src/Pure/logic.ML
author wenzelm
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simplified type attribute;
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(*  Title:      Pure/logic.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   Cambridge University 1992
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Abstract syntax operations of the Pure meta-logic.
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*)
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signature LOGIC =
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sig
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  val is_all: term -> bool
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  val mk_equals: term * term -> term
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  val dest_equals: term -> term * term
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  val is_equals: term -> bool
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  val mk_implies: term * term -> term
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  val dest_implies: term -> term * term
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  val is_implies: term -> bool
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  val list_implies: term list * term -> term
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  val strip_imp_prems: term -> term list
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  val strip_imp_concl: term -> term
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  val strip_prems: int * term list * term -> term list * term
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  val count_prems: term * int -> int
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  val nth_prem: int * term -> term
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  val mk_conjunction: term * term -> term
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  val mk_conjunction_list: term list -> term
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  val mk_conjunction_list2: term list list -> term
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  val dest_conjunction: term -> term * term
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  val dest_conjunctions: term -> term list
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  val strip_horn: term -> term list * term
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  val mk_cond_defpair: term list -> term * term -> string * term
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  val mk_defpair: term * term -> string * term
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  val mk_type: typ -> term
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  val dest_type: term -> typ
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  val mk_inclass: typ * class -> term
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  val dest_inclass: term -> typ * class
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  val protectC: term
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  val protect: term -> term
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  val unprotect: term -> term
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  val occs: term * term -> bool
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  val close_form: term -> term
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  val incr_indexes: typ list * int -> term -> term
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  val incr_tvar: int -> typ -> typ
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  val lift_abs: int -> term -> term -> term
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  val lift_all: int -> term -> term -> term
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  val strip_assums_hyp: term -> term list
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  val strip_assums_concl: term -> term
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  val strip_params: term -> (string * typ) list
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  val has_meta_prems: term -> int -> bool
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  val flatten_params: int -> term -> term
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  val auto_rename: bool ref
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  val set_rename_prefix: string -> unit
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  val list_rename_params: string list * term -> term
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  val assum_pairs: int * term -> (term*term)list
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  val varify: term -> term
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  val unvarify: term -> term
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  val get_goal: term -> int -> term
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  val goal_params: term -> int -> term * term list
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  val prems_of_goal: term -> int -> term list
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  val concl_of_goal: term -> int -> term
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end;
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structure Logic : LOGIC =
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struct
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(*** Abstract syntax operations on the meta-connectives ***)
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(** all **)
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fun is_all (Const ("all", _) $ _) = true
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  | is_all _ = false;
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(** equality **)
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(*Make an equality.  DOES NOT CHECK TYPE OF u*)
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fun mk_equals(t,u) = equals(fastype_of t) $ t $ u;
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fun dest_equals (Const("==",_) $ t $ u)  =  (t,u)
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  | dest_equals t = raise TERM("dest_equals", [t]);
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fun is_equals (Const ("==", _) $ _ $ _) = true
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  | is_equals _ = false;
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(** implies **)
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fun mk_implies(A,B) = implies $ A $ B;
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fun dest_implies (Const("==>",_) $ A $ B)  =  (A,B)
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  | dest_implies A = raise TERM("dest_implies", [A]);
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fun is_implies (Const ("==>", _) $ _ $ _) = true
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  | is_implies _ = false;
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(** nested implications **)
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(* [A1,...,An], B  goes to  A1==>...An==>B  *)
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fun list_implies ([], B) = B
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  | list_implies (A::As, B) = implies $ A $ list_implies(As,B);
