src/Pure/Proof/reconstruct.ML
author berghofe
Fri Sep 28 11:05:37 2001 +0200 (2001-09-28)
changeset 11613 c92a99a2b5b1
parent 11539 0f17da240450
child 11660 780ffc4d4600
permissions -rw-r--r--
- Exchanged % and %%
- Renamed reconstruct_prf to reconstruct_proof
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(*  Title:      Pure/Proof/reconstruct.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Reconstruction of partial proof terms.
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*)
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signature RECONSTRUCT =
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sig
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  val quiet_mode : bool ref
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  val reconstruct_proof : Sign.sg -> term -> Proofterm.proof -> Proofterm.proof
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  val expand_proof : Sign.sg -> string list -> Proofterm.proof -> Proofterm.proof
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end;
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structure Reconstruct : RECONSTRUCT =
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struct
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open Proofterm;
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val quiet_mode = ref true;
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fun message s = if !quiet_mode then () else writeln s;
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fun vars_of t = rev (foldl_aterms
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  (fn (vs, v as Var _) => v ins vs | (vs, _) => vs) ([], t));
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fun forall_intr (t, prop) =
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  let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
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  in all T $ Abs (a, T, abstract_over (t, prop)) end;
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fun forall_intr_vfs prop = foldr forall_intr
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  (vars_of prop @ sort (make_ord atless) (term_frees prop), prop);
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fun merge_envs (Envir.Envir {asol=asol1, iTs=iTs1, maxidx=maxidx1})
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  (Envir.Envir {asol=asol2, iTs=iTs2, maxidx=maxidx2}) =
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    Envir.Envir {asol=Vartab.merge (op aconv) (asol1, asol2),
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                 iTs=Vartab.merge (op =) (iTs1, iTs2),
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                 maxidx=Int.max (maxidx1, maxidx2)};
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fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
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  | strip_abs _ t = t;
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(********************************************************************************
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  generate constraints for proof term
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*********************************************************************************)
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fun mk_var env Ts T = 
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  let val (env', v) = Envir.genvar "a" (env, rev Ts ---> T)
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  in (env', list_comb (v, map Bound (length Ts - 1 downto 0))) end;
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fun mk_tvar (Envir.Envir {iTs, asol, maxidx}, s) =
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  (Envir.Envir {iTs = iTs, asol = asol, maxidx = maxidx+1},
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   TVar (("'t", maxidx+1), s));
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fun mk_abs Ts t = foldl (fn (u, T) => Abs ("", T, u)) (t, Ts);
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fun make_Tconstraints_cprf maxidx cprf =
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  let
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    fun mk_Tcnstrts maxidx Ts (Abst (s, Some T, cprf)) =
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          let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx (T::Ts) cprf;
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          in (cs, Abst (s, Some T, cprf'), maxidx') end
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      | mk_Tcnstrts maxidx Ts (Abst (s, None, cprf)) =
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          let
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            val T' = TVar (("'t", maxidx+1), ["logic"]);
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            val (cs, cprf', maxidx') = mk_Tcnstrts (maxidx+1) (T'::Ts) cprf;
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          in (cs, Abst (s, Some T', cprf'), maxidx') end
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      | mk_Tcnstrts maxidx Ts (AbsP (s, Some t, cprf)) =
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          let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf;
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          in ((mk_abs Ts t, rev Ts ---> propT)::cs, AbsP (s, Some t, cprf'), maxidx') end
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      | mk_Tcnstrts maxidx Ts (AbsP (s, None, cprf)) =
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          let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf;
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          in (cs, AbsP (s, None, cprf'), maxidx') end
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      | mk_Tcnstrts maxidx Ts (cprf1 %% cprf2) =
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          let
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            val (cs, cprf1', maxidx') = mk_Tcnstrts maxidx Ts cprf1;
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            val (cs', cprf2', maxidx'') = mk_Tcnstrts maxidx' Ts cprf2;
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          in (cs' @ cs, cprf1' %% cprf2', maxidx'') end
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      | mk_Tcnstrts maxidx Ts (cprf % Some t) =
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          let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf;
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          in ((mk_abs Ts t, rev Ts ---> TypeInfer.logicT)::cs,
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            cprf' % Some t, maxidx')
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          end
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      | mk_Tcnstrts maxidx Ts (cprf % None) =
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          let val (cs, cprf', maxidx') = mk_Tcnstrts maxidx Ts cprf;
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          in (cs, cprf % None, maxidx') end
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      | mk_Tcnstrts maxidx _ cprf = ([], cprf, maxidx);
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  in mk_Tcnstrts maxidx [] cprf end;
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fun unifyT sg env T U =
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  let
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    val Envir.Envir {asol, iTs, maxidx} = env;
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    val (iTs', maxidx') = Type.unify (Sign.tsig_of sg) maxidx iTs (T, U)
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  in Envir.Envir {asol=asol, iTs=iTs', maxidx=maxidx'} end;
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fun decompose sg env Ts
