(*  Title:      Pure/Isar/element.ML

    ID:         $Id$

    Author:     Makarius

Explicit data structures for some Isar language elements.

*)

signature ELEMENT =

sig

  datatype ('typ, 'term) stmt =

    Shows of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |

    Obtains of (string * ((string * 'typ option) list * 'term list)) list

  type statement  (*= (string, string) stmt*)

  type statement_i  (*= (typ, term) stmt*)

  datatype ('typ, 'term, 'fact) ctxt =

    Fixes of (string * 'typ option * mixfix) list |

    Constrains of (string * 'typ) list |

    Assumes of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |

    Defines of ((string * Attrib.src list) * ('term * 'term list)) list |

    Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list

  type context (*= (string, string, thmref) ctxt*)

  type context_i (*= (typ, term, thm list) ctxt*)

  val map_ctxt: {name: string -> string,

    var: string * mixfix -> string * mixfix,

    typ: 'typ -> 'a, term: 'term -> 'b, fact: 'fact -> 'c,

    attrib: Attrib.src -> Attrib.src} -> ('typ, 'term, 'fact) ctxt -> ('a, 'b, 'c) ctxt

  val map_ctxt_values: (typ -> typ) -> (term -> term) -> (thm -> thm) -> context_i -> context_i

  val rename: (string * (string * mixfix option)) list -> string -> string

  val rename_var: (string * (string * mixfix option)) list -> string * mixfix -> string * mixfix

  val rename_term: (string * (string * mixfix option)) list -> term -> term

  val rename_thm: (string * (string * mixfix option)) list -> thm -> thm

  val rename_ctxt: (string * (string * mixfix option)) list -> context_i -> context_i

  val instT_type: typ Symtab.table -> typ -> typ

  val instT_term: typ Symtab.table -> term -> term

  val instT_thm: theory -> typ Symtab.table -> thm -> thm

  val instT_ctxt: theory -> typ Symtab.table -> context_i -> context_i

  val inst_term: typ Symtab.table * term Symtab.table -> term -> term

  val inst_thm: theory -> typ Symtab.table * term Symtab.table -> thm -> thm

  val inst_ctxt: theory -> typ Symtab.table * term Symtab.table -> context_i -> context_i

  val pretty_stmt: ProofContext.context -> statement_i -> Pretty.T list

  val pretty_ctxt: ProofContext.context -> context_i -> Pretty.T list

  val pretty_statement: ProofContext.context -> string -> thm -> Pretty.T

end;

structure Element: ELEMENT =

struct

(** conclusions **)

datatype ('typ, 'term) stmt =

  Shows of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |

  Obtains of (string * ((string * 'typ option) list * 'term list)) list;

type statement = (string, string) stmt;

type statement_i = (typ, term) stmt;

(** context elements **)

(* datatype ctxt *)

datatype ('typ, 'term, 'fact) ctxt =

  Fixes of (string * 'typ option * mixfix) list |

  Constrains of (string * 'typ) list |

  Assumes of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |

  Defines of ((string * Attrib.src list) * ('term * 'term list)) list |

  Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list;

type context = (string, string, thmref) ctxt;

type context_i = (typ, term, thm list) ctxt;

fun map_ctxt {name, var, typ, term, fact, attrib} =

  fn Fixes fixes => Fixes (fixes |> map (fn (x, T, mx) =>

       let val (x', mx') = var (x, mx) in (x', Option.map typ T, mx') end))

   | Constrains xs => Constrains (xs |> map (fn (x, T) => (#1 (var (x, NoSyn)), typ T)))

   | Assumes asms => Assumes (asms |> map (fn ((a, atts), propps) =>

      ((name a, map attrib atts), propps |> map (fn (t, (ps, qs)) =>

        (term t, (map term ps, map term qs))))))

   | Defines defs => Defines (defs |> map (fn ((a, atts), (t, ps)) =>

      ((name a, map attrib atts), (term t, map term ps))))

   | Notes facts => Notes (facts |> map (fn ((a, atts), bs) =>

      ((name a, map attrib atts), bs |> map (fn (ths, btts) => (fact ths, map attrib btts)))));

fun map_ctxt_values typ term thm = map_ctxt

  {name = I, var = I, typ = typ, term = term, fact = map thm,

    attrib = Args.map_values I typ term thm};