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(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
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fun strip_imp_prems (Const("==>", _) $ A $ B) = A :: strip_imp_prems B
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  | strip_imp_prems _ = [];
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(* A1==>...An==>B  goes to B, where B is not an implication *)
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fun strip_imp_concl (Const("==>", _) $ A $ B) = strip_imp_concl B
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  | strip_imp_concl A = A : term;
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(*Strip and return premises: (i, [], A1==>...Ai==>B)
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    goes to   ([Ai, A(i-1),...,A1] , B)         (REVERSED)
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  if  i<0 or else i too big then raises  TERM*)
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fun strip_prems (0, As, B) = (As, B)
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  | strip_prems (i, As, Const("==>", _) $ A $ B) =
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        strip_prems (i-1, A::As, B)
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  | strip_prems (_, As, A) = raise TERM("strip_prems", A::As);
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(*Count premises -- quicker than (length o strip_prems) *)
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fun count_prems (Const("==>", _) $ A $ B, n) = count_prems (B,n+1)
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  | count_prems (_,n) = n;
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(*Select Ai from A1 ==>...Ai==>B*)
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fun nth_prem (1, Const ("==>", _) $ A $ _) = A
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  | nth_prem (i, Const ("==>", _) $ _ $ B) = nth_prem (i - 1, B)
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  | nth_prem (_, A) = raise TERM ("nth_prem", [A]);
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(*strip a proof state (Horn clause):
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  B1 ==> ... Bn ==> C   goes to   ([B1, ..., Bn], C)    *)
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fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);
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(** conjunction **)
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(*A && B*)
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fun mk_conjunction (t, u) =
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  Term.list_all ([("X", propT)],
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    mk_implies (list_implies (map (Term.incr_boundvars 1) [t, u], Bound 0), Bound 0));
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(*A && B && C -- improper*)
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fun mk_conjunction_list [] = Term.all propT $ Abs ("dummy", propT, mk_implies (Bound 0, Bound 0))
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  | mk_conjunction_list ts = foldr1 mk_conjunction ts;
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(*(A1 && B1 && C1) && (A2 && B2 && C2 && D2) && A3 && B3 -- improper*)
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fun mk_conjunction_list2 tss =
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  mk_conjunction_list (map mk_conjunction_list (filter_out null tss));
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(*A && B*)
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fun dest_conjunction
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      (t as Const ("all", _) $ Abs (_, _,
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        Const ("==>", _) $ (Const ("==>", _) $ A $ (Const ("==>", _) $ B $ Bound 0)) $ Bound 0)) =
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      if Term.loose_bvar1 (A, 0) orelse Term.loose_bvar1 (B, 0)
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      then raise TERM ("dest_conjunction", [t])
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      else (Term.incr_boundvars ~1 A, Term.incr_boundvars ~1 B)
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  | dest_conjunction t = raise TERM ("dest_conjunction", [t]);
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(*((A && B) && C) && D && E -- flat*)
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fun dest_conjunctions t =
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  (case try dest_conjunction t of
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    NONE => [t]
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  | SOME (A, B) => dest_conjunctions A @ dest_conjunctions B);
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(** definitions **)
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fun mk_cond_defpair As (lhs, rhs) =
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  (case Term.head_of lhs of
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    Const (name, _) =>
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      (Sign.base_name name ^ "_def", list_implies (As, mk_equals (lhs, rhs)))
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  | _ => raise TERM ("Malformed definition: head of lhs not a constant", [lhs, rhs]));
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fun mk_defpair lhs_rhs = mk_cond_defpair [] lhs_rhs;
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(** types as terms **)
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fun mk_type ty = Const ("TYPE", itselfT ty);
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fun dest_type (Const ("TYPE", Type ("itself", [ty]))) = ty
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  | dest_type t = raise TERM ("dest_type", [t]);
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(** class constraints **)
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fun mk_inclass (ty, c) =
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  Const (Sign.const_of_class c, itselfT ty --> propT) $ mk_type ty;
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fun dest_inclass (t as Const (c_class, _) $ ty) =
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      ((dest_type ty, Sign.class_of_const c_class)
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        handle TERM _ => raise TERM ("dest_inclass", [t]))
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  | dest_inclass t = raise TERM ("dest_inclass", [t]);
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(** protected propositions **)
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val protectC = Const ("prop", propT --> propT);
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fun protect t = protectC $ t;
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fun unprotect (Const ("prop", _) $ t) = t
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  | unprotect t = raise TERM ("unprotect", [t]);
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53d7ad5bec39 Logic.goal_const;
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(*** Low-level term operations ***)
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(*Does t occur in u?  Or is alpha-convertible to u?
