reorganize

29 files changed, 105 insertions, 2005 deletions

diff --git a/.gitignore b/.gitignore
index 160465a..fb8160e 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,3 +1,5 @@
 *~
 \#*.thy#
 \#*.ML#
+Test.thy
+
diff --git a/ROOT b/ROOT
index cc0badd..00d020a 100644
--- a/ROOT
+++ b/ROOT
@@ -1,18 +1,16 @@
 session Spartan_Core in "spartan/core" = Pure +
-  description "
-    Spartan type theory: a minimal dependent type theory based on intensional
+  description
+    "Spartan type theory: a minimal dependent type theory based on intensional
     Martin-Löf type theory with cumulative Russell-style universes, Pi types and
-    Sigma types. This session consists only of the very core theory files.
-  "
+    Sigma types."
   sessions
     "HOL-Eisbach"
   theories
     Spartan (global)
 
 session Spartan in spartan = Spartan_Core +
-  description "
-    Type theory based on Spartan, but with a few more bells and whistles.
-  "
+  description
+    "Dependent type theory based on Spartan."
   directories
     lib
   theories
@@ -21,15 +19,16 @@ session Spartan in spartan = Spartan_Core +
     List
 
 session HoTT in hott = Spartan +
-  description "
-    Homotopy type theory, following the development in
+  description
+    "Homotopy type theory, following the development in
       The Univalent Foundations Program,
       Homotopy Type Theory: Univalent Foundations of Mathematics,
       Institute for Advanced Study, (2013).
-      Available online at https://homotopytypetheory.org/book.
-  "
+      Available online at https://homotopytypetheory.org/book."
   theories
     Identity
     Equivalence
     Nat
     More_List
+    More_Nat
+
diff --git a/hott/More_Nat.thy b/hott/More_Nat.thy
new file mode 100644
index 0000000..8177170
--- /dev/null
+++ b/hott/More_Nat.thy
@@ -0,0 +1,43 @@
+theory More_Nat
+imports Nat Spartan.More_Types
+
+begin
+
+section \<open>Equality on Nat\<close>
+
+text \<open>Via the encode-decode method.\<close>
+
+context begin
+
+Lemma (derive) eq: shows "Nat \<rightarrow> Nat \<rightarrow> U O"
+  apply intro focus vars m apply elim
+    \<comment> \<open>m \<equiv> 0\<close>
+    apply intro focus vars n apply elim
+      \<guillemotright> by (rule TopF) \<comment> \<open>n \<equiv> 0\<close>
+      \<guillemotright> by (rule BotF) \<comment> \<open>n \<equiv> suc _\<close>
+      \<guillemotright> by (rule U_in_U)
+    done
+    \<comment> \<open>m \<equiv> suc k\<close>
+    apply intro focus vars k k_eq n apply (elim n)
+      \<guillemotright> by (rule BotF) \<comment> \<open>n \<equiv> 0\<close>
+      \<guillemotright> prems vars l proof - show "k_eq l: U O" by typechk qed
+      \<guillemotright> by (rule U_in_U)
+    done
+    by (rule U_in_U)
+  done
+
+text \<open>
+\<^term>\<open>eq\<close> is defined by
+  eq 0 0 \<equiv> \<top>
+  eq 0 (suc k) \<equiv> \<bottom>
+  eq (suc k) 0 \<equiv> \<bottom>
+  eq (suc k) (suc l) \<equiv> eq k l
+\<close>
+
+
+
+
+end
+
+
+end
diff --git a/spartan/core/Spartan.thy b/spartan/core/Spartan.thy
index 55eb657..0a5fe4c 100644
--- a/spartan/core/Spartan.thy
+++ b/spartan/core/Spartan.thy
@@ -69,10 +69,13 @@ axiomatization
   app :: \<open>o \<Rightarrow> o \<Rightarrow> o\<close> ("(1_ `_)" [120, 121] 120)
 
 syntax
-  "_Pi"   :: \<open>idt \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close> ("(2\<Prod>_: _./ _)" 30)
-  "_lam"  :: \<open>pttrns \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close> ("(2\<lambda>_: _./ _)" 30)
-  "_lam2" :: \<open>pttrns \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close>
+  "_Pi"   :: \<open>idts \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close> ("(2\<Prod>_: _./ _)" 30)
+  "_Pi2"  :: \<open>idts \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close>
+  "_lam"  :: \<open>idts \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close> ("(2\<lambda>_: _./ _)" 30)
+  "_lam2" :: \<open>idts \<Rightarrow> o \<Rightarrow> o \<Rightarrow> o\<close>
 translations
+  "\<Prod>x xs: A. B" \<rightharpoonup> "CONST Pi A (\<lambda>x. _Pi2 xs A B)"
+  "_Pi2 x A B" \<rightharpoonup> "\<Prod>x: A. B"
   "\<Prod>x: A. B"    \<rightleftharpoons> "CONST Pi A (\<lambda>x. B)"
   "\<lambda>x xs: A. b" \<rightharpoonup> "CONST lam A (\<lambda>x. _lam2 xs A b)"
   "_lam2 x A b" \<rightharpoonup> "\<lambda>x: A. b"
@@ -151,23 +154,23 @@ section \<open>Proof commands\<close>
 
