src/Pure/Isar/element.ML
author ballarin
Tue Jul 11 11:17:09 2006 +0200 (2006-07-11)
changeset 20068 19c7361db4a3
parent 20058 7d035e26e5f9
child 20150 baa589c574ff
permissions -rw-r--r--
New function transfer_witness lifting Thm.transfer to witnesses.
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(*  Title:      Pure/Isar/element.ML
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    ID:         $Id$
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    Author:     Makarius
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Explicit data structures for some Isar language elements, with derived
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logical operations.
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*)
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signature ELEMENT =
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sig
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  datatype ('typ, 'term) stmt =
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    Shows of ((string * Attrib.src list) * ('term * 'term list) list) list |
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    Obtains of (string * ((string * 'typ option) list * 'term list)) list
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  type statement  (*= (string, string) stmt*)
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  type statement_i  (*= (typ, term) stmt*)
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  datatype ('typ, 'term, 'fact) ctxt =
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    Fixes of (string * 'typ option * mixfix) list |
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    Constrains of (string * 'typ) list |
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    Assumes of ((string * Attrib.src list) * ('term * 'term list) list) list |
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    Defines of ((string * Attrib.src list) * ('term * 'term list)) list |
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    Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list
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  type context (*= (string, string, thmref) ctxt*)
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  type context_i (*= (typ, term, thm list) ctxt*)
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  val map_ctxt: {name: string -> string,
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    var: string * mixfix -> string * mixfix,
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    typ: 'typ -> 'a, term: 'term -> 'b, fact: 'fact -> 'c,
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    attrib: Attrib.src -> Attrib.src} -> ('typ, 'term, 'fact) ctxt -> ('a, 'b, 'c) ctxt
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  val map_ctxt_values: (typ -> typ) -> (term -> term) -> (thm -> thm) -> context_i -> context_i
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  val params_of: context_i -> (string * typ) list
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  val prems_of: context_i -> term list
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  val facts_of: theory -> context_i ->
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    ((string * Attrib.src list) * (thm list * Attrib.src list) list) list
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  val pretty_stmt: Proof.context -> statement_i -> Pretty.T list
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  val pretty_ctxt: Proof.context -> context_i -> Pretty.T list
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  val pretty_statement: Proof.context -> string -> thm -> Pretty.T
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  type witness
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  val map_witness: (term * thm -> term * thm) -> witness -> witness
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  val witness_prop: witness -> term
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  val witness_hyps: witness -> term list
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  val assume_witness: theory -> term -> witness
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  val prove_witness: Proof.context -> term -> tactic -> witness
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  val conclude_witness: witness -> thm
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  val mark_witness: term -> term
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  val make_witness: term -> thm -> witness
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  val dest_witness: witness -> term * thm
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  val transfer_witness: theory -> witness -> witness
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  val refine_witness: Proof.state -> Proof.state Seq.seq
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  val rename: (string * (string * mixfix option)) list -> string -> string
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  val rename_var: (string * (string * mixfix option)) list -> string * mixfix -> string * mixfix
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  val rename_term: (string * (string * mixfix option)) list -> term -> term
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  val rename_thm: (string * (string * mixfix option)) list -> thm -> thm
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  val rename_witness: (string * (string * mixfix option)) list -> witness -> witness
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  val rename_ctxt: (string * (string * mixfix option)) list -> context_i -> context_i
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  val instT_type: typ Symtab.table -> typ -> typ
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  val instT_term: typ Symtab.table -> term -> term
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  val instT_thm: theory -> typ Symtab.table -> thm -> thm
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  val instT_witness: theory -> typ Symtab.table -> witness -> witness
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  val instT_ctxt: theory -> typ Symtab.table -> context_i -> context_i
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  val inst_term: typ Symtab.table * term Symtab.table -> term -> term
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  val inst_thm: theory -> typ Symtab.table * term Symtab.table -> thm -> thm
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  val inst_witness: theory -> typ Symtab.table * term Symtab.table -> witness -> witness
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  val inst_ctxt: theory -> typ Symtab.table * term Symtab.table -> context_i -> context_i
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  val satisfy_thm: witness list -> thm -> thm
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  val satisfy_witness: witness list -> witness -> witness
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  val satisfy_ctxt: witness list -> context_i -> context_i
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end;
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structure Element: ELEMENT =
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struct
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(** language elements **)
