src/Pure/Proof/reconstruct.ML
author wenzelm
Thu Jul 28 15:19:49 2005 +0200 (2005-07-28)
changeset 16934 9ef19e3c7fdd
parent 16876 f57b38cced32
child 16983 c895701d55ea
permissions -rw-r--r--
Sign.typ_unify;
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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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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 : theory -> term -> Proofterm.proof -> Proofterm.proof
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  val prop_of' : term list -> Proofterm.proof -> term
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  val prop_of : Proofterm.proof -> term
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  val expand_proof : theory -> (string * term option) list ->
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    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 (fold_aterms
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  (fn v as Var _ => insert (op =) v | _ => I) 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 prop
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  (vars_of prop @ sort (make_ord atless) (term_frees prop));
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fun forall_intr_prf (t, prf) =
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  let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
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  in Abst (a, SOME T, prf_abstract_over t prf) end;
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fun forall_intr_vfs_prf prop prf = foldr forall_intr_prf prf
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  (vars_of prop @ sort (make_ord atless) (term_frees 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 =) (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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(**** generate constraints for proof term ****)
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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 = Library.foldl (fn (u, T) => Abs ("", T, u)) (t, Ts);
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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') = Sign.typ_unify sg (T, U) (iTs, maxidx)
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  in Envir.Envir {asol=asol, iTs=iTs', maxidx=maxidx'} end
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  handle Type.TUNIFY => error ("Non-unifiable types:\n" ^
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    Sign.string_of_typ sg T ^ "\n\n" ^ Sign.string_of_typ sg U);
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fun chaseT (env as Envir.Envir {iTs, ...}) (T as TVar ixnS) =
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      (case Type.lookup (iTs, ixnS) of NONE => T | SOME T' => chaseT env T')
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  | chaseT _ T = T;
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fun infer_type sg (env as Envir.Envir {maxidx, asol, iTs}) Ts vTs
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      (t as Const (s, T)) = if T = dummyT then (case Sign.const_type sg s of
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          NONE => error ("reconstruct_proof: No such constant: " ^ quote s)
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        | SOME T => 
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            let val T' = Logic.incr_tvar (maxidx + 1) T
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            in (Const (s, T'), T', vTs,
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              Envir.Envir {maxidx = maxidx + 1, asol = asol, iTs = iTs})
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            end)
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      else (t, T, vTs, env)
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  | infer_type sg env Ts vTs (t as Free (s, T)) =
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      if T = dummyT then (case Symtab.lookup (vTs, s) of
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          NONE =>
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            let val (env', T) = mk_tvar (env, [])
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            in (Free (s, T), T, Symtab.update_new ((s, T), vTs), env') end
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        | SOME T => (Free (s, T), T, vTs, env))
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      else (t, T, vTs, env)
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  | infer_type sg env Ts vTs (Var _) = error "reconstruct_proof: internal error"
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  | infer_type sg env Ts vTs (Abs (s, T, t)) =
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      let
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        val (env', T') = if T = dummyT then mk_tvar (env, []) else (env, T);
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        val (t', U, vTs', env'') = infer_type sg env' (T' :: Ts) vTs t
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      in (Abs (s, T', t'), T' --> U, vTs', env'') end
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  | infer_type sg env Ts vTs (t $ u) =
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      let
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        val (t', T, vTs1, env1) = infer_type sg env Ts vTs t;
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        val (u', U, vTs2, env2) = infer_type sg env1 Ts vTs1 u;
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      in (case chaseT env2 T of
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          Type ("fun", [U', V]) => (t' $ u', V, vTs2, unifyT sg env2 U U')
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        | _ =>
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          let val (env3, V) = mk_tvar (env2, [])
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          in (t' $ u', V, vTs2, unifyT sg env3 T (U --> V)) end)
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      end
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  | infer_type sg env Ts vTs (t as Bound i) = (t, List.nth (Ts, i), vTs, env);
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fun cantunify sg (t, u) = error ("Non-unifiable terms:\n" ^
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  Sign.string_of_term sg t ^ "\n\n" ^ Sign.string_of_term sg u);
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fun decompose sg Ts (env, p as (t, u)) =
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  let fun rigrig (a, T) (b, U) uT ts us = if a <> b then cantunify sg p