 named_theorems typechk
 
-ML_file \<open>lib/lib.ML\<close>
-ML_file \<open>lib/goals.ML\<close>
-ML_file \<open>lib/focus.ML\<close>
-ML_file \<open>lib/types.ML\<close>
+ML_file \<open>lib.ML\<close>
+ML_file \<open>goals.ML\<close>
+ML_file \<open>focus.ML\<close>
+ML_file \<open>types.ML\<close>
 
 
 section \<open>Congruence automation\<close>
 
 consts "rhs" :: \<open>'a\<close> ("..")
 
-ML_file \<open>lib/congruence.ML\<close>
+ML_file \<open>congruence.ML\<close>
 
 
 section \<open>Methods\<close>
 
-ML_file \<open>lib/elimination.ML\<close> \<comment> \<open>elimination rules\<close>
-ML_file \<open>lib/cases.ML\<close> \<comment> \<open>case reasoning rules\<close>
+ML_file \<open>elimination.ML\<close> \<comment> \<open>elimination rules\<close>
+ML_file \<open>cases.ML\<close> \<comment> \<open>case reasoning rules\<close>
 
 named_theorems intros and comps
 lemmas
@@ -177,7 +180,7 @@ lemmas
   [comps] = beta Sig_comp and
   [cong] = Pi_cong lam_cong Sig_cong
 
-ML_file \<open>lib/tactics.ML\<close>
+ML_file \<open>tactics.ML\<close>
 
 method_setup assumptions =
   \<open>Scan.succeed (fn ctxt => SIMPLE_METHOD (
@@ -238,7 +241,7 @@ ML_file \<open>~~/src/Tools/misc_legacy.ML\<close>
 ML_file \<open>~~/src/Tools/IsaPlanner/isand.ML\<close>
 ML_file \<open>~~/src/Tools/IsaPlanner/rw_inst.ML\<close>
 ML_file \<open>~~/src/Tools/IsaPlanner/zipper.ML\<close>
-ML_file \<open>lib/eqsubst.ML\<close>
+ML_file \<open>eqsubst.ML\<close>
 
 \<comment> \<open>\<open>rewrite\<close> method\<close>
 consts rewrite_HOLE :: "'a::{}"  ("\<hole>")
@@ -265,7 +268,7 @@ lemma imp_cong_eq:
   done
 
 ML_file \<open>~~/src/HOL/Library/cconv.ML\<close>
-ML_file \<open>lib/rewrite.ML\<close>
+ML_file \<open>rewrite.ML\<close>
 
 \<comment> \<open>\<open>reduce\<close> computes terms via judgmental equalities\<close>
 setup \<open>map_theory_simpset (fn ctxt => ctxt addSolver (mk_solver "" typechk_tac))\<close>
@@ -284,7 +287,7 @@ consts
   iarg :: \<open>'a\<close> ("?")
   hole :: \<open>'b\<close> ("{}")
 
-ML_file \<open>lib/implicits.ML\<close>
+ML_file \<open>implicits.ML\<close>
 
 attribute_setup implicit = \<open>Scan.succeed Implicits.implicit_defs_attr\<close>
 
diff --git a/spartan/core/lib/cases.ML b/spartan/core/cases.ML
index 560a9f1..560a9f1 100644
--- a/spartan/core/lib/cases.ML
+++ b/spartan/core/cases.ML
diff --git a/spartan/core/lib/congruence.ML b/spartan/core/congruence.ML
index d9f4ffa..d9f4ffa 100644
--- a/spartan/core/lib/congruence.ML
+++ b/spartan/core/congruence.ML
diff --git a/spartan/core/lib/elimination.ML b/spartan/core/elimination.ML
index 617f83e..11b3af9 100644
--- a/spartan/core/lib/elimination.ML
+++ b/spartan/core/elimination.ML
@@ -6,6 +6,7 @@ Type elimination setup.
 