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(* statement *)
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datatype ('typ, 'term) stmt =
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  Shows of ((string * Attrib.src list) * ('term * 'term list) list) list |
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  Obtains of (string * ((string * 'typ option) list * 'term list)) list;
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type statement = (string, string) stmt;
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type statement_i = (typ, term) stmt;
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(* context *)
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datatype ('typ, 'term, 'fact) ctxt =
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  Fixes of (string * 'typ option * mixfix) list |
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  Constrains of (string * 'typ) list |
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  Assumes of ((string * Attrib.src list) * ('term * 'term list) list) list |
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  Defines of ((string * Attrib.src list) * ('term * 'term list)) list |
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  Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list;
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type context = (string, string, thmref) ctxt;
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type context_i = (typ, term, thm list) ctxt;
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fun map_ctxt {name, var, typ, term, fact, attrib} =
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  fn Fixes fixes => Fixes (fixes |> map (fn (x, T, mx) =>
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       let val (x', mx') = var (x, mx) in (x', Option.map typ T, mx') end))
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   | Constrains xs => Constrains (xs |> map (fn (x, T) => (#1 (var (x, NoSyn)), typ T)))
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   | Assumes asms => Assumes (asms |> map (fn ((a, atts), propps) =>
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      ((name a, map attrib atts), propps |> map (fn (t, ps) => (term t, map term ps)))))
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   | Defines defs => Defines (defs |> map (fn ((a, atts), (t, ps)) =>
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      ((name a, map attrib atts), (term t, map term ps))))
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   | Notes facts => Notes (facts |> map (fn ((a, atts), bs) =>
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      ((name a, map attrib atts), bs |> map (fn (ths, btts) => (fact ths, map attrib btts)))));
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fun map_ctxt_values typ term thm = map_ctxt
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  {name = I, var = I, typ = typ, term = term, fact = map thm,
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    attrib = Args.map_values I typ term thm};
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(* logical content *)
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fun params_of (Fixes fixes) = fixes |> map
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    (fn (x, SOME T, _) => (x, T)
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      | (x, _, _) => raise TERM ("Untyped context element parameter " ^ quote x, []))
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  | params_of _ = [];
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fun prems_of (Assumes asms) = maps (map fst o snd) asms
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  | prems_of (Defines defs) = map (fst o snd) defs
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  | prems_of _ = [];
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fun assume thy t = Goal.norm_hhf (Thm.assume (Thm.cterm_of thy t));
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fun facts_of thy (Assumes asms) = map (apsnd (map (fn (t, _) => ([assume thy t], [])))) asms
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  | facts_of thy (Defines defs) = map (apsnd (fn (t, _) => [([assume thy t], [])])) defs
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  | facts_of _ (Notes facts) = facts
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  | facts_of _ _ = [];
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(** pretty printing **)
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fun pretty_items _ _ [] = []
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  | pretty_items keyword sep (x :: ys) =
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      Pretty.block [Pretty.keyword keyword, Pretty.brk 1, x] ::
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        map (fn y => Pretty.block [Pretty.str "  ", Pretty.keyword sep, Pretty.brk 1, y]) ys;
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fun pretty_name_atts ctxt (name, atts) sep =
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  if name = "" andalso null atts then []
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  else [Pretty.block
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    (Pretty.breaks (Pretty.str name :: Args.pretty_attribs ctxt atts @ [Pretty.str sep]))];
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(* pretty_stmt *)
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fun pretty_stmt ctxt =
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  let
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    val prt_typ = Pretty.quote o ProofContext.pretty_typ ctxt;
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    val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;
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    val prt_terms = separate (Pretty.keyword "and") o map prt_term;
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    val prt_name_atts = pretty_name_atts ctxt;
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    fun prt_show (a, ts) =
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      Pretty.block (Pretty.breaks (prt_name_atts a ":" @ prt_terms (map fst ts)));
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    fun prt_var (x, SOME T) = Pretty.block [Pretty.str (x ^ " ::"), Pretty.brk 1, prt_typ T]
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      | prt_var (x, NONE) = Pretty.str x;
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    val prt_vars =  separate (Pretty.keyword "and") o map prt_var;
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    fun prt_obtain (_, ([], ts)) = Pretty.block (Pretty.breaks (prt_terms ts))
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      | prt_obtain (_, (xs, ts)) = Pretty.block (Pretty.breaks
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          (prt_vars xs @ [Pretty.keyword "where"] @ prt_terms ts));
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  in
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    fn Shows shows => pretty_items "shows" "and" (map prt_show shows)
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     | Obtains obtains => pretty_items "obtains" "|" (map prt_obtain obtains)
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  end;
