src/Pure/logic.ML
author paulson
Thu Jun 05 13:30:24 1997 +0200 (1997-06-05)
changeset 3408 98a2d517cabe
parent 2508 ce48daa388a7
child 3893 5a1f22e7b359
permissions -rw-r--r--
Removal of freeze_vars and thaw_vars (quite unused...)
     1 (*  Title: 	Pure/logic.ML
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   Cambridge University 1992
     5 
     6 Supporting code for defining the abstract type "thm"
     7 *)
     8 
     9 infix occs;
    10 
    11 signature LOGIC = 
    12   sig
    13   val assum_pairs	: term -> (term*term)list
    14   val auto_rename	: bool ref   
    15   val close_form	: term -> term   
    16   val count_prems	: term * int -> int
    17   val dest_equals	: term -> term * term
    18   val dest_flexpair	: term -> term * term
    19   val dest_implies	: term -> term * term
    20   val dest_inclass	: term -> typ * class
    21   val dest_type		: term -> typ
    22   val flatten_params	: int -> term -> term
    23   val incr_indexes	: typ list * int -> term -> term
    24   val lift_fns		: term * int -> (term -> term) * (term -> term)
    25   val list_flexpairs	: (term*term)list * term -> term
    26   val list_implies	: term list * term -> term
    27   val list_rename_params: string list * term -> term
    28   val is_equals         : term -> bool
    29   val mk_equals		: term * term -> term
    30   val mk_flexpair	: term * term -> term
    31   val mk_implies	: term * term -> term
    32   val mk_inclass	: typ * class -> term
    33   val mk_type		: typ -> term
    34   val occs		: term * term -> bool
    35   val rule_of		: (term*term)list * term list * term -> term
    36   val set_rename_prefix	: string -> unit   
    37   val skip_flexpairs	: term -> term
    38   val strip_assums_concl: term -> term
    39   val strip_assums_hyp	: term -> term list
    40   val strip_flexpairs	: term -> (term*term)list * term
    41   val strip_horn	: term -> (term*term)list * term list * term
    42   val strip_imp_concl	: term -> term
    43   val strip_imp_prems	: term -> term list
    44   val strip_params	: term -> (string * typ) list
    45   val strip_prems	: int * term list * term -> term list * term
    46   val unvarify		: term -> term
    47   val varify		: term -> term
    48   val termord		: term * term -> order
    49   val lextermord	: term list * term list -> order
    50   val termless		: term * term -> bool
    51   end;
    52 
    53 structure Logic : LOGIC =
    54 struct
    55 
    56 (*** Abstract syntax operations on the meta-connectives ***)
    57 
    58 (** equality **)
    59 
    60 (*Make an equality.  DOES NOT CHECK TYPE OF u*)
    61 fun mk_equals(t,u) = equals(fastype_of t) $ t $ u;
    62 
    63 fun dest_equals (Const("==",_) $ t $ u)  =  (t,u)
    64   | dest_equals t = raise TERM("dest_equals", [t]);
    65 
    66 fun is_equals (Const ("==", _) $ _ $ _) = true
    67   | is_equals _ = false;
    68 
    69 
    70 (** implies **)
    71 
    72 fun mk_implies(A,B) = implies $ A $ B;
    73 
    74 fun dest_implies (Const("==>",_) $ A $ B)  =  (A,B)
    75   | dest_implies A = raise TERM("dest_implies", [A]);
    76 
    77 (** nested implications **)
    78 
    79 (* [A1,...,An], B  goes to  A1==>...An==>B  *)
    80 fun list_implies ([], B) = B : term
    81   | list_implies (A::AS, B) = implies $ A $ list_implies(AS,B);
    82 
    83 (* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
    84 fun strip_imp_prems (Const("==>", _) $ A $ B) = A :: strip_imp_prems B
    85   | strip_imp_prems _ = [];
    86 
    87 (* A1==>...An==>B  goes to B, where B is not an implication *)
    88 fun strip_imp_concl (Const("==>", _) $ A $ B) = strip_imp_concl B
    89   | strip_imp_concl A = A : term;
    90 
    91 (*Strip and return premises: (i, [], A1==>...Ai==>B)
    92     goes to   ([Ai, A(i-1),...,A1] , B) 	(REVERSED) 
    93   if  i<0 or else i too big then raises  TERM*)
    94 fun strip_prems (0, As, B) = (As, B) 
