--- a/src/Pure/deriv.ML Fri Aug 31 16:14:34 2001 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,151 +0,0 @@
-(* Title: Pure/deriv.ML
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1996 University of Cambridge
-
-Derivations (proof objects) and functions for examining them
-*)
-
-signature DERIV =
- sig
- (*Object-level rules*)
- datatype orule = Subgoal of cterm
- | Asm of int
- | Res of deriv
- | Equal of deriv
- | Thm of string * tag list
- | Other of deriv;
-
- val size : deriv -> int
- val drop : 'a mtree * int -> 'a mtree
- val linear : deriv -> deriv list
- val tree : deriv -> orule mtree
- end;
-
-structure Deriv : DERIV =
-struct
-
-fun size (Join(Theorem _, _)) = 1
- | size (Join(_, ders)) = foldl op+ (1, map size ders);
-
-(*Conversion to linear format. Children of a node are the LIST of inferences
- justifying ONE of the premises*)
-fun rev_deriv (Join (rl, [])) = [Join(rl,[])]
- | rev_deriv (Join (Theorem name, _)) = [Join(Theorem name, [])]
- | rev_deriv (Join (Assumption arg, [der])) =
- Join(Assumption arg,[]) :: rev_deriv der
- | rev_deriv (Join (Bicompose arg, [rder, sder])) =
- Join (Bicompose arg, linear rder) :: rev_deriv sder
- | rev_deriv (Join (_, [der])) = rev_deriv der
- | rev_deriv (Join (rl, der::ders)) = (*catch-all case; doubtful?*)
- Join(rl, List.concat (map linear ders)) :: rev_deriv der
-and linear der = rev (rev_deriv der);
-
-
-(*** Conversion of object-level proof trees ***)
-
-(*Object-level rules*)
-datatype orule = Subgoal of cterm
- | Asm of int
- | Res of deriv
- | Equal of deriv
- | Thm of string * tag list
- | Other of deriv;
-
-(*At position i, splice in value x, removing ngoal elements*)
-fun splice (i,x,ngoal,prfs) =
- let val prfs0 = take(i-1,prfs)
- and prfs1 = drop(i-1,prfs)
- val prfs2 = Join (x, take(ngoal, prfs1)) :: drop(ngoal, prfs1)
- in prfs0 @ prfs2 end;
-
-(*Deletes trivial uses of Equal_elim; hides derivations of Theorems*)
-fun simp_deriv (Join (Equal_elim, [Join (Rewrite_cterm _, []), der])) =
- simp_deriv der
- | simp_deriv (Join (Equal_elim, [Join (Reflexive _, []), der])) =
- simp_deriv der
- | simp_deriv (Join (rule as Theorem name, [_])) = Join (rule, [])
- | simp_deriv (Join (rule, ders)) = Join (rule, map simp_deriv ders);
-
-(*Proof term is an equality: first premise of equal_elim.
- Attempt to decode proof terms made by Drule.goals_conv.
- Subgoal numbers are returned; they are wrong if original subgoal
- had flexflex pairs!
- NEGATIVE i means "could affect all subgoals starting from i"*)
-fun scan_equals (i, Join (Combination,
- [Join (Combination, [_, der1]), der2])) =
- (case der1 of (*ignore trivial cases*)
- Join (Reflexive _, _) => scan_equals (i+1, der2)
- | Join (Rewrite_cterm _, []) => scan_equals (i+1, der2)
- | Join (Rewrite_cterm _, _) => (i,der1) :: scan_equals (i+1, der2)
- | _ (*impossible in gconv*) => [])
- | scan_equals (i, Join (Reflexive _, [])) = []
- | scan_equals (i, Join (Rewrite_cterm _, [])) = []
- (*Anything else could affect ALL following goals*)
- | scan_equals (i, der) = [(~i,der)];
-
-(*Record uses of equality reasoning on 1 or more subgoals*)
-fun update_equals ((i,der), prfs) =
- if i>0 then splice (i, Equal (simp_deriv der), 1, prfs)
- else take (~i-1, prfs) @
- map (fn prf => Join (Equal (simp_deriv der), [prf]))
- (drop (~i-1, prfs));
-
-fun delift (Join (Lift_rule _, [der])) = der
- | delift der = der;
-
-(*Conversion to an object-level proof tree.
- Uses embedded Lift_rules to "annotate" the proof tree with subgoals;
- -- assumes that Lift_rule never occurs except with resolution
- -- may contain Vars that, in fact, are instantiated in that step*)
-fun tree_aux (Join (Trivial ct, []), prfs) = Join(Subgoal ct, prfs)
- | tree_aux (Join (Assumption(i,_), [der]), prfs) =
- tree_aux (der, splice (i, Asm i, 0, prfs))
- | tree_aux (Join (Equal_elim, [der1,der2]), prfs) =
- tree_aux (der2, foldr update_equals (scan_equals (1, der1), prfs))
- | tree_aux (Join (Bicompose (match,true,i,ngoal,env), ders), prfs) =
- (*change eresolve_tac to proof by assumption*)
- tree_aux (Join (Assumption(i, Some env),
- [Join (Bicompose (match,false,i,ngoal,env), ders)]),
- prfs)
- | tree_aux (Join (Lift_rule (ct,i), [der]), prfs) =
- tree_aux (der, splice (i, Subgoal ct, 1, prfs))
- | tree_aux (Join (Bicompose arg,
- [Join (Instantiate _, [rder]), sder]), prfs) =
- (*Ignore Instantiate*)
- tree_aux (Join (Bicompose arg, [rder, sder]), prfs)
- | tree_aux (Join (Bicompose arg,
- [Join (Lift_rule larg, [rder]), sder]), prfs) =
- (*Move Lift_rule: to make a Subgoal on the result*)
- tree_aux (Join (Bicompose arg, [rder,
- Join(Lift_rule larg, [sder])]), prfs)
- | tree_aux (Join (Bicompose (match,ef,i,ngoal,env),
- [Join (Bicompose (match',ef',i',ngoal',env'),
- [der1,der2]),
- der3]), prfs) =
- (*associate resolutions to the right*)
- tree_aux (Join (Bicompose (match', ef', i'+i-1, ngoal', env'),
- [delift der1, (*This Lift_rule would be wrong!*)
- Join (Bicompose (match, ef, i, ngoal-ngoal'+1, env),
- [der2, der3])]), prfs)
- | tree_aux (Join (Bicompose (arg as (_,_,i,ngoal,_)),
- [rder, sder]), prfs) =
- (*resolution with basic rule/assumption -- we hope!*)
- tree_aux (sder, splice (i, Res (simp_deriv rder), ngoal, prfs))
- | tree_aux (Join (Theorem name, _), prfs) = Join(Thm name, prfs)
- | tree_aux (Join (_, [der]), prfs) = tree_aux (der,prfs)
- | tree_aux (der, prfs) = Join(Other (simp_deriv der), prfs);
-
-
-fun tree der = tree_aux (der,[]);
-
-(*Currently declared at end, to avoid conflicting with library's drop
- Can put it after "size" once we switch to List.drop*)
-fun drop (der,0) = der
- | drop (Join (_, der::_), n) = drop (der, n-1)
- | drop (der,_) = der;
-
-end;
-
-
-(*We do NOT open this structure*)