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(* pretty_ctxt *)
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fun pretty_ctxt ctxt =
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  let
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    val prt_typ = Pretty.quote o ProofContext.pretty_typ ctxt;
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    val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;
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    val prt_thm = Pretty.backquote o ProofContext.pretty_thm ctxt;
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    val prt_name_atts = pretty_name_atts ctxt;
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    fun prt_mixfix NoSyn = []
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      | prt_mixfix mx = [Pretty.brk 2, Syntax.pretty_mixfix mx];
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    fun prt_fix (x, SOME T, mx) = Pretty.block (Pretty.str (x ^ " ::") :: Pretty.brk 1 ::
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          prt_typ T :: Pretty.brk 1 :: prt_mixfix mx)
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      | prt_fix (x, NONE, mx) = Pretty.block (Pretty.str x :: Pretty.brk 1 :: prt_mixfix mx);
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    fun prt_constrain (x, T) = prt_fix (x, SOME T, NoSyn);
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    fun prt_asm (a, ts) =
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      Pretty.block (Pretty.breaks (prt_name_atts a ":" @ map (prt_term o fst) ts));
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    fun prt_def (a, (t, _)) =
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      Pretty.block (Pretty.breaks (prt_name_atts a ":" @ [prt_term t]));
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    fun prt_fact (ths, []) = map prt_thm ths
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      | prt_fact (ths, atts) = Pretty.enclose "(" ")"
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          (Pretty.breaks (map prt_thm ths)) :: Args.pretty_attribs ctxt atts;
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    fun prt_note (a, ths) =
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      Pretty.block (Pretty.breaks (flat (prt_name_atts a "=" :: map prt_fact ths)));
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  in
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    fn Fixes fixes => pretty_items "fixes" "and" (map prt_fix fixes)
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     | Constrains xs => pretty_items "constrains" "and" (map prt_constrain xs)
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     | Assumes asms => pretty_items "assumes" "and" (map prt_asm asms)
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     | Defines defs => pretty_items "defines" "and" (map prt_def defs)
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     | Notes facts => pretty_items "notes" "and" (map prt_note facts)
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  end;
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(* pretty_statement *)
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local
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fun thm_name kind th prts =
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  let val head =
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    (case #1 (Thm.get_name_tags th) of
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      "" => Pretty.command kind
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    | a => Pretty.block [Pretty.command kind, Pretty.brk 1, Pretty.str (Sign.base_name a ^ ":")])
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  in Pretty.block (Pretty.fbreaks (head :: prts)) end;
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fun obtain prop ctxt =
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  let
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    val xs = Variable.rename_wrt ctxt [] (Logic.strip_params prop);
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    val args = rev (map Free xs);
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    val As = Logic.strip_assums_hyp prop |> map (fn t => Term.subst_bounds (args, t));
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    val ctxt' = ctxt |> fold Variable.declare_term args;
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  in (("", (map (apsnd SOME) xs, As)), ctxt') end;
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in
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fun pretty_statement ctxt kind raw_th =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val th = Goal.norm_hhf raw_th;
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    fun standard_thesis t =
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      let
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        val C = ObjectLogic.drop_judgment thy (Thm.concl_of th);
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        val C' = Var ((AutoBind.thesisN, Thm.maxidx_of th + 1), Term.fastype_of C);
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      in Term.subst_atomic [(C, C')] t end;
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    val raw_prop =
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      Thm.prop_of th
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      |> singleton (Variable.monomorphic ctxt)
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      |> K (ObjectLogic.is_elim th) ? standard_thesis
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      |> Term.zero_var_indexes;
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    val vars = Term.add_vars raw_prop [];
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    val frees = Variable.rename_wrt ctxt [raw_prop] (map (apfst fst) vars);
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    val fixes = rev (filter_out (fn (x, _) => x = AutoBind.thesisN) frees);
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    val prop = Term.instantiate ([], vars ~~ map Free frees) raw_prop;
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    val (prems, concl) = Logic.strip_horn prop;
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    val thesis = ObjectLogic.fixed_judgment thy AutoBind.thesisN;
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    val (asms, cases) = take_suffix (fn prem => thesis aconv Logic.strip_assums_concl prem) prems;
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  in
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    pretty_ctxt ctxt (Fixes (map (fn (x, T) => (x, SOME T, NoSyn)) fixes)) @
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    pretty_ctxt ctxt (Assumes (map (fn t => (("", []), [(t, [])])) asms)) @
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    pretty_stmt ctxt
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     (if null cases then Shows [(("", []), [(concl, [])])]
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      else Obtains (#1 (fold_map obtain cases (ctxt |> Variable.declare_term prop))))
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  end |> thm_name kind raw_th;
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end;
