(*  Title:      Pure/logic.ML

     ID:         $Id$

     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

     Copyright   Cambridge University 1992

 Abstract syntax operations of the Pure meta-logic.

 *)

 infix occs;

 signature LOGIC =

 sig

   val is_all            : term -> bool

   val mk_equals         : term * term -> term

   val dest_equals       : term -> term * term

   val is_equals         : term -> bool

   val mk_implies        : term * term -> term

   val dest_implies      : term -> term * term

   val is_implies        : term -> bool

   val list_implies      : term list * term -> term

   val strip_imp_prems   : term -> term list

   val strip_imp_concl   : term -> term

   val strip_prems       : int * term list * term -> term list * term

   val count_prems       : term * int -> int

   val mk_conjunction    : term * term -> term

   val mk_conjunction_list: term list -> term

   val mk_flexpair       : term * term -> term

   val dest_flexpair     : term -> term * term

   val list_flexpairs    : (term*term)list * term -> term

   val rule_of           : (term*term)list * term list * term -> term

   val strip_flexpairs   : term -> (term*term)list * term

   val skip_flexpairs    : term -> term

   val strip_horn        : term -> (term*term)list * term list * term

   val mk_cond_defpair   : term list -> term * term -> string * term

   val mk_defpair        : term * term -> string * term

   val mk_type           : typ -> term

   val dest_type         : term -> typ

   val mk_inclass        : typ * class -> term

   val dest_inclass      : term -> typ * class

   val goal_const        : term

   val mk_goal           : term -> term

   val dest_goal         : term -> term

   val occs              : term * term -> bool

   val close_form        : term -> term

   val incr_indexes      : typ list * int -> term -> term

   val lift_fns          : term * int -> (term -> term) * (term -> term)

   val strip_assums_hyp  : term -> term list

   val strip_assums_concl: term -> term

   val strip_params      : term -> (string * typ) list

   val has_meta_prems    : term -> int -> bool

   val flatten_params    : int -> term -> term

   val auto_rename       : bool ref

   val set_rename_prefix : string -> unit

   val list_rename_params: string list * term -> term

   val assum_pairs       : term -> (term*term)list

   val varify            : term -> term

   val unvarify          : term -> term

 end;

 structure Logic : LOGIC =

 struct

 (*** Abstract syntax operations on the meta-connectives ***)

 (** all **)

 fun is_all (Const ("all", _) $ _) = true

   | is_all _ = false;

 (** equality **)

 (*Make an equality.  DOES NOT CHECK TYPE OF u*)

 fun mk_equals(t,u) = equals(fastype_of t) $ t $ u;

 fun dest_equals (Const("==",_) $ t $ u)  =  (t,u)

   | dest_equals t = raise TERM("dest_equals", [t]);

 fun is_equals (Const ("==", _) $ _ $ _) = true

   | is_equals _ = false;

 (** implies **)

 fun mk_implies(A,B) = implies $ A $ B;

 fun dest_implies (Const("==>",_) $ A $ B)  =  (A,B)

   | dest_implies A = raise TERM("dest_implies", [A]);

 fun is_implies (Const ("==>", _) $ _ $ _) = true

   | is_implies _ = false;

 (** nested implications **)

 (* [A1,...,An], B  goes to  A1==>...An==>B  *)

 fun list_implies ([], B) = B : term

   | list_implies (A::AS, B) = implies $ A $ list_implies(AS,B);

 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)

 fun strip_imp_prems (Const("==>", _) $ A $ B) = A :: strip_imp_prems B

   | strip_imp_prems _ = [];

 (* A1==>...An==>B  goes to B, where B is not an implication *)

 fun strip_imp_concl (Const("==>", _) $ A $ B) = strip_imp_concl B

   | strip_imp_concl A = A : term;

 (*Strip and return premises: (i, [], A1==>...Ai==>B)

     goes to   ([Ai, A(i-1),...,A1] , B)         (REVERSED)

   if  i<0 or else i too big then raises  TERM*)

 fun strip_prems (0, As, B) = (As, B)

   | strip_prems (i, As, Const("==>", _) $ A $ B) =

         strip_prems (i-1, A::As, B)

   | strip_prems (_, As, A) = raise TERM("strip_prems", A::As);

