src/Pure/deriv.ML
author paulson
Wed Mar 20 18:42:31 1996 +0100 (1996-03-20)
changeset 1593 69ed69a9c32a
child 1601 0ef6ea27ab15
permissions -rw-r--r--
New module for proof objects (deriviations)
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(*  Title:      Pure/deriv.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1996  University of Cambridge
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Derivations (proof objects) and functions for examining them
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*)
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signature DERIV = 
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  sig
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  (*Object-level rules*)
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  datatype orule = Subgoal of cterm
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		 | Asm of int
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		 | Res of deriv
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		 | Equal of deriv
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		 | Thm   of theory * string
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		 | Other of deriv;
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  val size : deriv -> int
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  val drop : 'a mtree * int -> 'a mtree
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  val linear : deriv -> deriv list
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  val tree : deriv -> orule mtree
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  end;  
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structure Deriv : DERIV =
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struct
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fun size (Join(Theorem _, _)) = 1
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  | size (Join(_, ders)) = foldl op+ (1, map size ders);
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(*Conversion to linear format.  Children of a node are the LIST of inferences
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  justifying ONE of the premises*)
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fun rev_deriv (Join (rl, [])) 	= [Join(rl,[])]
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  | rev_deriv (Join (Theorem arg, _)) 	= [Join(Theorem arg, [])]
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  | rev_deriv (Join (Assumption arg, [der])) = 
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              Join(Assumption arg,[]) :: rev_deriv der
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  | rev_deriv (Join (Bicompose arg, [rder, sder])) =
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	Join (Bicompose arg, linear rder) :: rev_deriv sder
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  | rev_deriv (Join (_, [der]))	= rev_deriv der
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  | rev_deriv (Join (rl, der::ders)) =	(*catch-all case; doubtful?*)
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        Join(rl, flat (map linear ders)) :: rev_deriv der
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and linear der 	= rev (rev_deriv der);
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(*** Conversion of object-level proof trees ***)
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(*Object-level rules*)
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datatype orule = Subgoal of cterm
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	       | Asm of int
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               | Res of deriv
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               | Equal of deriv
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               | Thm   of theory * string
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               | Other of deriv;
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(*At position i, splice in value x, removing ngoal elements*)
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fun splice (i,x,ngoal,prfs) =
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    let val prfs0 = take(i-1,prfs)
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        and prfs1 = drop(i-1,prfs)
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        val prfs2 = Join (x, take(ngoal, prfs1)) :: drop(ngoal, prfs1)
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    in  prfs0 @ prfs2  end;
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(*Deletes trivial uses of Equal_elim; hides derivations of Theorems*)
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fun simp_deriv (Join (Equal_elim, [Join (Rewrite_cterm _, []), der])) =
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      simp_deriv der
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  | simp_deriv (Join (Equal_elim, [Join (Reflexive _, []), der])) =
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      simp_deriv der
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  | simp_deriv (Join (rule as Theorem arg, [_])) = Join (rule, [])
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  | simp_deriv (Join (rule, ders)) = Join (rule, map simp_deriv ders);
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(*Proof term is an equality: first premise of equal_elim.
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  Attempt to decode proof terms made by Drule.goals_conv.
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  Subgoal numbers are returned; they are wrong if original subgoal
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	had flexflex pairs!