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(** logical operations **)
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(* witnesses -- hypotheses as protected facts *)
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datatype witness = Witness of term * thm;
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fun map_witness f (Witness witn) = Witness (f witn);
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fun witness_prop (Witness (t, _)) = t;
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fun witness_hyps (Witness (_, th)) = #hyps (Thm.rep_thm th);
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fun assume_witness thy t =
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  Witness (t, Goal.protect (Thm.assume (Thm.cterm_of thy t)));
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fun prove_witness ctxt t tac =
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  Witness (t, Goal.prove ctxt [] [] (Logic.protect t) (fn _ =>
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    Tactic.rtac Drule.protectI 1 THEN tac));
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fun conclude_witness (Witness (_, th)) = Goal.norm_hhf (Goal.conclude th);
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val mark_witness = Logic.protect;
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fun make_witness t th = Witness (t, th);
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fun dest_witness (Witness w) = w;
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fun transfer_witness thy (Witness (t, th)) = Witness (t, Thm.transfer thy th);
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val refine_witness =
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  Proof.refine (Method.Basic (K (Method.RAW_METHOD
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    (K (ALLGOALS
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      (PRECISE_CONJUNCTS ~1 (ALLGOALS
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        (PRECISE_CONJUNCTS ~1 (TRYALL (Tactic.rtac Drule.protectI))))))))));
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(* derived rules *)
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fun instantiate_tfrees thy subst th =
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  let
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    val certT = Thm.ctyp_of thy;
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    val idx = Thm.maxidx_of th + 1;
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    fun cert_inst (a, (S, T)) = (certT (TVar ((a, idx), S)), certT T);
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    fun add_inst (a, S) insts =
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      if AList.defined (op =) insts a then insts
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      else (case AList.lookup (op =) subst a of NONE => insts | SOME T => (a, (S, T)) :: insts);
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    val insts =
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      Term.fold_types (Term.fold_atyps (fn TFree v => add_inst v | _ => I))
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        (Thm.full_prop_of th) [];
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  in
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    th
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    |> Thm.generalize (map fst insts, []) idx
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    |> Thm.instantiate (map cert_inst insts, [])
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  end;
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fun instantiate_frees thy subst =
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  let val cert = Thm.cterm_of thy in
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    Drule.forall_intr_list (map (cert o Free o fst) subst) #>
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    Drule.forall_elim_list (map (cert o snd) subst)
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  end;
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fun hyps_rule rule th =
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  let
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    val cterm_rule = Drule.mk_term #> rule #> Drule.dest_term;
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    val {hyps, ...} = Thm.crep_thm th;
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  in
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    Drule.implies_elim_list
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      (rule (Drule.implies_intr_list hyps th))
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      (map (Thm.assume o cterm_rule) hyps)
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  end;
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(* rename *)
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fun rename ren x =
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  (case AList.lookup (op =) ren (x: string) of
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    NONE => x
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  | SOME (x', _) => x');
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fun rename_var ren (x, mx) =
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  (case (AList.lookup (op =) ren (x: string), mx) of
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    (NONE, _) => (x, mx)
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  | (SOME (x', NONE), Structure) => (x', mx)
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  | (SOME (x', SOME _), Structure) =>
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      error ("Attempt to change syntax of structure parameter " ^ quote x)
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  | (SOME (x', NONE), _) => (x', NoSyn)
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  | (SOME (x', SOME mx'), _) => (x', mx'));
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fun rename_term ren (Free (x, T)) = Free (rename ren x, T)
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  | rename_term ren (t $ u) = rename_term ren t $ rename_term ren u
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  | rename_term ren (Abs (x, T, t)) = Abs (x, T, rename_term ren t)
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  | rename_term _ a = a;
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fun rename_thm ren th =
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  let
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    val subst = Drule.frees_of th
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      |> map_filter (fn (x, T) =>
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        let val x' = rename ren x
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        in if x = x' then NONE else SOME ((x, T), (Free (x', T))) end);
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  in
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    if null subst then th
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    else th |> hyps_rule (instantiate_frees (Thm.theory_of_thm th) subst)
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  end;
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fun rename_witness ren =