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    (Const ("all", _) $ Abs (_, T, t)) (Const ("all", _) $ Abs (_, U, u)) =
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      decompose sg (unifyT sg env T U) (T::Ts) t u
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  | decompose sg env Ts
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    (Const ("==>", _) $ t1 $ t2) (Const ("==>", _) $ u1 $ u2) =
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      apsnd (cons (mk_abs Ts t1, mk_abs Ts u1)) (decompose sg env Ts t2 u2)
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  | decompose sg env Ts t u = (env, [(mk_abs Ts t, mk_abs Ts u)]);
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fun cantunify sg t u = error ("Cannot unify:\n" ^
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  Sign.string_of_term sg t ^ "\n\n" ^ Sign.string_of_term sg u);
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fun make_constraints_cprf sg env ts cprf =
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  let
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    fun add_cnstrt Ts prop prf cs env ts (t, u) =
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      let
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        val t' = mk_abs Ts t;
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        val u' = mk_abs Ts u;
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        val nt = Envir.norm_term env t';
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        val nu = Envir.norm_term env u'
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      in
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        if Pattern.pattern nt andalso Pattern.pattern nu then
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          let
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            val env' = (Pattern.unify (sg, env, [(nt, nu)]) handle Pattern.Unif =>
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                       cantunify sg nt nu);
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          in (Envir.norm_term env' prop, prf, cs, env', ts) end
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        else
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          let val (env', cs') = decompose sg env [] nt nu
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          in (Envir.norm_term env' prop, prf, cs @ cs', env', ts) end
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      end;
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    fun mk_cnstrts_atom env ts prop opTs mk_prf =
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          let
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            val tvars = term_tvars prop;
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            val (env', Ts) = if_none (apsome (pair env) opTs)
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              (foldl_map (mk_tvar o apsnd snd) (env, tvars));
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            val prop' = subst_TVars (map fst tvars ~~ Ts) (forall_intr_vfs prop);
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          in (prop', mk_prf (Some Ts), [], env', ts) end;
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    fun mk_cnstrts env _ Hs ts (PBound i) = (nth_elem (i, Hs), PBound i, [], env, ts)
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      | mk_cnstrts env Ts Hs ts (Abst (s, Some T, cprf)) =
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          let val (t, prf, cnstrts, env', ts') =
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              mk_cnstrts env (T::Ts) (map (incr_boundvars 1) Hs) ts cprf;
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          in (Const ("all", (T --> propT) --> propT) $ Abs (s, T, t), Abst (s, Some T, prf),
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            cnstrts, env', ts')
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          end
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      | mk_cnstrts env Ts Hs (t::ts) (AbsP (s, Some _, cprf)) =
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          let
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            val (u, prf, cnstrts, env', ts') = mk_cnstrts env Ts (t::Hs) ts cprf;
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            val t' = strip_abs Ts t;
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          in (Logic.mk_implies (t', u), AbsP (s, Some t', prf), cnstrts, env', ts')
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          end
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      | mk_cnstrts env Ts Hs ts (AbsP (s, None, cprf)) =
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          let
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            val (env', t) = mk_var env Ts propT;
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            val (u, prf, cnstrts, env'', ts') = mk_cnstrts env' Ts (t::Hs) ts cprf;
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          in (Logic.mk_implies (t, u), AbsP (s, Some t, prf), cnstrts, env'', ts')
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          end
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      | mk_cnstrts env Ts Hs ts (cprf1 %% cprf2) =
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          let val (u, prf2, cnstrts, env', ts') = mk_cnstrts env Ts Hs ts cprf2
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          in (case mk_cnstrts env' Ts Hs ts' cprf1 of
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              (Const ("==>", _) $ u' $ t', prf1, cnstrts', env'', ts'') =>
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                add_cnstrt Ts t' (prf1 %% prf2) (cnstrts' @ cnstrts)
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                  env'' ts'' (u, u')
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            | (t, prf1, cnstrts', env'', ts'') =>
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                let val (env''', v) = mk_var env'' Ts propT
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                in add_cnstrt Ts v (prf1 %% prf2) (cnstrts' @ cnstrts)
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                  env''' ts'' (t, Logic.mk_implies (u, v))
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                end)
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          end
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      | mk_cnstrts env Ts Hs (t::ts) (cprf % Some _) =
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          let val t' = strip_abs Ts t
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          in (case mk_cnstrts env Ts Hs ts cprf of
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             (Const ("all", Type ("fun", [Type ("fun", [T, _]), _])) $ f,
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                 prf, cnstrts, env', ts') =>
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               let val env'' = unifyT sg env' T
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                 (fastype_of1 (map (Envir.norm_type env') Ts, t'))
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               in (betapply (f, t'), prf % Some t', cnstrts, env'', ts')
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               end
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           | (u, prf, cnstrts, env', ts') =>
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               let
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                 val T = fastype_of1 (map (Envir.norm_type env') Ts, t');