 (*Count premises -- quicker than (length ostrip_prems) *)

 fun count_prems (Const("==>", _) $ A $ B, n) = count_prems (B,n+1)

   | count_prems (_,n) = n;

 (** conjunction **)

 fun mk_conjunction (t, u) =

   Term.list_all ([("C", propT)], mk_implies (list_implies ([t, u], Bound 0), Bound 0));

 fun mk_conjunction_list [] = Term.all propT $ Abs ("dummy", propT, mk_implies (Bound 0, Bound 0))

   | mk_conjunction_list ts = foldr1 mk_conjunction ts;

 (** flex-flex constraints **)

 (*Make a constraint.*)

 fun mk_flexpair(t,u) = flexpair(fastype_of t) $ t $ u;

 fun dest_flexpair (Const("=?=",_) $ t $ u)  =  (t,u)

   | dest_flexpair t = raise TERM("dest_flexpair", [t]);

 (*make flexflex antecedents: ( [(a1,b1),...,(an,bn)] , C )

     goes to (a1=?=b1) ==>...(an=?=bn)==>C *)

 fun list_flexpairs ([], A) = A

   | list_flexpairs ((t,u)::pairs, A) =

         implies $ (mk_flexpair(t,u)) $ list_flexpairs(pairs,A);

 (*Make the object-rule tpairs==>As==>B   *)

 fun rule_of (tpairs, As, B) = list_flexpairs(tpairs, list_implies(As, B));

 (*Remove and return flexflex pairs:

     (a1=?=b1)==>...(an=?=bn)==>C  to  ( [(a1,b1),...,(an,bn)] , C )

   [Tail recursive in order to return a pair of results] *)

 fun strip_flex_aux (pairs, Const("==>", _) $ (Const("=?=",_)$t$u) $ C) =

         strip_flex_aux ((t,u)::pairs, C)

   | strip_flex_aux (pairs,C) = (rev pairs, C);

 fun strip_flexpairs A = strip_flex_aux([], A);

 (*Discard flexflex pairs*)

 fun skip_flexpairs (Const("==>", _) $ (Const("=?=",_)$_$_) $ C) =

         skip_flexpairs C

   | skip_flexpairs C = C;

 (*strip a proof state (Horn clause):

    (a1==b1)==>...(am==bm)==>B1==>...Bn==>C

     goes to   ( [(a1,b1),...,(am,bm)] , [B1,...,Bn] , C)    *)

 fun strip_horn A =

   let val (tpairs,horn) = strip_flexpairs A

   in  (tpairs, strip_imp_prems horn, strip_imp_concl horn)   end;

 (** definitions **)

 fun mk_cond_defpair As (lhs, rhs) =

   (case Term.head_of lhs of

     Const (name, _) =>

       (Sign.base_name name ^ "_def", list_implies (As, mk_equals (lhs, rhs)))

   | _ => raise TERM ("Malformed definition: head of lhs not a constant", [lhs, rhs]));

 fun mk_defpair lhs_rhs = mk_cond_defpair [] lhs_rhs;

 (** types as terms **)

 fun mk_type ty = Const ("TYPE", itselfT ty);

 fun dest_type (Const ("TYPE", Type ("itself", [ty]))) = ty

   | dest_type t = raise TERM ("dest_type", [t]);

 (** class constraints **)

 fun mk_inclass (ty, c) =

   Const (Sign.const_of_class c, itselfT ty --> propT) $ mk_type ty;

 fun dest_inclass (t as Const (c_class, _) $ ty) =

       ((dest_type ty, Sign.class_of_const c_class)

         handle TERM _ => raise TERM ("dest_inclass", [t]))

   | dest_inclass t = raise TERM ("dest_inclass", [t]);

 (** atomic goals **)

 val goal_const = Const ("Goal", propT --> propT);

 fun mk_goal t = goal_const $ t;

 fun dest_goal (Const ("Goal", _) $ t) = t

   | dest_goal t = raise TERM ("dest_goal", [t]);

 (*** Low-level term operations ***)

 (*Does t occur in u?  Or is alpha-convertible to u?

