src/Provers/hypsubst.ML
 author paulson Tue Jul 22 11:12:55 1997 +0200 (1997-07-22 ago) changeset 3537 79ac9b475621 parent 2750 fe3799355b5e child 4179 cc4b6791d5dc permissions -rw-r--r--
Removal of the tactical STATE
```     1 (*  Title: 	Provers/hypsubst
```
```     2     ID:         \$Id\$
```
```     3     Authors: 	Martin D Coen, Tobias Nipkow and Lawrence C Paulson
```
```     4     Copyright   1995  University of Cambridge
```
```     5
```
```     6 Tactic to substitute using the assumption x=t in the rest of the subgoal,
```
```     7 and to delete that assumption.  Original version due to Martin Coen.
```
```     8
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```     9 This version uses the simplifier, and requires it to be already present.
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```    10
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```    11 Test data:
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```    12
```
```    13 goal thy "!!x.[| Q(x,y,z); y=x; a=x; z=y; P(y) |] ==> P(z)";
```
```    14 goal thy "!!x.[| Q(x,y,z); z=f(x); x=z |] ==> P(z)";
```
```    15 goal thy "!!y. [| ?x=y; P(?x) |] ==> y = a";
```
```    16 goal thy "!!z. [| ?x=y; P(?x) |] ==> y = a";
```
```    17
```
```    18 by (hyp_subst_tac 1);
```
```    19 by (bound_hyp_subst_tac 1);
```
```    20
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```    21 Here hyp_subst_tac goes wrong; harder still to prove P(f(f(a))) & P(f(a))
```
```    22 goal thy "P(a) --> (EX y. a=y --> P(f(a)))";
```
```    23 *)
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```    24
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```    25 signature HYPSUBST_DATA =
```
```    26   sig
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```    27   structure Simplifier : SIMPLIFIER
```
```    28   val dest_eq	       : term -> term*term
```
```    29   val eq_reflection    : thm		   (* a=b ==> a==b *)
```
```    30   val imp_intr	       : thm		   (* (P ==> Q) ==> P-->Q *)
```
```    31   val rev_mp	       : thm		   (* [| P;  P-->Q |] ==> Q *)
```
```    32   val subst	       : thm		   (* [| a=b;  P(a) |] ==> P(b) *)
```
```    33   val sym	       : thm		   (* a=b ==> b=a *)
```
```    34   end;
```
```    35
```
```    36
```
```    37 signature HYPSUBST =
```
```    38   sig
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```    39   val bound_hyp_subst_tac    : int -> tactic
```
```    40   val hyp_subst_tac          : int -> tactic
```
```    41     (*exported purely for debugging purposes*)
```
```    42   val gen_hyp_subst_tac      : bool -> int -> tactic
```
```    43   val vars_gen_hyp_subst_tac : bool -> int -> tactic
```
```    44   val eq_var                 : bool -> bool -> term -> int * bool
```
```    45   val inspect_pair           : bool -> bool -> term * term -> bool
```
```    46   val mk_eqs                 : thm -> thm list
```
```    47   val thin_leading_eqs_tac   : bool -> int -> int -> tactic
```
```    48   end;
```
```    49
```
```    50
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```    51
```
```    52 functor HypsubstFun(Data: HYPSUBST_DATA): HYPSUBST =
```
```    53 struct
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```    54
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```    55 local open Data in
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```    56
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```    57 exception EQ_VAR;
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```    58
```
```    59 fun loose (i,t) = 0 mem_int add_loose_bnos(t,i,[]);
```
```    60
```
```    61 local val odot = ord"."
```
```    62 in
```
```    63 (*Simplifier turns Bound variables to dotted Free variables:
```
```    64   change it back (any Bound variable will do)
```
```    65 *)
```
```    66 fun contract t =
```
```    67     case Pattern.eta_contract_atom t of
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```    68 	Free(a,T) => if (ord a = odot) then Bound 0 else Free(a,T)
```
```    69       | t'        => t'
```
```    70 end;
```
```    71
```
```    72 fun has_vars t = maxidx_of_term t <> ~1;
```
```    73
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```    74 (*If novars then we forbid Vars in the equality.
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```    75   If bnd then we only look for Bound (or dotted Free) variables to eliminate.
```
```    76   When can we safely delete the equality?
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```    77     Not if it equates two constants; consider 0=1.
```
```    78     Not if it resembles x=t[x], since substitution does not eliminate x.
```
```    79     Not if it resembles ?x=0; another goal could instantiate ?x to Suc(i)
```
```    80     Not if it involves a variable free in the premises,
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```    81         but we can't check for this -- hence bnd and bound_hyp_subst_tac
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```    82   Prefer to eliminate Bound variables if possible.