    95   | strip_prems (i, As, Const("==>", _) $ A $ B) = 
    96 	strip_prems (i-1, A::As, B)
    97   | strip_prems (_, As, A) = raise TERM("strip_prems", A::As);
    98 
    99 (*Count premises -- quicker than (length ostrip_prems) *)
   100 fun count_prems (Const("==>", _) $ A $ B, n) = count_prems (B,n+1)
   101   | count_prems (_,n) = n;
   102 
   103 (** flex-flex constraints **)
   104 
   105 (*Make a constraint.*)
   106 fun mk_flexpair(t,u) = flexpair(fastype_of t) $ t $ u;
   107 
   108 fun dest_flexpair (Const("=?=",_) $ t $ u)  =  (t,u)
   109   | dest_flexpair t = raise TERM("dest_flexpair", [t]);
   110 
   111 (*make flexflex antecedents: ( [(a1,b1),...,(an,bn)] , C )
   112     goes to (a1=?=b1) ==>...(an=?=bn)==>C *)
   113 fun list_flexpairs ([], A) = A
   114   | list_flexpairs ((t,u)::pairs, A) =
   115 	implies $ (mk_flexpair(t,u)) $ list_flexpairs(pairs,A);
   116 
   117 (*Make the object-rule tpairs==>As==>B   *)
   118 fun rule_of (tpairs, As, B) = list_flexpairs(tpairs, list_implies(As, B));
   119 
   120 (*Remove and return flexflex pairs: 
   121     (a1=?=b1)==>...(an=?=bn)==>C  to  ( [(a1,b1),...,(an,bn)] , C )	
   122   [Tail recursive in order to return a pair of results] *)
   123 fun strip_flex_aux (pairs, Const("==>", _) $ (Const("=?=",_)$t$u) $ C) =
   124         strip_flex_aux ((t,u)::pairs, C)
   125   | strip_flex_aux (pairs,C) = (rev pairs, C);
   126 
   127 fun strip_flexpairs A = strip_flex_aux([], A);
   128 
   129 (*Discard flexflex pairs*)
   130 fun skip_flexpairs (Const("==>", _) $ (Const("=?=",_)$_$_) $ C) =
   131 	skip_flexpairs C
   132   | skip_flexpairs C = C;
   133 
   134 (*strip a proof state (Horn clause): 
   135    (a1==b1)==>...(am==bm)==>B1==>...Bn==>C
   136     goes to   ( [(a1,b1),...,(am,bm)] , [B1,...,Bn] , C)    *)
   137 fun strip_horn A =
   138   let val (tpairs,horn) = strip_flexpairs A 
   139   in  (tpairs, strip_imp_prems horn, strip_imp_concl horn)   end;
   140 
   141 (** types as terms **)
   142 
   143 fun mk_type ty = Const ("TYPE", itselfT ty);
   144 
   145 fun dest_type (Const ("TYPE", Type ("itself", [ty]))) = ty
   146   | dest_type t = raise TERM ("dest_type", [t]);
   147 
   148 (** class constraints **)
   149 
   150 fun mk_inclass (ty, c) =
   151   Const (Sign.const_of_class c, itselfT ty --> propT) $ mk_type ty;
   152 
   153 fun dest_inclass (t as Const (c_class, _) $ ty) =
   154       ((dest_type ty, Sign.class_of_const c_class)
   155         handle TERM _ => raise TERM ("dest_inclass", [t]))
   156   | dest_inclass t = raise TERM ("dest_inclass", [t]);
   157 
   158 
   159 (*** Low-level term operations ***)
   160 
   161 (*Does t occur in u?  Or is alpha-convertible to u?
   162   The term t must contain no loose bound variables*)
   163 fun t occs u = (t aconv u) orelse 
   164       (case u of
   165           Abs(_,_,body) => t occs body
   166 	| f$t' => t occs f  orelse  t occs t'
   167 	| _ => false);
   168 
   169 (*Close up a formula over all free variables by quantification*)
   170 fun close_form A =
   171     list_all_free (map dest_Free (sort atless (term_frees A)),   
   172 		   A);
   173 
   174 
   175 (*** Specialized operations for resolution... ***)
   176 
   177 (*For all variables in the term, increment indexnames and lift over the Us
   178     result is ?Gidx(B.(lev+n-1),...,B.lev) where lev is abstraction level *)
   179 fun incr_indexes (Us: typ list, inc:int) t = 
   180   let fun incr (Var ((a,i), T), lev) = 
   181 		Unify.combound (Var((a, i+inc), Us---> incr_tvar inc T),
   182 				lev, length Us)
   183 	| incr (Abs (a,T,body), lev) =
   184 		Abs (a, incr_tvar inc T, incr(body,lev+1))
   185 	| incr (Const(a,T),_) = Const(a, incr_tvar inc T)
   186 	| incr (Free(a,T),_) = Free(a, incr_tvar inc T)
   187 	| incr (f$t, lev) = incr(f,lev) $ incr(t,lev)
   188 	| incr (t,lev) = t
   189   in  incr(t,0)  end;
   190 
   191 (*Make lifting functions from subgoal and increment.
