev (fold_proof_terms_types (fold_types add_hiddenT) add_hiddenT proof []) end; fun standard_hidden_types term proof = let val hidden = hidden_types term proof; val idx = Term.maxidx_term term (maxidx_proof proof ~1) + 1; fun smash T = if member (op =) hidden T then TVar (("'", idx), Type.sort_of_atyp T) else T; val smashT = map_atyps smash; in map_proof_terms (map_types smashT) smashT proof end; fun standard_hidden_terms term proof = let fun add_not excl x = ((is_Free x orelse is_Var x) andalso not (member (op =) excl x)) ? insert (op =) x; val visible = fold_aterms (add_not []) term []; val hidden = fold_proof_terms (fold_aterms (add_not visible)) proof []; val dummy_term = Term.map_aterms (fn x => if member (op =) hidden x then Term.dummy_pattern (Term.fastype_of x) else x); in proof |> not (null hidden) ? map_proof_terms dummy_term I end; in fun standard_vars used (term, opt_proof) = let val proofs = opt_proof |> Option.map (standard_hidden_types term #> standard_hidden_terms term) |> the_list; val proof_terms = rev (fold (fold_proof_terms_types cons (cons o Logic.mk_type)) proofs []); val used_frees = used |> used_frees_term term |> fold used_frees_proof proofs; val inst = Term_Subst.zero_var_indexes_inst used_frees (term :: proof_terms); val term' = term |> Term_Subst.instantiate inst |> unvarify |> variant_term []; val proofs' = proofs |> map (instantiate inst #> unvarify_proof #> variant_proof []); in (term', try hd proofs') end; fun standard_vars_term used t = #1 (standard_vars used (t, NONE)); val add_standard_vars_term = fold_aterms (fn Free (x, T) => (fn env => (case AList.lookup (op =) env x of NONE => (x, T) :: env | SOME T' => if T = T' then env else raise TYPE ("standard_vars_env: type conflict for variable " ^ quote x, [T, T'], []))) | _ => I); val add_standard_vars = fold_proof_terms add_standard_vars_term; end; (* PThm nodes *) fun export_enabled () = Options.default_bool "export_proofs"; fun export_standard_enabled () = Options.default_bool "export_standard_proofs"; fun export_proof_boxes_required thy = Context.theory_name thy = Context.PureN orelse (export_enabled () andalso not (export_standard_enabled ())); fun export_proof_boxes proofs = let fun export_boxes (AbsP (_, _, prf)) = export_boxes prf | export_boxes (Abst (_, _, prf)) = export_boxes prf | export_boxes (prf1 %% prf2) = export_boxes prf1 #> export_boxes prf2 | export_boxes (prf % _) = export_boxes prf | export_boxes (PThm ({serial = i, ...}, thm_body)) = (fn boxes => if Inttab.defined boxes i then boxes else let val prf' = thm_body_proof_raw thm_body; val export = thm_body_export_proof thm_body; val boxes' = Inttab.update (i, export) boxes; in export_boxes prf' boxes' end) | export_boxes _ = I; val boxes = (proofs, Inttab.empty) |-> fold export_boxes |> Inttab.dest; in List.app (Lazy.force o #2) boxes end; local fun unconstrainT_proof algebra classrel_proof arity_proof (ucontext: Logic.unconstrain_context) = let fun hyp_map hyp = (case AList.lookup (op =) (#constraints ucontext) hyp of SOME t => Hyp t | NONE => raise Fail "unconstrainT_proof: missing constraint"); val typ = Term_Subst.map_atypsT_same (Type.strip_sorts o #atyp_map ucontext); fun ofclass (ty, c) = let val ty' = Term.map_atyps (#atyp_map ucontext) ty; in the_single (of_sort_proof algebra classrel_proof arity_proof hyp_map (ty', [c])) end; in Same.commit (map_proof_same (Term_Subst.map_types_same typ) typ ofclass) #> fold_rev (implies_intr_proof o snd) (#constraints ucontext) end; fun export_proof thy i prop prf0 = let val prf = prf0 |> reconstruct_proof thy prop |> apply_preproc thy; val (prop', SOME prf') = (prop, SOME prf) |> standard_vars Name.context; val args = [] |> add_standard_vars_term prop' |> add_standard_vars prf' |> rev; val typargs = [] |> Term.add_tfrees prop' |> fold_proof_terms Term.add_tfrees prf' |> rev; val consts = Sign.consts_of thy; val xml = (typargs, (args, (prop', no_thm_names prf'))) |> let open XML.Encode Term_XML.Encode; val encode_vars = list (pair string typ); val encode_term = encode_standard_term consts; val encode_proof = encode_standard_proof consts; in pair (list (pair string sort)) (pair encode_vars (pair encode_term encode_proof)) end; in Export.export_params {theory = thy, binding = Path.binding0 (Path.make ["proofs", string_of_int i]), executable = false, compress = true, strict = false} xml end; fun export thy i prop prf = if export_enabled () then let val _ = export_proof_boxes [prf]; val _ = export_proof thy i prop prf; in () end else (); fun prune proof = if Options.default_bool "prune_proofs" then MinProof else proof; fun