(** logical operations **)

(* derived rules *)

fun instantiate_tfrees thy subst =

  let

    val certT = Thm.ctyp_of thy;

    fun inst vs (a, T) = AList.lookup (op =) vs a

      |> Option.map (fn v => (certT (TVar v), certT T));

  in

    Drule.tvars_intr_list (map fst subst) #->

    (fn vs => Thm.instantiate (map_filter (inst vs) subst, []))

  end;

fun instantiate_frees thy subst =

  let val cert = Thm.cterm_of thy in

    Drule.forall_intr_list (map (cert o Free o fst) subst) #>

    Drule.forall_elim_list (map (cert o snd) subst)

  end;

fun hyps_rule rule th =

  let

    val cterm_rule = Thm.reflexive #> rule #> Thm.cprop_of #> Drule.dest_equals #> #1;

    val {hyps, ...} = Thm.crep_thm th;

  in

    Drule.implies_elim_list

      (rule (Drule.implies_intr_list hyps th))

      (map (Thm.assume o cterm_rule) hyps)

  end;

(* renaming *)

fun rename ren x =

  (case AList.lookup (op =) ren (x: string) of

    NONE => x

  | SOME (x', _) => x');

fun rename_var ren (x, mx) =

  (case (AList.lookup (op =) ren (x: string), mx) of

    (NONE, _) => (x, mx)

  | (SOME (x', NONE), Structure) => (x', mx)

  | (SOME (x', SOME _), Structure) =>

      error ("Attempt to change syntax of structure parameter " ^ quote x)

  | (SOME (x', NONE), _) => (x', NoSyn)

  | (SOME (x', SOME mx'), _) => (x', mx'));

fun rename_term ren (Free (x, T)) = Free (rename ren x, T)

  | rename_term ren (t $ u) = rename_term ren t $ rename_term ren u

  | rename_term ren (Abs (x, T, t)) = Abs (x, T, rename_term ren t)

  | rename_term _ a = a;

fun rename_thm ren th =

  let

    val subst = Drule.frees_of th

      |> map_filter (fn (x, T) =>

        let val x' = rename ren x

        in if x = x' then NONE else SOME ((x, T), (Free (x', T))) end);

  in

    if null subst then th

    else th |> hyps_rule (instantiate_frees (Thm.theory_of_thm th) subst)

  end;

fun rename_ctxt ren =

  map_ctxt_values I (rename_term ren) (rename_thm ren)

  #> map_ctxt {name = I, typ = I, term = I, fact = I, attrib = I, var = rename_var ren};

(* type instantiation *)

fun instT_type env =

  if Symtab.is_empty env then I

  else Term.map_type_tfree (fn (x, S) => the_default (TFree (x, S)) (Symtab.lookup env x));

fun instT_term env =

  if Symtab.is_empty env then I

  else Term.map_term_types (instT_type env);

fun instT_subst env th =

  Drule.tfrees_of th

  |> map_filter (fn (a, S) =>

    let

      val T = TFree (a, S);

      val T' = the_default T (Symtab.lookup env a);

    in if T = T' then NONE else SOME (a, T') end);

fun instT_thm thy env th =

  if Symtab.is_empty env then th

  else

    let val subst = instT_subst env th

    in if null subst then th else th |> hyps_rule (instantiate_tfrees thy subst) end;

fun instT_ctxt thy env =

  map_ctxt_values (instT_type env) (instT_term env) (instT_thm thy env);