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    else apsnd List.concat (foldl_map (decompose sg Ts) (uT env T U, ts ~~ us))
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  in case pairself (strip_comb o Envir.head_norm env) p of
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      ((Const c, ts), (Const d, us)) => rigrig c d (unifyT sg) ts us
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    | ((Free c, ts), (Free d, us)) => rigrig c d (unifyT sg) ts us
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    | ((Bound i, ts), (Bound j, us)) =>
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        rigrig (i, dummyT) (j, dummyT) (K o K) ts us
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    | ((Abs (_, T, t), []), (Abs (_, U, u), [])) =>
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        decompose sg (T::Ts) (unifyT sg env T U, (t, u))
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    | ((Abs (_, T, t), []), _) =>
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        decompose sg (T::Ts) (env, (t, incr_boundvars 1 u $ Bound 0))
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    | (_, (Abs (_, T, u), [])) =>
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        decompose sg (T::Ts) (env, (incr_boundvars 1 t $ Bound 0, u))
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    | _ => (env, [(mk_abs Ts t, mk_abs Ts u)])
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  end;
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fun make_constraints_cprf sg env cprf =
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  let
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    fun add_cnstrt Ts prop prf cs env vTs (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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      in
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        (prop, prf, cs, Pattern.unify (sg, env, [(t', u')]), vTs)
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        handle Pattern.Pattern =>
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            let val (env', cs') = decompose sg [] (env, (t', u'))
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            in (prop, prf, cs @ cs', env', vTs) end
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        | Pattern.Unif =>
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            cantunify sg (Envir.norm_term env t', Envir.norm_term env u')
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      end;
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    fun mk_cnstrts_atom env vTs prop opTs prf =
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          let
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            val tvars = term_tvars prop;
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            val tfrees = term_tfrees prop;
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            val (prop', fmap) = Type.varify (prop, []);
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            val (env', Ts) = (case opTs of
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                NONE => foldl_map mk_tvar (env, map snd tvars @ map snd tfrees)
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              | SOME Ts => (env, Ts));
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            val prop'' = subst_TVars (map fst tvars @ map snd fmap ~~ Ts)
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              (forall_intr_vfs prop') handle UnequalLengths =>
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                error ("Wrong number of type arguments for " ^
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                  quote (fst (get_name_tags [] prop prf)))
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          in (prop'', change_type (SOME Ts) prf, [], env', vTs) end;
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    fun head_norm (prop, prf, cnstrts, env, vTs) =
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      (Envir.head_norm env prop, prf, cnstrts, env, vTs);
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    fun mk_cnstrts env _ Hs vTs (PBound i) = (List.nth (Hs, i), PBound i, [], env, vTs)
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      | mk_cnstrts env Ts Hs vTs (Abst (s, opT, cprf)) =
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          let
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            val (env', T) = (case opT of
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              NONE => mk_tvar (env, []) | SOME T => (env, T));
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            val (t, prf, cnstrts, env'', vTs') =
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              mk_cnstrts env' (T::Ts) (map (incr_boundvars 1) Hs) vTs 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'', vTs')
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          end
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      | mk_cnstrts env Ts Hs vTs (AbsP (s, SOME t, cprf)) =
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          let
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            val (t', _, vTs', env') = infer_type sg env Ts vTs t;
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            val (u, prf, cnstrts, env'', vTs'') = mk_cnstrts env' Ts (t'::Hs) vTs' cprf;
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          in (Logic.mk_implies (t', u), AbsP (s, SOME t', prf), cnstrts, env'', vTs'')
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          end
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      | mk_cnstrts env Ts Hs vTs (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'', vTs') = mk_cnstrts env' Ts (t::Hs) vTs cprf;
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          in (Logic.mk_implies (t, u), AbsP (s, SOME t, prf), cnstrts, env'', vTs')
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          end
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      | mk_cnstrts env Ts Hs vTs (cprf1 %% cprf2) =
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          let val (u, prf2, cnstrts, env', vTs') = mk_cnstrts env Ts Hs vTs cprf2
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          in (case head_norm (mk_cnstrts env' Ts Hs vTs' cprf1) of
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              (Const ("==>", _) $ u' $ t', prf1, cnstrts', env'', vTs'') =>
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                add_cnstrt Ts t' (prf1 %% prf2) (cnstrts' @ cnstrts)
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                  env'' vTs'' (u, u')
