(*  Title: 	Pure/logic.ML

     ID:         $Id$

     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory

     Copyright   Cambridge University 1992

 Supporting code for defining the abstract type "thm"

 *)

 infix occs;

 signature LOGIC = 

   sig

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

   val auto_rename	: bool ref   

   val close_form	: term -> term   

   val count_prems	: term * int -> int

   val dest_equals	: term -> term * term

   val dest_flexpair	: term -> term * term

   val dest_implies	: term -> term * term

   val dest_inclass	: term -> typ * class

   val dest_type		: term -> typ

   val flatten_params	: int -> term -> term

   val freeze_vars	: term -> term

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

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

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

   val list_implies	: term list * term -> term

   val list_rename_params: string list * term -> term

   val mk_equals		: term * term -> term

   val mk_flexpair	: term * term -> term

   val mk_implies	: term * term -> term

   val mk_inclass	: typ * class -> term

   val mk_type		: typ -> term

   val occs		: term * term -> bool

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

   val set_rename_prefix	: string -> unit   

   val skip_flexpairs	: term -> term

   val strip_assums_concl: term -> term

   val strip_assums_hyp	: term -> term list

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

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

   val strip_imp_concl	: term -> term

   val strip_imp_prems	: term -> term list

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

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

   val thaw_vars		: term -> term

   val unvarify		: term -> term  

   val varify		: term -> term  

   end;

 functor LogicFun (structure Unify: UNIFY and Net:NET): LOGIC =

 struct

 structure Sign = Unify.Sign;

 structure Type = Sign.Type;

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

 (** equality **)

 (*Make an equality.*)

 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]);

 (** 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]);

 (** 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;

 (** 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;

 (** 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]);

 (*** 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 = (t aconv u) orelse 

       (case u of

           Abs(_,_,body) => t occs body

 	| f$t' => t occs f  orelse  t occs t'

 	| _ => false);

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

 fun close_form A =

     list_all_free (map dest_Free (sort atless (term_frees A)),   

 		   A);

 (*Freeze all (T)Vars by turning them into (T)Frees*)

 fun freeze_vars(Var(ixn,T)) = Free(Syntax.string_of_vname ixn,

                                    Type.freeze_vars T)

   | freeze_vars(Const(a,T)) = Const(a,Type.freeze_vars T)

   | freeze_vars(Free(a,T))  = Free(a,Type.freeze_vars T)

   | freeze_vars(s$t)        = freeze_vars s $ freeze_vars t

   | freeze_vars(Abs(a,T,t)) = Abs(a,Type.freeze_vars T,freeze_vars t)

   | freeze_vars(b)          = b;

 (*Reverse the effect of freeze_vars*)

 fun thaw_vars(Const(a,T)) = Const(a,Type.thaw_vars T)

   | thaw_vars(Free(a,T))  =

       let val T' = Type.thaw_vars T

       in case explode a of

 	   "?"::vn => let val (ixn,_) = Syntax.scan_varname vn

                       in Var(ixn,T') end

 	 | _       => Free(a,T')

       end

   | thaw_vars(Abs(a,T,t)) = Abs(a,Type.thaw_vars T, thaw_vars t)

   | thaw_vars(s$t)        = thaw_vars s $ thaw_vars t

   | thaw_vars(b)          = b;

 (*** 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 = [];

 (*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 is_letter (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 (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 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  ( [Hn,...,H1], [xm,...,x1], B )

   where H1,...,Hn are the hypotheses and x1...xm are the parameters.   *)

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

 	strip_assums_aux (H::Hs, params, B)

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

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

   | strip_assums_aux (Hs, params, B) = (Hs, 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 (Hs, params, B) = strip_assums A

       val D = Unify.rlist_abs(params, B)

       fun pairrev ([],pairs) = pairs  

         | pairrev (H::Hs,pairs) = 

 	    pairrev(Hs, (Unify.rlist_abs(params,H), D) :: pairs)

   in  pairrev (Hs,[])   (*WAS:  map pair (rev Hs)  *)

   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;