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                 val (env'', v) = mk_var env' Ts (T --> propT);
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               in
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                 add_cnstrt Ts (v $ t') (prf % Some t') cnstrts env'' ts'
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                   (u, Const ("all", (T --> propT) --> propT) $ v)
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               end)
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          end
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      | mk_cnstrts env Ts Hs ts (cprf % None) =
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          (case mk_cnstrts env Ts Hs ts cprf of
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             (Const ("all", Type ("fun", [Type ("fun", [T, _]), _])) $ f,
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                 prf, cnstrts, env', ts') =>
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               let val (env'', t) = mk_var env' Ts T
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               in (betapply (f, t), prf % Some t, cnstrts, env'', ts')
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               end
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           | (u, prf, cnstrts, env', ts') =>
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               let
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                 val (env1, T) = mk_tvar (env', ["logic"]);
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                 val (env2, v) = mk_var env1 Ts (T --> propT);
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                 val (env3, t) = mk_var env2 Ts T
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               in
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                 add_cnstrt Ts (v $ t) (prf % Some t) cnstrts env3 ts'
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                   (u, Const ("all", (T --> propT) --> propT) $ v)
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               end)
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      | mk_cnstrts env _ _ ts (PThm (name, prf, prop, opTs)) =
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          mk_cnstrts_atom env ts prop opTs (fn x => PThm (name, prf, prop, x))
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      | mk_cnstrts env _ _ ts (PAxm (name, prop, opTs)) =
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          mk_cnstrts_atom env ts prop opTs (fn x => PAxm (name, prop, x))
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      | mk_cnstrts env _ _ ts (Oracle (name, prop, opTs)) =
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          mk_cnstrts_atom env ts prop opTs (fn x => Oracle (name, prop, x))
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      | mk_cnstrts env _ _ ts (Hyp t) = (t, Hyp t, [], env, ts)
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      | mk_cnstrts _ _ _ _ _ = error "reconstruct_proof: minimal proof object"
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  in mk_cnstrts env [] [] ts cprf end;
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fun add_term_ixns (is, Var (i, T)) = add_typ_ixns (i ins is, T)
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  | add_term_ixns (is, Free (_, T)) = add_typ_ixns (is, T)
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  | add_term_ixns (is, Const (_, T)) = add_typ_ixns (is, T)
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  | add_term_ixns (is, t1 $ t2) = add_term_ixns (add_term_ixns (is, t1), t2)
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  | add_term_ixns (is, Abs (_, T, t)) = add_term_ixns (add_typ_ixns (is, T), t)
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  | add_term_ixns (is, _) = is;
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(********************************************************************************
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  update list of free variables of constraints
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*********************************************************************************)
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fun upd_constrs env cs =
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  let
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    val Envir.Envir {asol, iTs, ...} = env;
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    val dom = Vartab.foldl (uncurry (cons o fst) o Library.swap)
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      (Vartab.foldl (uncurry (cons o fst) o Library.swap) ([], asol), iTs); 
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    val vran = Vartab.foldl (add_typ_ixns o apsnd snd)
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      (Vartab.foldl (add_term_ixns o apsnd snd) ([], asol), iTs);
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    fun check_cs [] = []
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      | check_cs ((u, p, vs)::ps) =
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          let val vs' = vs \\ dom;
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          in if vs = vs' then (u, p, vs)::check_cs ps
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             else (true, p, vs' union vran)::check_cs ps
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          end
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  in check_cs cs end;
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(********************************************************************************
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  solution of constraints
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*********************************************************************************)
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exception IMPOSS;
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fun solve _ [] bigenv = bigenv
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  | solve sg cs bigenv =
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      let
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        fun search env [] = raise IMPOSS
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          | search env ((u, p as (t1, t2), vs)::ps) =
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              if u then
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                let
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                  val tn1 = Envir.norm_term bigenv t1;
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                  val tn2 = Envir.norm_term bigenv t2
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                in
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                  if Pattern.pattern tn1 andalso Pattern.pattern tn2 then
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                    ((Pattern.unify (sg, env, [(tn1, tn2)]), ps) handle Pattern.Unif =>
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                       cantunify sg tn1 tn2)
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                  else
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                    let val (env', cs') = decompose sg env [] tn1 tn2
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                    in if cs' = [(tn1, tn2)] then
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                         apsnd (cons (false, (tn1, tn2), vs)) (search env ps)