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  The term t must contain no loose bound variables*)
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fun occs (t, u) = exists_subterm (fn s => t aconv s) u;
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(*Close up a formula over all free variables by quantification*)
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fun close_form A =
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  list_all_free (sort_wrt fst (map dest_Free (term_frees A)), A);
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(*** Specialized operations for resolution... ***)
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local exception SAME in
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fun incrT k =
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  let
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    fun incr (TVar ((a, i), S)) = TVar ((a, i + k), S)
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      | incr (Type (a, Ts)) = Type (a, incrs Ts)
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      | incr _ = raise SAME
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    and incrs (T :: Ts) =
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        (incr T :: (incrs Ts handle SAME => Ts)
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          handle SAME => T :: incrs Ts)
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      | incrs [] = raise SAME;
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  in incr end;
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(*For all variables in the term, increment indexnames and lift over the Us
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    result is ?Gidx(B.(lev+n-1),...,B.lev) where lev is abstraction level *)
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fun incr_indexes ([], 0) t = t
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  | incr_indexes (Ts, k) t =
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  let
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    val n = length Ts;
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    val incrT = if k = 0 then I else incrT k;
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    fun incr lev (Var ((x, i), T)) =
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          Unify.combound (Var ((x, i + k), Ts ---> (incrT T handle SAME => T)), lev, n)
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      | incr lev (Abs (x, T, body)) =
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          (Abs (x, incrT T, incr (lev + 1) body handle SAME => body)
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            handle SAME => Abs (x, T, incr (lev + 1) body))
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      | incr lev (t $ u) =
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          (incr lev t $ (incr lev u handle SAME => u)
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            handle SAME => t $ incr lev u)
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      | incr _ (Const (c, T)) = Const (c, incrT T)
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      | incr _ (Free (x, T)) = Free (x, incrT T)
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      | incr _ (t as Bound _) = t;
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  in incr 0 t handle SAME => t end;
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fun incr_tvar 0 T = T
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  | incr_tvar k T = incrT k T handle SAME => T;
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end;
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(* Lifting functions from subgoal and increment:
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    lift_abs operates on terms
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    lift_all operates on propositions *)
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fun lift_abs inc =
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  let
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    fun lift Ts (Const ("==>", _) $ _ $ B) t = lift Ts B t
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      | lift Ts (Const ("all", _) $ Abs (a, T, B)) t = Abs (a, T, lift (T :: Ts) B t)
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      | lift Ts _ t = incr_indexes (rev Ts, inc) t;
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  in lift [] end;
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fun lift_all inc =
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  let
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    fun lift Ts ((c as Const ("==>", _)) $ A $ B) t = c $ A $ lift Ts B t
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      | lift Ts ((c as Const ("all", _)) $ Abs (a, T, B)) t = c $ Abs (a, T, lift (T :: Ts) B t)
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      | lift Ts _ t = incr_indexes (rev Ts, inc) t;
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  in lift [] end;
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(*Strips assumptions in goal, yielding list of hypotheses.   *)
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fun strip_assums_hyp (Const("==>", _) $ H $ B) = H :: strip_assums_hyp B
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  | strip_assums_hyp (Const("all",_)$Abs(a,T,t)) = strip_assums_hyp t
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  | strip_assums_hyp B = [];
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(*Strips assumptions in goal, yielding conclusion.   *)
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fun strip_assums_concl (Const("==>", _) $ H $ B) = strip_assums_concl B
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  | strip_assums_concl (Const("all",_)$Abs(a,T,t)) = strip_assums_concl t
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  | strip_assums_concl B = B;
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(*Make a list of all the parameters in a subgoal, even if nested*)
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fun strip_params (Const("==>", _) $ H $ B) = strip_params B
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  | strip_params (Const("all",_)$Abs(a,T,t)) = (a,T) :: strip_params t
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  | strip_params B = [];
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(*test for meta connectives in prems of a 'subgoal'*)
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fun has_meta_prems prop i =
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  let
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    fun is_meta (Const ("==>", _) $ _ $ _) = true
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      | is_meta (Const ("==", _) $ _ $ _) = true
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      | is_meta (Const ("all", _) $ _) = true
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      | is_meta _ = false;
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  in
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    (case strip_prems (i, [], prop) of
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      (B :: _, _) => exists is_meta (strip_assums_hyp B)
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    | _ => false) handle TERM _ => false
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  end;
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(*Removes the parameters from a subgoal and renumber bvars in hypotheses,
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    where j is the total number of parameters (precomputed)
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  If n>0 then deletes assumption n. *)
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fun remove_params j n A =
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    if j=0 andalso n<=0 then A  (*nothing left to do...*)
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    else case A of
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        Const("==>", _) $ H $ B =>
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          if n=1 then                           (remove_params j (n-1) B)
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          else implies $ (incr_boundvars j H) $ (remove_params j (n-1) B)
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      | Const("all",_)$Abs(a,T,t) => remove_params (j-1) n t
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      | _ => if n>0 then raise TERM("remove_params", [A])
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             else A;
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(** Auto-renaming of parameters in subgoals **)
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val auto_rename = ref false
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and rename_prefix = ref "ka";
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(*rename_prefix is not exported; it is set by this function.*)
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fun set_rename_prefix a =
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    if a<>"" andalso forall Symbol.is_letter (Symbol.explode a)
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    then  (rename_prefix := a;  auto_rename := true)
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    else  error"rename prefix must be nonempty and consist of letters";
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(*Makes parameters in a goal have distinctive names (not guaranteed unique!)