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```    83   Result:  true = use as is,  false = reorient first *)
```
```    84 fun inspect_pair bnd novars (t,u) =
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```    85   case (contract t, contract u) of
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```    86        (Bound i, _) => if loose(i,u) orelse novars andalso has_vars u
```
```    87 		       then raise Match
```
```    88 		       else true		(*eliminates t*)
```
```    89      | (_, Bound i) => if loose(i,t) orelse novars andalso has_vars t
```
```    90 		       then raise Match
```
```    91 		       else false		(*eliminates u*)
```
```    92      | (Free _, _) =>  if bnd orelse Logic.occs(t,u) orelse
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```    93 		          novars andalso has_vars u
```
```    94 		       then raise Match
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```    95 		       else true		(*eliminates t*)
```
```    96      | (_, Free _) =>  if bnd orelse Logic.occs(u,t) orelse
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```    97 		          novars andalso has_vars t
```
```    98 		       then raise Match
```
```    99 		       else false		(*eliminates u*)
```
```   100      | _ => raise Match;
```
```   101
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```   102 (*Locates a substitutable variable on the left (resp. right) of an equality
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```   103    assumption.  Returns the number of intervening assumptions. *)
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```   104 fun eq_var bnd novars =
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```   105   let fun eq_var_aux k (Const("all",_) \$ Abs(_,_,t)) = eq_var_aux k t
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```   106 	| eq_var_aux k (Const("==>",_) \$ A \$ B) =
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```   107 	      ((k, inspect_pair bnd novars (dest_eq A))
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```   108 		      (*Exception comes from inspect_pair or dest_eq*)
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```   109 	       handle Match => eq_var_aux (k+1) B)
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```   110 	| eq_var_aux k _ = raise EQ_VAR
```
```   111   in  eq_var_aux 0  end;
```
```   112
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```   113 (*We do not try to delete ALL equality assumptions at once.  But
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```   114   it is easy to handle several consecutive equality assumptions in a row.
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```   115   Note that we have to inspect the proof state after doing the rewriting,
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```   116   since e.g. z=f(x); x=z changes to z=f(x); x=f(x) and the second equality
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```   117   must NOT be deleted.  Tactic must rotate or delete m assumptions.
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```   118 *)
```
```   119 fun thin_leading_eqs_tac bnd m = SUBGOAL (fn (Bi,i) =>
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```   120     let fun count []      = 0
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```   121 	  | count (A::Bs) = ((inspect_pair bnd true (dest_eq A);
```
```   122 			      1 + count Bs)
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```   123                              handle Match => 0)
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```   124         val j = Int.min(m, count (Logic.strip_assums_hyp Bi))
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```   125     in  REPEAT_DETERM_N j (etac thin_rl i)  THEN  rotate_tac (m-j) i
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```   126     end);
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```   127
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```   128 (*For the simpset.  Adds ALL suitable equalities, even if not first!
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```   129   No vars are allowed here, as simpsets are built from meta-assumptions*)
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```   130 fun mk_eqs th =
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```   131     [ if inspect_pair false false (Data.dest_eq (#prop (rep_thm th)))
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```   132       then th RS Data.eq_reflection
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```   133       else symmetric(th RS Data.eq_reflection) (*reorient*) ]
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```   134     handle Match => [];  (*Exception comes from inspect_pair or dest_eq*)
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```   135
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```   136 local open Simplifier
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```   137 in
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```   138
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```   139   val hyp_subst_ss = empty_ss setmksimps mk_eqs
```
```   140
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```   141   (*Select a suitable equality assumption and substitute throughout the subgoal
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```   142     Replaces only Bound variables if bnd is true*)
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```   143   fun gen_hyp_subst_tac bnd = SUBGOAL(fn (Bi,i) =>
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```   144 	let val n = length(Logic.strip_assums_hyp Bi) - 1
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```   145 	    val (k,_) = eq_var bnd true Bi
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```   146 	in
```
```   147 	   DETERM (EVERY [rotate_tac k i,
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```   148 			  asm_full_simp_tac hyp_subst_ss i,
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```   149 			  etac thin_rl i,
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```   150 			  thin_leading_eqs_tac bnd (n-k) i])
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```   151 	end
```
```   152 	handle THM _ => no_tac | EQ_VAR => no_tac);
```
```   153
```
```   154 end;
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```   155
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```   156 val ssubst = standard (sym RS subst);
```
```   157
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```   158 (*Old version of the tactic above -- slower but the only way
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```   159   to handle equalities containing Vars.*)
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```   160 fun vars_gen_hyp_subst_tac bnd = SUBGOAL(fn (Bi,i) =>
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```   161       let val n = length(Logic.strip_assums_hyp Bi) - 1
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```   162 	  val (k,symopt) = eq_var bnd false Bi
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```   163       in
```
```   164 	 DETERM
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```   165            (EVERY [REPEAT_DETERM_N k (etac rev_mp i),
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```   166 		   etac revcut_rl i,
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```   167 		   REPEAT_DETERM_N (n-k) (etac rev_mp i),
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```   168 		   etac (if symopt then ssubst else subst) i,
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```   169 		   REPEAT_DETERM_N n (rtac imp_intr i THEN rotate_tac ~1 i)])
```
```   170       end
```
```   171       handle THM _ => no_tac | EQ_VAR => no_tac);
```
```   172
```
```   173 (*Substitutes for Free or Bound variables*)
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```   174 val hyp_subst_tac =
```
```   175     gen_hyp_subst_tac false ORELSE' vars_gen_hyp_subst_tac false;
```
```   176
```
```   177 (*Substitutes for Bound variables only -- this is always safe*)
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```   178 val bound_hyp_subst_tac =
```
```   179     gen_hyp_subst_tac true ORELSE' vars_gen_hyp_subst_tac true;
```
```   180
```
```   181 end
```
```   182 end;
```
```   183
```