(* type and term instantiation *)

fun inst_term (envT, env) =

  if Symtab.is_empty env then instT_term envT

  else

    let

      val instT = instT_type envT;

      fun inst (Const (x, T)) = Const (x, instT T)

        | inst (Free (x, T)) =

            (case Symtab.lookup env x of

              NONE => Free (x, instT T)

            | SOME t => t)

        | inst (Var (xi, T)) = Var (xi, instT T)

        | inst (b as Bound _) = b

        | inst (Abs (x, T, t)) = Abs (x, instT T, inst t)

        | inst (t $ u) = inst t $ inst u;

    in Envir.beta_norm o inst end;

fun inst_thm thy (envT, env) th =

  if Symtab.is_empty env then instT_thm thy envT th

  else

    let

      val substT = instT_subst envT th;

      val subst = Drule.frees_of th

        |> map_filter (fn (x, T) =>

          let

            val T' = instT_type envT T;

            val t = Free (x, T');

            val t' = the_default t (Symtab.lookup env x);

          in if t aconv t' then NONE else SOME ((x, T'), t') end);

    in

      if null substT andalso null subst then th

      else th |> hyps_rule

       (instantiate_tfrees thy substT #>

        instantiate_frees thy subst #>

        Drule.fconv_rule (Thm.beta_conversion true))

    end;

fun inst_ctxt thy envs =

  map_ctxt_values (instT_type (#1 envs)) (inst_term envs) (inst_thm thy envs);

(** pretty printing **)

fun pretty_items _ _ [] = []

  | pretty_items keyword sep (x :: ys) =

      Pretty.block [Pretty.keyword keyword, Pretty.brk 1, x] ::

        map (fn y => Pretty.block [Pretty.str "  ", Pretty.keyword sep, Pretty.brk 1, y]) ys;

fun pretty_name_atts ctxt (name, atts) sep =

  if name = "" andalso null atts then []

  else [Pretty.block (Pretty.breaks (Pretty.str (ProofContext.extern_thm ctxt name) ::

    Args.pretty_attribs ctxt atts @ [Pretty.str sep]))];

(* pretty_stmt *)

fun pretty_stmt ctxt =

  let

    val prt_typ = Pretty.quote o ProofContext.pretty_typ ctxt;

    val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;

    val prt_terms = separate (Pretty.keyword "and") o map prt_term;

    val prt_name_atts = pretty_name_atts ctxt;

    fun prt_show (a, ts) =

      Pretty.block (Pretty.breaks (prt_name_atts a ":" @ prt_terms (map fst ts)));

    fun prt_var (x, SOME T) = Pretty.block [Pretty.str (x ^ " ::"), Pretty.brk 1, prt_typ T]

      | prt_var (x, NONE) = Pretty.str x;

    fun prt_obtain (_, ([], ts)) = Pretty.block (Pretty.breaks (prt_terms ts))

      | prt_obtain (_, (xs, ts)) = Pretty.block (Pretty.breaks

          (map prt_var xs @ [Pretty.keyword "where"] @ prt_terms ts));

  in

    fn Shows shows => pretty_items "shows" "and" (map prt_show shows)

     | Obtains obtains => pretty_items "obtains" "|" (map prt_obtain obtains)

  end;

(* pretty_ctxt *)

fun pretty_ctxt ctxt =

  let

    val prt_typ = Pretty.quote o ProofContext.pretty_typ ctxt;

    val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;

    val prt_thm = Pretty.backquote o ProofContext.pretty_thm ctxt;

    val prt_name_atts = pretty_name_atts ctxt;

    fun prt_mixfix NoSyn = []

      | prt_mixfix mx = [Pretty.brk 2, Syntax.pretty_mixfix mx];

    fun prt_fix (x, SOME T, mx) = Pretty.block (Pretty.str (x ^ " ::") :: Pretty.brk 1 ::

          prt_typ T :: Pretty.brk 1 :: prt_mixfix mx)