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  map_witness (fn (t, th) => (rename_term ren t, rename_thm ren th));
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fun rename_ctxt ren =
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  map_ctxt_values I (rename_term ren) (rename_thm ren)
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  #> map_ctxt {name = I, typ = I, term = I, fact = I, attrib = I, var = rename_var ren};
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   374
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   375
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(* instantiate types *)
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fun instT_type env =
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  if Symtab.is_empty env then I
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  else Term.map_type_tfree (fn (x, S) => the_default (TFree (x, S)) (Symtab.lookup env x));
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fun instT_term env =
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  if Symtab.is_empty env then I
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  else Term.map_term_types (instT_type env);
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   385
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   386
fun instT_subst env th =
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  Drule.tfrees_of th
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  |> map_filter (fn (a, S) =>
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   389
    let
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      val T = TFree (a, S);
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      val T' = the_default T (Symtab.lookup env a);
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    in if T = T' then NONE else SOME (a, T') end);
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   393
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   394
fun instT_thm thy env th =
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  if Symtab.is_empty env then th
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   396
  else
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    let val subst = instT_subst env th
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   398
    in if null subst then th else th |> hyps_rule (instantiate_tfrees thy subst) end;
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   399
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   400
fun instT_witness thy env =
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  map_witness (fn (t, th) => (instT_term env t, instT_thm thy env th));
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   402
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   403
fun instT_ctxt thy env =
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  map_ctxt_values (instT_type env) (instT_term env) (instT_thm thy env);
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   405
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   406
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   407
(* instantiate types and terms *)
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   408
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   409
fun inst_term (envT, env) =
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   410
  if Symtab.is_empty env then instT_term envT
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   411
  else
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   412
    let
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   413
      val instT = instT_type envT;
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      fun inst (Const (x, T)) = Const (x, instT T)
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   415
        | inst (Free (x, T)) =
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   416
            (case Symtab.lookup env x of
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   417
              NONE => Free (x, instT T)
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   418
            | SOME t => t)
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   419
        | inst (Var (xi, T)) = Var (xi, instT T)
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   420
        | inst (b as Bound _) = b
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   421
        | inst (Abs (x, T, t)) = Abs (x, instT T, inst t)
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   422
        | inst (t $ u) = inst t $ inst u;
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   423
    in Envir.beta_norm o inst end;
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   424
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   425
fun inst_thm thy (envT, env) th =
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   426
  if Symtab.is_empty env then instT_thm thy envT th
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   427
  else
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   428
    let
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   429
      val substT = instT_subst envT th;
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   430
      val subst = Drule.frees_of th
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   431
        |> map_filter (fn (x, T) =>
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   432
          let
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   433
            val T' = instT_type envT T;
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   434
            val t = Free (x, T');
wenzelm@19777
   435
            val t' = the_default t (Symtab.lookup env x);
wenzelm@19777
   436
          in if t aconv t' then NONE else SOME ((x, T'), t') end);
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   437
    in
wenzelm@19777
   438
      if null substT andalso null subst then th
wenzelm@19777
   439
      else th |> hyps_rule
wenzelm@19777
   440
       (instantiate_tfrees thy substT #>
wenzelm@19777
   441
        instantiate_frees thy subst #>
wenzelm@19777
   442
        Drule.fconv_rule (Thm.beta_conversion true))
wenzelm@19777
   443
    end;
wenzelm@19777
   444
wenzelm@19777
   445
fun inst_witness thy envs =
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   446
  map_witness (fn (t, th) => (inst_term envs t, inst_thm thy envs th));
wenzelm@19777
   447
wenzelm@19777
   448
fun inst_ctxt thy envs =
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   449
  map_ctxt_values (instT_type (#1 envs)) (inst_term envs) (inst_thm thy envs);
wenzelm@19777
   450
wenzelm@19777
   451
wenzelm@19777
   452
(* satisfy hypotheses *)
wenzelm@19777
   453
wenzelm@19777
   454
fun satisfy_thm witns thm = thm |> fold (fn hyp =>
wenzelm@19777
   455
    (case find_first (fn Witness (t, _) => Thm.term_of hyp aconv t) witns of
wenzelm@19777
   456
      NONE => I
wenzelm@19777
   457
    | SOME (Witness (_, th)) => Drule.implies_intr_protected [hyp] #> Goal.comp_hhf th))
wenzelm@19777
   458
  (#hyps (Thm.crep_thm thm));
wenzelm@19777
   459
wenzelm@19777
   460
fun satisfy_witness witns = map_witness (apsnd (satisfy_thm witns));
wenzelm@19777
   461
wenzelm@19843
   462
fun satisfy_ctxt witns = map_ctxt_values I I (satisfy_thm witns);
wenzelm@19843
   463
wenzelm@19267
   464
end;