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  NEGATIVE i means "could affect all subgoals starting from i"*)
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fun scan_equals (i, Join (Combination, 
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			   [Join (Combination, [_, der1]), der2])) =
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    (case der1 of	(*ignore trivial cases*)
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         Join (Reflexive _, _)      => scan_equals (i+1, der2)
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       | Join (Rewrite_cterm _, []) => scan_equals (i+1, der2)
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       | Join (Rewrite_cterm _, _)  => (i,der1) :: scan_equals (i+1, der2)
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       | _ (*impossible in gconv*)  => [])
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  | scan_equals (i, Join (Reflexive _, [])) = []
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  | scan_equals (i, Join (Rewrite_cterm _, [])) = []
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	(*Anything else could affect ALL following goals*)
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  | scan_equals (i, der) = [(~i,der)];
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(*Record uses of equality reasoning on 1 or more subgoals*)
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fun update_equals ((i,der), prfs) = 
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      if i>0 then splice (i, Equal (simp_deriv der), 1, prfs)
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      else take (~i-1, prfs) @
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	   map (fn prf => Join (Equal (simp_deriv der), [prf])) 
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	       (drop (~i-1, prfs));
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fun delift (Join (Lift_rule _, [der])) = der
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  | delift der = der;
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(*Conversion to an object-level proof tree.
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  Uses embedded Lift_rules to "annotate" the proof tree with subgoals;
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    -- assumes that Lift_rule never occurs except with resolution
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    -- may contain Vars that, in fact, are instantiated in that step*)
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fun tree_aux (Join (Trivial ct, []), prfs) = Join(Subgoal ct, prfs)
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  | tree_aux (Join (Assumption(i,_), [der]), prfs) = 
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      tree_aux (der, splice (i, Asm i, 0, prfs))
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  | tree_aux (Join (Equal_elim, [der1,der2]), prfs) = 
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      tree_aux (der2, foldr update_equals (scan_equals (1, der1), prfs))
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  | tree_aux (Join (Bicompose (match,true,i,ngoal,env), ders), prfs) =
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		(*change eresolve_tac to proof by assumption*)
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      tree_aux (Join (Assumption(i, Some env), 
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			 [Join (Bicompose (match,false,i,ngoal,env), ders)]),
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		   prfs)
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  | tree_aux (Join (Lift_rule (ct,i), [der]), prfs) = 
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      tree_aux (der, splice (i, Subgoal ct, 1, prfs))
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  | tree_aux (Join (Bicompose arg, 
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		       [Join (Instantiate _, [rder]), sder]), prfs) =
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		(*Ignore Instantiate*)
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      tree_aux (Join (Bicompose arg, [rder, sder]), prfs)
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  | tree_aux (Join (Bicompose arg, 
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		       [Join (Lift_rule larg, [rder]), sder]), prfs) =
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		(*Move Lift_rule: to make a Subgoal on the result*)
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      tree_aux (Join (Bicompose arg, [rder, 
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					 Join(Lift_rule larg, [sder])]), prfs)
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  | tree_aux (Join (Bicompose (match,ef,i,ngoal,env), 
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		       [Join (Bicompose (match',ef',i',ngoal',env'),
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			      [der1,der2]), 
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			der3]), prfs) =
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		(*associate resolutions to the right*)
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      tree_aux (Join (Bicompose (match', ef', i'+i-1, ngoal', env'), 
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			 [delift der1,	(*This Lift_rule would be wrong!*)
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			  Join (Bicompose (match, ef, i, ngoal-ngoal'+1, env),
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				[der2, der3])]), prfs)
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  | tree_aux (Join (Bicompose (arg as (_,_,i,ngoal,_)), 
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		       [rder, sder]), prfs) =
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		(*resolution with basic rule/assumption -- we hope!*)
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      tree_aux (sder, splice (i, Res (simp_deriv rder), ngoal, prfs))
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  | tree_aux (Join (Theorem arg, _), prfs)	= Join(Thm arg, prfs)
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  | tree_aux (Join (_, [der]), prfs)	= tree_aux (der,prfs)
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  | tree_aux (der, prfs) = Join(Other (simp_deriv der), prfs);
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fun tree der = tree_aux (der,[]);
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(*Currently declared at end, to avoid conflicting with library's drop
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  Can put it after "size" once we switch to List.drop*)
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fun drop (der,0) = der
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  | drop (Join (_, der::_), n) = drop (der, n-1);
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end;
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(*We do NOT open this structure*)