prepare_thm_proof unconstrain thy classrel_proof arity_proof (name, pos) shyps hyps concl promises body = let val named = name <> ""; val prop = Logic.list_implies (hyps, concl); val args = prop_args prop; val (ucontext, prop1) = Logic.unconstrainT shyps prop; val PBody {oracles = oracles0, thms = thms0, proof = prf} = body; val body0 = Future.value (PBody {oracles = oracles0, thms = thms0, proof = if proofs_enabled () then fold_rev implies_intr_proof hyps prf else MinProof}); fun publish i = map_proof_of (rew_proof thy #> tap (export thy i prop1) #> prune); val open_proof = not named ? rew_proof thy; fun new_prf () = let val i = serial (); val unconstrainT = unconstrainT_proof (Sign.classes_of thy) classrel_proof arity_proof ucontext; val postproc = map_proof_of unconstrainT #> named ? publish i; in (i, fulfill_proof_future thy promises postproc body0) end; val (i, body') = (*non-deterministic, depends on unknown promises*) (case strip_combt (fst (strip_combP prf)) of (PThm ({serial = ser, name = a, prop = prop', types = NONE, ...}, thm_body'), args') => if (a = "" orelse a = name) andalso prop' = prop1 andalso args' = args then let val Thm_Body {body = body', ...} = thm_body'; val i = if a = "" andalso named then serial () else ser; in (i, body' |> ser <> i ? Future.map (publish i)) end else new_prf () | _ => new_prf ()); val export_proof = if named orelse not (export_enabled ()) then no_export_proof else Lazy.lazy (fn () => join_proof body' |> open_proof |> export_proof thy i prop1 handle exn => if Exn.is_interrupt exn then raise Fail ("Interrupt: potential resource problems while exporting proof " ^ string_of_int i) else Exn.reraise exn); val theory_name = Context.theory_long_name thy; val thm = (i, make_thm_node theory_name name prop1 body'); val header = thm_header i ([pos, Position.thread_data ()]) theory_name name prop1 NONE; val thm_body = Thm_Body {export_proof = export_proof, open_proof = open_proof, body = body'}; val head = PThm (header, thm_body); val proof = if unconstrain then proof_combt' (head, (map o Option.map o Term.map_types) (#map_atyps ucontext) args) else proof_combP (proof_combt' (head, args), map OfClass (#outer_constraints ucontext) @ map Hyp hyps); in (thm, proof) end; in fun thm_proof thy = prepare_thm_proof false thy; fun unconstrain_thm_proof thy classrel_proof arity_proof shyps concl promises body = prepare_thm_proof true thy classrel_proof arity_proof ("", Position.none) shyps [] concl promises body; end; (* PThm identity *) fun get_identity shyps hyps prop prf = let val (_, prop) = Logic.unconstrainT shyps (Logic.list_implies (hyps, prop)) in (case fst (strip_combt (fst (strip_combP prf))) of PThm ({serial, theory_name, name, prop = prop', ...}, _) => if prop = prop' then SOME {serial = serial, theory_name = theory_name, name = name} else NONE | _ => NONE) end; fun get_approximative_name shyps hyps prop prf = Option.map #name (get_identity shyps hyps prop prf) |> the_default ""; (* thm_id *) type thm_id = {serial: serial, theory_name: string}; fun make_thm_id (serial, theory_name) : thm_id = {serial = serial, theory_name = theory_name}; fun thm_header_id ({serial, theory_name, ...}: thm_header) = make_thm_id (serial, theory_name); fun thm_id (serial, thm_node) : thm_id = make_thm_id (serial, thm_node_theory_name thm_node); fun get_id shyps hyps prop prf : thm_id option = (case get_identity shyps hyps prop prf of NONE => NONE | SOME {name = "", ...} => NONE | SOME {serial, theory_name, ...} => SOME (make_thm_id (serial, theory_name))); fun this_id NONE _ = false | this_id (SOME (thm_id: thm_id)) (thm_id': thm_id) = #serial thm_id = #serial thm_id'; (* proof boxes: intermediate PThm nodes *) fun proof_boxes {included, excluded} proofs = let fun boxes_of (Abst (_, _, prf)) = boxes_of prf | boxes_of (AbsP (_, _, prf)) = boxes_of prf | boxes_of (prf % _) = boxes_of prf | boxes_of (prf1 %% prf2) = boxes_of prf1 #> boxes_of prf2 | boxes_of (PThm (header as {serial = i, ...}, thm_body)) = (fn boxes => let val thm_id = thm_header_id header in if Inttab.defined boxes i orelse (excluded thm_id andalso not (included thm_id)) then boxes else let val prf' = thm_body_proof_open thm_body; val boxes' = Inttab.update (i, (header, prf')) boxes; in boxes_of prf' boxes' end end) | boxes_of MinProof = raise MIN_PROOF () | boxes_of _ = I; in Inttab.fold_rev (cons o #2) (fold boxes_of proofs Inttab.empty) [] end; end; structure Basic_Proofterm = struct datatype proof = datatype Proofterm.proof datatype proof_body = datatype Proofterm.proof_body val op %> = Proofterm.%> end; open Basic_Proofterm;