flushOut ensures that no recent error message are lost (not certain this is
necessary)
(* 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
| 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
| 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*)