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            | (t, prf1, cnstrts', env'', vTs'') =>
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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''' vTs'' (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 vTs (cprf % SOME t) =
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          let val (t', U, vTs1, env1) = infer_type sg env Ts vTs t
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          in (case head_norm (mk_cnstrts env1 Ts Hs vTs1 cprf) of
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             (Const ("all", Type ("fun", [Type ("fun", [T, _]), _])) $ f,
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                 prf, cnstrts, env2, vTs2) =>
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               let val env3 = unifyT sg env2 T U
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               in (betapply (f, t'), prf % SOME t', cnstrts, env3, vTs2)
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               end
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           | (u, prf, cnstrts, env2, vTs2) =>
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               let val (env3, v) = mk_var env2 Ts (U --> propT);
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               in
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                 add_cnstrt Ts (v $ t') (prf % SOME t') cnstrts env3 vTs2
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                   (u, Const ("all", (U --> propT) --> propT) $ v)
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               end)
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          end
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      | mk_cnstrts env Ts Hs vTs (cprf % NONE) =
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          (case head_norm (mk_cnstrts env Ts Hs vTs cprf) of
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             (Const ("all", Type ("fun", [Type ("fun", [T, _]), _])) $ f,
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                 prf, cnstrts, env', vTs') =>
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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'', vTs')
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               end
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           | (u, prf, cnstrts, env', vTs') =>
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               let
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                 val (env1, T) = mk_tvar (env', []);
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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 vTs'
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                   (u, Const ("all", (T --> propT) --> propT) $ v)
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               end)
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      | mk_cnstrts env _ _ vTs (prf as PThm (_, _, prop, opTs)) =
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          mk_cnstrts_atom env vTs prop opTs prf
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      | mk_cnstrts env _ _ vTs (prf as PAxm (_, prop, opTs)) =
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          mk_cnstrts_atom env vTs prop opTs prf
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      | mk_cnstrts env _ _ vTs (prf as Oracle (_, prop, opTs)) =
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          mk_cnstrts_atom env vTs prop opTs prf
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      | mk_cnstrts env _ _ vTs (Hyp t) = (t, Hyp t, [], env, vTs)
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      | mk_cnstrts _ _ _ _ _ = error "reconstruct_proof: minimal proof object"
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  in mk_cnstrts env [] [] Symtab.empty cprf end;
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fun add_term_ixns (is, t) = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I) t is;
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(**** update list of free variables of constraints ****)
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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 o snd))
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      (Vartab.foldl (add_term_ixns o apsnd (snd o 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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(**** solution of constraints ****)
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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 [] = error ("Unsolvable constraints:\n" ^
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              Pretty.string_of (Pretty.chunks (map (fn (_, p, _) =>
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                Display.pretty_flexpair (Sign.pp sg) (pairself
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                  (Envir.norm_term bigenv) p)) cs)))
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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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berghofe@11522
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berghofe@13669
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(**** reconstruction of proofs ****)
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berghofe@11613
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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 constraints...";
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    val (t, prf, cs, env, _) = make_constraints_cprf sg
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      (Envir.empty (maxidx_of_proof cprf)) 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 prop_of_atom prop Ts =
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  let val (prop', fmap) = Type.varify (prop, []);
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  in subst_TVars (map fst (term_tvars prop) @ map snd fmap ~~ Ts)
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    (forall_intr_vfs prop')
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  end;
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val head_norm = Envir.head_norm (Envir.empty 0);
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skalberg@15570
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fun prop_of0 Hs (PBound i) = List.nth (Hs, i)
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  | prop_of0 Hs (Abst (s, SOME T, prf)) =
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      all T $ (Abs (s, T, prop_of0 Hs prf))