      | prt_fix (x, NONE, mx) = Pretty.block (Pretty.str x :: Pretty.brk 1 :: prt_mixfix mx);

    fun prt_constrain (x, T) = prt_fix (x, SOME T, NoSyn);

    fun prt_asm (a, ts) =

      Pretty.block (Pretty.breaks (prt_name_atts a ":" @ map (prt_term o fst) ts));

    fun prt_def (a, (t, _)) =

      Pretty.block (Pretty.breaks (prt_name_atts a ":" @ [prt_term t]));

    fun prt_fact (ths, []) = map prt_thm ths

      | prt_fact (ths, atts) = Pretty.enclose "(" ")"

          (Pretty.breaks (map prt_thm ths)) :: Args.pretty_attribs ctxt atts;

    fun prt_note (a, ths) =

      Pretty.block (Pretty.breaks (flat (prt_name_atts a "=" :: map prt_fact ths)));

  in

    fn Fixes fixes => pretty_items "fixes" "and" (map prt_fix fixes)

     | Constrains xs => pretty_items "constrains" "and" (map prt_constrain xs)

     | Assumes asms => pretty_items "assumes" "and" (map prt_asm asms)

     | Defines defs => pretty_items "defines" "and" (map prt_def defs)

     | Notes facts => pretty_items "notes" "and" (map prt_note facts)

  end;

(* pretty_statement *)

local

fun thm_name kind th prts =

  let val head =

    (case #1 (Thm.get_name_tags th) of

      "" => Pretty.command kind

    | a => Pretty.block [Pretty.command kind, Pretty.brk 1, Pretty.str (Sign.base_name a ^ ":")])

  in Pretty.block (Pretty.fbreaks (head :: prts)) end;

fun obtain prop ctxt =

  let

    val xs = ProofContext.rename_frees ctxt [] (Logic.strip_params prop);

    val args = rev (map Free xs);

    val As = Logic.strip_assums_hyp prop |> map (fn t => Term.subst_bounds (args, t));

    val ctxt' = ctxt |> fold ProofContext.declare_term args;

  in (("", (map (apsnd SOME) xs, As)), ctxt') end;

in

fun pretty_statement ctxt kind raw_th =

  let

    val thy = ProofContext.theory_of ctxt;

    val th = Goal.norm_hhf raw_th;

    fun standard_thesis t =

      let

        val C = ObjectLogic.drop_judgment thy (Thm.concl_of th);

        val C' = Var ((AutoBind.thesisN, Thm.maxidx_of th + 1), Term.fastype_of C);

      in Term.subst_atomic [(C, C')] t end;

    val raw_prop =

      Thm.prop_of th

      |> singleton (ProofContext.monomorphic ctxt)

      |> K (ObjectLogic.is_elim th) ? standard_thesis

      |> Term.zero_var_indexes;

    val vars = Term.add_vars raw_prop [];

    val frees = ProofContext.rename_frees ctxt [raw_prop] (map (apfst fst) vars);

    val fixes = rev (filter_out (fn (x, _) => x = AutoBind.thesisN) frees);

    val prop = Term.instantiate ([], vars ~~ map Free frees) raw_prop;

    val (prems, concl) = Logic.strip_horn prop;

    val thesis = ObjectLogic.fixed_judgment thy AutoBind.thesisN;

    val (asms, cases) = take_suffix (fn prem => thesis aconv Logic.strip_assums_concl prem) prems;

  in

    pretty_ctxt ctxt (Fixes (map (fn (x, T) => (x, SOME T, NoSyn)) fixes)) @

    pretty_ctxt ctxt (Assumes (map (fn t => (("", []), [(t, ([], []))])) asms)) @

    pretty_stmt ctxt

     (if null cases then Shows [(("", []), [(concl, ([], []))])]

      else Obtains (#1 (fold_map obtain cases (ctxt |> ProofContext.declare_term prop))))

  end |> thm_name kind raw_th;

end;

end;