   The term t must contain no loose bound variables*)

 fun t occs u = exists_subterm (fn s => t aconv s) u;

 (*Close up a formula over all free variables by quantification*)

 fun close_form A =

   list_all_free (sort_wrt fst (map dest_Free (term_frees A)), A);

 (*** Specialized operations for resolution... ***)

 (*For all variables in the term, increment indexnames and lift over the Us

     result is ?Gidx(B.(lev+n-1),...,B.lev) where lev is abstraction level *)

 fun incr_indexes (Us: typ list, inc:int) t =

   let fun incr (Var ((a,i), T), lev) =

                 Unify.combound (Var((a, i+inc), Us---> incr_tvar inc T),

                                 lev, length Us)

         | incr (Abs (a,T,body), lev) =

                 Abs (a, incr_tvar inc T, incr(body,lev+1))

         | incr (Const(a,T),_) = Const(a, incr_tvar inc T)

         | incr (Free(a,T),_) = Free(a, incr_tvar inc T)

         | incr (f$t, lev) = incr(f,lev) $ incr(t,lev)

         | incr (t,lev) = t

   in  incr(t,0)  end;

 (*Make lifting functions from subgoal and increment.

     lift_abs operates on tpairs (unification constraints)

     lift_all operates on propositions     *)

 fun lift_fns (B,inc) =

   let fun lift_abs (Us, Const("==>", _) $ _ $ B) u = lift_abs (Us,B) u

         | lift_abs (Us, Const("all",_)$Abs(a,T,t)) u =

               Abs(a, T, lift_abs (T::Us, t) u)

         | lift_abs (Us, _) u = incr_indexes(rev Us, inc) u

       fun lift_all (Us, Const("==>", _) $ A $ B) u =

               implies $ A $ lift_all (Us,B) u

         | lift_all (Us, Const("all",_)$Abs(a,T,t)) u =

               all T $ Abs(a, T, lift_all (T::Us,t) u)

         | lift_all (Us, _) u = incr_indexes(rev Us, inc) u;

   in  (lift_abs([],B), lift_all([],B))  end;

 (*Strips assumptions in goal, yielding list of hypotheses.   *)

 fun strip_assums_hyp (Const("==>", _) $ H $ B) = H :: strip_assums_hyp B

   | strip_assums_hyp (Const("all",_)$Abs(a,T,t)) = strip_assums_hyp t

   | strip_assums_hyp B = [];

 (*Strips assumptions in goal, yielding conclusion.   *)

 fun strip_assums_concl (Const("==>", _) $ H $ B) = strip_assums_concl B

   | strip_assums_concl (Const("all",_)$Abs(a,T,t)) = strip_assums_concl t

   | strip_assums_concl B = B;

 (*Make a list of all the parameters in a subgoal, even if nested*)

 fun strip_params (Const("==>", _) $ H $ B) = strip_params B

   | strip_params (Const("all",_)$Abs(a,T,t)) = (a,T) :: strip_params t

   | strip_params B = [];

 (*test for meta connectives in prems of a 'subgoal'*)

 fun has_meta_prems prop i =

   let

     fun is_meta (Const ("==>", _) $ _ $ _) = true

       | is_meta (Const ("==", _) $ _ $ _) = true

       | is_meta (Const ("all", _) $ _) = true

       | is_meta _ = false;

     val horn = skip_flexpairs prop;

   in

     (case strip_prems (i, [], horn) of

       (B :: _, _) => exists is_meta (strip_assums_hyp B)

     | _ => false) handle TERM _ => false

   end;

 (*Removes the parameters from a subgoal and renumber bvars in hypotheses,

     where j is the total number of parameters (precomputed)

   If n>0 then deletes assumption n. *)

 fun remove_params j n A =

     if j=0 andalso n<=0 then A  (*nothing left to do...*)

     else case A of

         Const("==>", _) $ H $ B =>

           if n=1 then                           (remove_params j (n-1) B)

           else implies $ (incr_boundvars j H) $ (remove_params j (n-1) B)

       | Const("all",_)$Abs(a,T,t) => remove_params (j-1) n t

       | _ => if n>0 then raise TERM("remove_params", [A])

              else A;

 (** Auto-renaming of parameters in subgoals **)

 val auto_rename = ref false

 and rename_prefix = ref "ka";

 (*rename_prefix is not exported; it is set by this function.*)

 fun set_rename_prefix a =

     if a<>"" andalso forall Symbol.is_letter (Symbol.explode a)

     then  (rename_prefix := a;  auto_rename := true)

     else  error"rename prefix must be nonempty and consist of letters";

 (*Makes parameters in a goal have distinctive names (not guaranteed unique!)