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                       else search env' (map (fn q => (true, q, vs)) cs' @ ps)
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                    end
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                end
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              else apsnd (cons (false, p, vs)) (search env ps);
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        val Envir.Envir {maxidx, ...} = bigenv;
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        val (env, cs') = search (Envir.empty maxidx) cs;
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      in
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        solve sg (upd_constrs env cs') (merge_envs bigenv env)
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      end;
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(********************************************************************************
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  reconstruction of proofs
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*********************************************************************************)
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fun reconstruct_proof sg prop cprf =
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  let
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    val (cprf' % Some prop', thawf) = freeze_thaw_prf (cprf % Some prop);
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    val _ = message "Collecting type constraints...";
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    val (Tcs, cprf'', maxidx) = make_Tconstraints_cprf 0 cprf';
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    val (ts, Ts) = ListPair.unzip Tcs;
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    val tsig = Sign.tsig_of sg;
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    val {classrel, arities, ...} = Type.rep_tsig tsig;
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    val _ = message "Solving type constraints...";
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    val (ts', _, unifier) = TypeInfer.infer_types (Sign.pretty_term sg) (Sign.pretty_typ sg)
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      (Sign.const_type sg) classrel arities [] false (K true) ts Ts;
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    val env = Envir.Envir {asol = Vartab.empty, iTs = Vartab.make unifier, maxidx = maxidx};
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    val _ = message "Collecting term constraints...";
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    val (t, prf, cs, env, _) = make_constraints_cprf sg env ts' cprf'';
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    val cs' = map (fn p => (true, p, op union
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      (pairself (map (fst o dest_Var) o term_vars) p))) (map (pairself (Envir.norm_term env)) ((t, prop')::cs));
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    val _ = message ("Solving remaining constraints (" ^ string_of_int (length cs') ^ ") ...");
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    val env' = solve sg cs' env
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  in
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    thawf (norm_proof env' prf)
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  end;
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fun full_prf_of thm =
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  let val {prop, der = (_, prf), sign, ...} = rep_thm thm
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  in reconstruct_proof sign prop prf end;
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(********************************************************************************
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  expand and reconstruct subproofs
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*********************************************************************************)
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fun full_forall_intr_proof prf x a T = Abst (a, Some T, prf_abstract_over x prf);
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fun expand_proof sg names prf =
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  let
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    fun expand prfs (AbsP (s, t, prf)) = 
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          let val (prfs', prf') = expand prfs prf
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          in (prfs', AbsP (s, t, prf')) end
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      | expand prfs (Abst (s, T, prf)) = 
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          let val (prfs', prf') = expand prfs prf
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          in (prfs', Abst (s, T, prf')) end
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      | expand prfs (prf1 %% prf2) =
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          let
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            val (prfs', prf1') = expand prfs prf1;
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            val (prfs'', prf2') = expand prfs' prf2;
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          in (prfs'', prf1' %% prf2') end
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      | expand prfs (prf % t) =
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          let val (prfs', prf') = expand prfs prf
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          in (prfs', prf' % t) end
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      | expand prfs (prf as PThm ((a, _), cprf, prop, Some Ts)) =
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          if not (a mem names) then (prfs, prf) else
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          let
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            val (prf, prfs') = (case assoc (prfs, (a, prop)) of
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                None =>
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                  let
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                    val _ = message ("Reconstructing proof of " ^ a);
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                    val _ = message (Sign.string_of_term sg prop);
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                    val prf = reconstruct_proof sg prop cprf
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                  in (prf, ((a, prop), prf)::prfs) end
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              | Some prf => (prf, prfs));
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            val tvars = term_tvars prop;
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            val vars = vars_of prop;
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            val tye = map fst tvars ~~ Ts;
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            fun abst (t as Var ((s, _), T), prf) = full_forall_intr_proof prf t s T;
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            val prf' = map_proof_terms (subst_TVars tye) (typ_subst_TVars tye) prf
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          in
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            expand prfs' (foldr abst (map (subst_TVars tye) vars, prf'))
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          end
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      | expand prfs prf = (prfs, prf);
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  in snd (expand [] prf) end;
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end;