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  A name clash could cause the printer to rename bound vars;
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    then res_inst_tac would not work properly.*)
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fun rename_vars (a, []) = []
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  | rename_vars (a, (_,T)::vars) =
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        (a,T) :: rename_vars (Symbol.bump_string a, vars);
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(*Move all parameters to the front of the subgoal, renaming them apart;
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  if n>0 then deletes assumption n. *)
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fun flatten_params n A =
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    let val params = strip_params A;
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        val vars = if !auto_rename
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                   then rename_vars (!rename_prefix, params)
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                   else ListPair.zip (variantlist(map #1 params,[]),
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                                      map #2 params)
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    in  list_all (vars, remove_params (length vars) n A)
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    end;
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(*Makes parameters in a goal have the names supplied by the list cs.*)
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fun list_rename_params (cs, Const("==>", _) $ A $ B) =
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      implies $ A $ list_rename_params (cs, B)
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  | list_rename_params (c::cs, Const("all",_)$Abs(_,T,t)) =
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      all T $ Abs(c, T, list_rename_params (cs, t))
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  | list_rename_params (cs, B) = B;
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(*** Treatmsent of "assume", "erule", etc. ***)
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(*Strips assumptions in goal yielding
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   HS = [Hn,...,H1],   params = [xm,...,x1], and B,
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  where x1...xm are the parameters. This version (21.1.2005) REQUIRES
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  the the parameters to be flattened, but it allows erule to work on
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  assumptions of the form !!x. phi. Any !! after the outermost string
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  will be regarded as belonging to the conclusion, and left untouched.
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  Used ONLY by assum_pairs.
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      Unless nasms<0, it can terminate the recursion early; that allows
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  erule to work on assumptions of the form P==>Q.*)
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fun strip_assums_imp (0, Hs, B) = (Hs, B)  (*recursion terminated by nasms*)
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  | strip_assums_imp (nasms, Hs, Const("==>", _) $ H $ B) =
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      strip_assums_imp (nasms-1, H::Hs, B)
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  | strip_assums_imp (_, Hs, B) = (Hs, B); (*recursion terminated by B*)
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(*Strips OUTER parameters only, unlike similar legacy versions.*)
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fun strip_assums_all (params, Const("all",_)$Abs(a,T,t)) =
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      strip_assums_all ((a,T)::params, t)
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  | strip_assums_all (params, B) = (params, B);
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(*Produces disagreement pairs, one for each assumption proof, in order.
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  A is the first premise of the lifted rule, and thus has the form
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    H1 ==> ... Hk ==> B   and the pairs are (H1,B),...,(Hk,B).
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  nasms is the number of assumptions in the original subgoal, needed when B
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    has the form B1 ==> B2: it stops B1 from being taken as an assumption. *)
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fun assum_pairs(nasms,A) =
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  let val (params, A') = strip_assums_all ([],A)
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      val (Hs,B) = strip_assums_imp (nasms,[],A')
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      fun abspar t = Unify.rlist_abs(params, t)
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      val D = abspar B
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      fun pairrev ([], pairs) = pairs
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        | pairrev (H::Hs, pairs) = pairrev(Hs,  (abspar H, D) :: pairs)
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  in  pairrev (Hs,[])
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  end;
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(*Converts Frees to Vars and TFrees to TVars so that axioms can be written
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  without (?) everywhere*)
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fun varify (Const(a, T)) = Const (a, Type.varifyT T)
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  | varify (Free (a, T)) = Var ((a, 0), Type.varifyT T)
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  | varify (Var (ixn, T)) = Var (ixn, Type.varifyT T)
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  | varify (t as Bound _) = t
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  | varify (Abs (a, T, body)) = Abs (a, Type.varifyT T, varify body)
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  | varify (f $ t) = varify f $ varify t;
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(*Inverse of varify.  Converts axioms back to their original form.*)
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fun unvarify (Const (a, T)) = Const (a, Type.unvarifyT T)
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  | unvarify (Free (a, T)) = Free (a, Type.unvarifyT T)
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  | unvarify (Var ((a, 0), T)) = Free (a, Type.unvarifyT T)
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  | unvarify (Var (ixn, T)) = Var (ixn, Type.unvarifyT T)  (*non-0 index!*)
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  | unvarify (t as Bound _) = t
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  | unvarify (Abs (a, T, body)) = Abs (a, Type.unvarifyT T, unvarify body)
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  | unvarify (f $ t) = unvarify f $ unvarify t;
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(* goal states *)
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fun get_goal st i = nth_prem (i, st)
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  handle TERM _ => error "Goal number out of range";
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(*reverses parameters for substitution*)
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fun goal_params st i =
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  let val gi = get_goal st i
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      val rfrees = map Free (rename_wrt_term gi (strip_params gi))
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  in (gi, rfrees) end;
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fun concl_of_goal st i =
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  let val (gi, rfrees) = goal_params st i
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      val B = strip_assums_concl gi
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  in subst_bounds (rfrees, B) end;
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fun prems_of_goal st i =
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  let val (gi, rfrees) = goal_params st i
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      val As = strip_assums_hyp gi
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  in map (fn A => subst_bounds (rfrees, A)) As end;
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end;