   A name clash could cause the printer to rename bound vars;

     then res_inst_tac would not work properly.*)

 fun rename_vars (a, []) = []

   | rename_vars (a, (_,T)::vars) =

         (a,T) :: rename_vars (Symbol.bump_string a, vars);

 (*Move all parameters to the front of the subgoal, renaming them apart;

   if n>0 then deletes assumption n. *)

 fun flatten_params n A =

     let val params = strip_params A;

         val vars = if !auto_rename

                    then rename_vars (!rename_prefix, params)

                    else ListPair.zip (variantlist(map #1 params,[]),

                                       map #2 params)

     in  list_all (vars, remove_params (length vars) n A)

     end;

 (*Makes parameters in a goal have the names supplied by the list cs.*)

 fun list_rename_params (cs, Const("==>", _) $ A $ B) =

       implies $ A $ list_rename_params (cs, B)

   | list_rename_params (c::cs, Const("all",_)$Abs(_,T,t)) =

       all T $ Abs(c, T, list_rename_params (cs, t))

   | list_rename_params (cs, B) = B;

 (*Strips assumptions in goal yielding  ( [HPn,...,HP1], [xm,...,x1], B ).

   Where HPi has the form (Hi,nparams_i) and x1...xm are the parameters.

   We need nparams_i only when the parameters aren't flattened; then we

     must call incr_boundvars to make up the difference.  See assum_pairs.

   Without this refinement we can get the wrong answer, e.g. by

         Goal "!!f. EX B. Q(f,B) ==> (!!y. P(f,y))";

         by (etac exE 1);

  *)

 fun strip_assums_aux (HPs, params, Const("==>", _) $ H $ B) =

         strip_assums_aux ((H,length params)::HPs, params, B)

   | strip_assums_aux (HPs, params, Const("all",_)$Abs(a,T,t)) =

         strip_assums_aux (HPs, (a,T)::params, t)

   | strip_assums_aux (HPs, params, B) = (HPs, params, B);

 fun strip_assums A = strip_assums_aux ([],[],A);

 (*Produces disagreement pairs, one for each assumption proof, in order.

   A is the first premise of the lifted rule, and thus has the form

     H1 ==> ... Hk ==> B   and the pairs are (H1,B),...,(Hk,B) *)

 fun assum_pairs A =

   let val (HPs, params, B) = strip_assums A

       val nparams = length params

       val D = Unify.rlist_abs(params, B)

       fun incr_hyp(H,np) =

           Unify.rlist_abs(params, incr_boundvars (nparams-np) H)

       fun pairrev ([],pairs) = pairs

         | pairrev ((H,np)::HPs, pairs) =

             pairrev(HPs,  (incr_hyp(H,np),D) :: pairs)

   in  pairrev (HPs,[])

   end;

 (*Converts Frees to Vars and TFrees to TVars so that axioms can be written

   without (?) everywhere*)

 fun varify (Const(a,T)) = Const(a, Type.varifyT T)

   | varify (Free(a,T)) = Var((a,0), Type.varifyT T)

   | varify (Var(ixn,T)) = Var(ixn, Type.varifyT T)

   | varify (Abs (a,T,body)) = Abs (a, Type.varifyT T, varify body)

   | varify (f$t) = varify f $ varify t

   | varify t = t;

 (*Inverse of varify.  Converts axioms back to their original form.*)

 fun unvarify (Const(a,T))    = Const(a, Type.unvarifyT T)

   | unvarify (Var((a,0), T)) = Free(a, Type.unvarifyT T)

   | unvarify (Var(ixn,T))    = Var(ixn, Type.unvarifyT T)  (*non-0 index!*)

   | unvarify (Abs (a,T,body)) = Abs (a, Type.unvarifyT T, unvarify body)

   | unvarify (f$t) = unvarify f $ unvarify t

   | unvarify t = t;

 end;