   192     lift_abs operates on tpairs (unification constraints)
   193     lift_all operates on propositions     *)
   194 fun lift_fns (B,inc) =
   195   let fun lift_abs (Us, Const("==>", _) $ _ $ B) u = lift_abs (Us,B) u
   196 	| lift_abs (Us, Const("all",_)$Abs(a,T,t)) u =
   197 	      Abs(a, T, lift_abs (T::Us, t) u)
   198 	| lift_abs (Us, _) u = incr_indexes(rev Us, inc) u
   199       fun lift_all (Us, Const("==>", _) $ A $ B) u =
   200 	      implies $ A $ lift_all (Us,B) u
   201 	| lift_all (Us, Const("all",_)$Abs(a,T,t)) u = 
   202 	      all T $ Abs(a, T, lift_all (T::Us,t) u)
   203 	| lift_all (Us, _) u = incr_indexes(rev Us, inc) u;
   204   in  (lift_abs([],B), lift_all([],B))  end;
   205 
   206 (*Strips assumptions in goal, yielding list of hypotheses.   *)
   207 fun strip_assums_hyp (Const("==>", _) $ H $ B) = H :: strip_assums_hyp B
   208   | strip_assums_hyp (Const("all",_)$Abs(a,T,t)) = strip_assums_hyp t
   209   | strip_assums_hyp B = [];
   210 
   211 (*Strips assumptions in goal, yielding conclusion.   *)
   212 fun strip_assums_concl (Const("==>", _) $ H $ B) = strip_assums_concl B
   213   | strip_assums_concl (Const("all",_)$Abs(a,T,t)) = strip_assums_concl t
   214   | strip_assums_concl B = B;
   215 
   216 (*Make a list of all the parameters in a subgoal, even if nested*)
   217 fun strip_params (Const("==>", _) $ H $ B) = strip_params B
   218   | strip_params (Const("all",_)$Abs(a,T,t)) = (a,T) :: strip_params t
   219   | strip_params B = [];
   220 
   221 (*Removes the parameters from a subgoal and renumber bvars in hypotheses,
   222     where j is the total number of parameters (precomputed) 
   223   If n>0 then deletes assumption n. *)
   224 fun remove_params j n A = 
   225     if j=0 andalso n<=0 then A  (*nothing left to do...*)
   226     else case A of
   227         Const("==>", _) $ H $ B => 
   228 	  if n=1 then                           (remove_params j (n-1) B)
   229 	  else implies $ (incr_boundvars j H) $ (remove_params j (n-1) B)
   230       | Const("all",_)$Abs(a,T,t) => remove_params (j-1) n t
   231       | _ => if n>0 then raise TERM("remove_params", [A])
   232              else A;
   233 
   234 (** Auto-renaming of parameters in subgoals **)
   235 
   236 val auto_rename = ref false
   237 and rename_prefix = ref "ka";
   238 
   239 (*rename_prefix is not exported; it is set by this function.*)
   240 fun set_rename_prefix a =
   241     if a<>"" andalso forall is_letter (explode a)
   242     then  (rename_prefix := a;  auto_rename := true)
   243     else  error"rename prefix must be nonempty and consist of letters";
   244 
   245 (*Makes parameters in a goal have distinctive names (not guaranteed unique!)
   246   A name clash could cause the printer to rename bound vars;
   247     then res_inst_tac would not work properly.*)
   248 fun rename_vars (a, []) = []
   249   | rename_vars (a, (_,T)::vars) =
   250         (a,T) :: rename_vars (bump_string a, vars);
   251 
   252 (*Move all parameters to the front of the subgoal, renaming them apart;
   253   if n>0 then deletes assumption n. *)
   254 fun flatten_params n A =
   255     let val params = strip_params A;
   256 	val vars = if !auto_rename 
   257 		   then rename_vars (!rename_prefix, params)
   258 		   else ListPair.zip (variantlist(map #1 params,[]),
   259 				      map #2 params)
   260     in  list_all (vars, remove_params (length vars) n A)
   261     end;
   262 
   263 (*Makes parameters in a goal have the names supplied by the list cs.*)
   264 fun list_rename_params (cs, Const("==>", _) $ A $ B) =
   265       implies $ A $ list_rename_params (cs, B)
   266   | list_rename_params (c::cs, Const("all",_)$Abs(_,T,t)) = 
   267       all T $ Abs(c, T, list_rename_params (cs, t))
   268   | list_rename_params (cs, B) = B;
   269 
   270 (*Strips assumptions in goal yielding  ( [Hn,...,H1], [xm,...,x1], B )
   271   where H1,...,Hn are the hypotheses and x1...xm are the parameters.   *)
   272 fun strip_assums_aux (Hs, params, Const("==>", _) $ H $ B) = 
   273 	strip_assums_aux (H::Hs, params, B)
   274   | strip_assums_aux (Hs, params, Const("all",_)$Abs(a,T,t)) =
   275 	strip_assums_aux (Hs, (a,T)::params, t)
   276   | strip_assums_aux (Hs, params, B) = (Hs, params, B);
   277 
   278 fun strip_assums A = strip_assums_aux ([],[],A);
   279 
   280 
   281 (*Produces disagreement pairs, one for each assumption proof, in order.