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  | prop_of0 Hs (AbsP (s, SOME t, prf)) =
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      Logic.mk_implies (t, prop_of0 (t :: Hs) prf)
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  | prop_of0 Hs (prf % SOME t) = (case head_norm (prop_of0 Hs prf) of
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      Const ("all", _) $ f => f $ t
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    | _ => error "prop_of: all expected")
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  | prop_of0 Hs (prf1 %% prf2) = (case head_norm (prop_of0 Hs prf1) of
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      Const ("==>", _) $ P $ Q => Q
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    | _ => error "prop_of: ==> expected")
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  | prop_of0 Hs (Hyp t) = t
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  | prop_of0 Hs (PThm (_, _, prop, SOME Ts)) = prop_of_atom prop Ts
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  | prop_of0 Hs (PAxm (_, prop, SOME Ts)) = prop_of_atom prop Ts
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  | prop_of0 Hs (Oracle (_, prop, SOME Ts)) = prop_of_atom prop Ts
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  | prop_of0 _ _ = error "prop_of: partial proof object";
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val prop_of' = Pattern.eta_contract oo (Envir.beta_norm oo prop_of0);
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val prop_of = prop_of' [];
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berghofe@11522
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berghofe@13669
   333
(**** expand and reconstruct subproofs ****)
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berghofe@13342
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fun expand_proof sg thms prf =
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  let
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    fun expand maxidx prfs (AbsP (s, t, prf)) = 
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          let val (maxidx', prfs', prf') = expand maxidx prfs prf
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          in (maxidx', prfs', AbsP (s, t, prf')) end
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   340
      | expand maxidx prfs (Abst (s, T, prf)) = 
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          let val (maxidx', prfs', prf') = expand maxidx prfs prf
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          in (maxidx', prfs', Abst (s, T, prf')) end
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   343
      | expand maxidx prfs (prf1 %% prf2) =
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          let
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            val (maxidx', prfs', prf1') = expand maxidx prfs prf1;
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            val (maxidx'', prfs'', prf2') = expand maxidx' prfs' prf2;
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          in (maxidx'', prfs'', prf1' %% prf2') end
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   348
      | expand maxidx prfs (prf % t) =
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          let val (maxidx', prfs', prf') = expand maxidx prfs prf
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          in (maxidx', prfs', prf' % t) end
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      | expand maxidx prfs (prf as PThm ((a, _), cprf, prop, SOME Ts)) =
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          if not (exists
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   353
            (fn (b, NONE) => a = b
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              | (b, SOME prop') => a = b andalso prop = prop') thms)
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   355
          then (maxidx, prfs, prf) else
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   356
          let
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   357
            fun inc i =
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   358
              map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i);
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   359
            val (maxidx', prf, prfs') =
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   360
              (case gen_assoc (op =) (prfs, (a, prop)) of
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   361
                NONE =>
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   362
                  let
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   363
                    val _ = message ("Reconstructing proof of " ^ a);
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   364
                    val _ = message (Sign.string_of_term sg prop);
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   365
                    val prf' = forall_intr_vfs_prf prop
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   366
                      (reconstruct_proof sg prop cprf);
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   367
                    val (maxidx', prfs', prf) = expand
berghofe@12870
   368
                      (maxidx_of_proof prf') prfs prf'
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   369
                  in (maxidx' + maxidx + 1, inc (maxidx + 1) prf,
berghofe@13610
   370
                    ((a, prop), (maxidx', prf)) :: prfs')
berghofe@13610
   371
                  end
skalberg@15531
   372
              | SOME (maxidx', prf) => (maxidx' + maxidx + 1,
berghofe@13669
   373
                  inc (maxidx + 1) prf, prfs));
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   374
            val tfrees = term_tfrees prop;
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   375
            val tye = map (fn ((s, j), _) => (s, maxidx + 1 + j))
berghofe@13669
   376
              (term_tvars prop) @ map (rpair ~1 o fst) tfrees ~~ Ts;
berghofe@13669
   377
            val varify = map_type_tfree (fn p as (a, S) =>
berghofe@13669
   378
              if p mem tfrees then TVar ((a, ~1), S) else TFree p)
berghofe@11522
   379
          in
berghofe@13669
   380
            (maxidx', prfs', map_proof_terms (subst_TVars tye o
berghofe@13669
   381
               map_term_types varify) (typ_subst_TVars tye o varify) prf)
berghofe@11522
   382
          end
berghofe@12870
   383
      | expand maxidx prfs prf = (maxidx, prfs, prf);
berghofe@11522
   384
berghofe@12870
   385
  in #3 (expand (maxidx_of_proof prf) [] prf) end;
berghofe@11522
   386
berghofe@11522
   387
end;