   282   A is the first premise of the lifted rule, and thus has the form
   283     H1 ==> ... Hk ==> B   and the pairs are (H1,B),...,(Hk,B) *)
   284 fun assum_pairs A =
   285   let val (Hs, params, B) = strip_assums A
   286       val D = Unify.rlist_abs(params, B)
   287       fun pairrev ([],pairs) = pairs  
   288         | pairrev (H::Hs,pairs) = 
   289 	    pairrev(Hs, (Unify.rlist_abs(params,H), D) :: pairs)
   290   in  pairrev (Hs,[])   (*WAS:  map pair (rev Hs)  *)
   291   end;
   292 
   293 
   294 (*Converts Frees to Vars and TFrees to TVars so that axioms can be written
   295   without (?) everywhere*)
   296 fun varify (Const(a,T)) = Const(a, Type.varifyT T)
   297   | varify (Free(a,T)) = Var((a,0), Type.varifyT T)
   298   | varify (Var(ixn,T)) = Var(ixn, Type.varifyT T)
   299   | varify (Abs (a,T,body)) = Abs (a, Type.varifyT T, varify body)
   300   | varify (f$t) = varify f $ varify t
   301   | varify t = t;
   302 
   303 (*Inverse of varify.  Converts axioms back to their original form.*)
   304 fun unvarify (Const(a,T))    = Const(a, Type.unvarifyT T)
   305   | unvarify (Var((a,0), T)) = Free(a, Type.unvarifyT T)
   306   | unvarify (Var(ixn,T))    = Var(ixn, Type.unvarifyT T)  (*non-0 index!*)
   307   | unvarify (Abs (a,T,body)) = Abs (a, Type.unvarifyT T, unvarify body)
   308   | unvarify (f$t) = unvarify f $ unvarify t
   309   | unvarify t = t;
   310 
   311 
   312 (*** term order ***)
   313 
   314 (* NB: non-linearity of the ordering is not a soundness problem *)
   315 
   316 (* FIXME: "***ABSTRACTION***" is a hack and makes the ordering non-linear *)
   317 fun string_of_hd(Const(a,_)) = a
   318   | string_of_hd(Free(a,_))  = a
   319   | string_of_hd(Var(v,_))   = Syntax.string_of_vname v
   320   | string_of_hd(Bound i)    = string_of_int i
   321   | string_of_hd(Abs _)      = "***ABSTRACTION***";
   322 
   323 (* a strict (not reflexive) linear well-founded AC-compatible ordering
   324  * for terms:
   325  * s < t <=> 1. size(s) < size(t) or
   326              2. size(s) = size(t) and s=f(...) and t = g(...) and f<g or
   327              3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
   328                 (s1..sn) < (t1..tn) (lexicographically)
   329  *)
   330 
   331 (* FIXME: should really take types into account as well.
   332  * Otherwise non-linear *)
   333 fun termord(Abs(_,_,t),Abs(_,_,u)) = termord(t,u)
   334   | termord(t,u) =
   335       (case intord(size_of_term t,size_of_term u) of
   336          EQUAL => let val (f,ts) = strip_comb t and (g,us) = strip_comb u
   337                   in case stringord(string_of_hd f, string_of_hd g) of
   338                        EQUAL => lextermord(ts,us)
   339                      | ord   => ord
   340                   end
   341        | ord => ord)
   342 and lextermord(t::ts,u::us) =
   343       (case termord(t,u) of
   344          EQUAL => lextermord(ts,us)
   345        | ord   => ord)
   346   | lextermord([],[]) = EQUAL
   347   | lextermord _ = error("lextermord");
   348 
   349 fun termless tu = (termord tu = LESS);
   350 
   351 end;