 structure Elim: sig
 
+val Rules: Proof.context -> (thm * indexname list) Termtab.table
 val rules: Proof.context -> (thm * indexname list) list
 val lookup_rule: Proof.context -> Termtab.key -> (thm * indexname list) option
 val register_rule: term list -> thm -> Context.generic -> Context.generic
@@ -25,8 +26,9 @@ structure Rules = Generic_Data (
   val merge = Termtab.merge (eq_fst Thm.eq_thm_prop)
 )
 
-fun rules ctxt = map (op #2) (Termtab.dest (Rules.get (Context.Proof ctxt)))
-fun lookup_rule ctxt = Termtab.lookup (Rules.get (Context.Proof ctxt))
+val Rules = Rules.get o Context.Proof
+fun rules ctxt = map (op #2) (Termtab.dest (Rules ctxt))
+fun lookup_rule ctxt = Termtab.lookup (Rules ctxt)
 fun register_rule tms rl =
   let val hd = Term.head_of (Lib.type_of_typing (Thm.major_prem_of rl))
   in Rules.map (Termtab.update (hd, (rl, map (#1 o dest_Var) tms))) end
diff --git a/spartan/core/lib/eqsubst.ML b/spartan/core/eqsubst.ML
index ea6f098..ea6f098 100644
--- a/spartan/core/lib/eqsubst.ML
+++ b/spartan/core/eqsubst.ML
diff --git a/spartan/core/lib/equality.ML b/spartan/core/equality.ML
index 023147b..023147b 100644
--- a/spartan/core/lib/equality.ML
+++ b/spartan/core/equality.ML
diff --git a/spartan/core/lib/focus.ML b/spartan/core/focus.ML
index 1d8de78..1d8de78 100644
--- a/spartan/core/lib/focus.ML
+++ b/spartan/core/focus.ML
diff --git a/spartan/core/lib/goals.ML b/spartan/core/goals.ML
index 9f394f0..9f394f0 100644
--- a/spartan/core/lib/goals.ML
+++ b/spartan/core/goals.ML
diff --git a/spartan/core/lib/implicits.ML b/spartan/core/implicits.ML
index 4d73c8d..4d73c8d 100644
--- a/spartan/core/lib/implicits.ML
+++ b/spartan/core/implicits.ML
diff --git a/spartan/core/lib/lib.ML b/spartan/core/lib.ML
index 615f601..615f601 100644
--- a/spartan/core/lib/lib.ML
+++ b/spartan/core/lib.ML
diff --git a/spartan/core/lib/tactics.ML b/spartan/core/lib/tactics.ML
deleted file mode 100644
index 172ae90..0000000
--- a/spartan/core/lib/tactics.ML
+++ /dev/null
@@ -1,221 +0,0 @@
-(*  Title:      tactics.ML
-    Author:     Joshua Chen
-
-General tactics for dependent type theory.
-*)
-
-structure Tactics:
-sig
-
-val assumptions_tac: Proof.context -> int -> tactic
-val known_tac: Proof.context -> int -> tactic
-val typechk_tac: Proof.context -> int -> tactic
-val auto_typechk: bool Config.T
-val SIDE_CONDS: (int -> tactic) -> Proof.context -> int -> tactic
-val rule_tac: thm list -> Proof.context -> int -> tactic
-val dest_tac: int option -> thm list -> Proof.context -> int -> tactic
-val intro_tac: Proof.context -> int -> tactic
-val intros_tac: Proof.context -> int -> tactic
-val elim_context_tac: term list -> Proof.context -> int -> context_tactic
-val cases_tac: term -> Proof.context -> int -> tactic
-
-end = struct
-
-(*An assumption tactic that only solves typing goals with rigid terms and
-  judgmental equalities without schematic variables*)
-fun assumptions_tac ctxt = SUBGOAL (fn (goal, i) =>
-  let
-    val concl = Logic.strip_assums_concl goal
-  in
-    if
-      Lib.is_typing concl andalso Lib.is_rigid (Lib.term_of_typing concl)
-      orelse not ((exists_subterm is_Var) concl)
-    then assume_tac ctxt i
-    else no_tac
-  end)
-
-(*Solves typing goals with rigid term by resolving with context facts and
-  simplifier premises, or arbitrary goals by *non-unifying* assumption*)
-fun known_tac ctxt = SUBGOAL (fn (goal, i) =>
-  let
-    val concl = Logic.strip_assums_concl goal
-  in
-    ((if Lib.is_typing concl andalso Lib.is_rigid (Lib.term_of_typing concl)
-      then
-        let val ths = map fst (Facts.props (Proof_Context.facts_of ctxt))
-        in resolve_tac ctxt (ths @ Simplifier.prems_of ctxt) end
-      else K no_tac)
-    ORELSE' assumptions_tac ctxt) i
-  end)
-
-(*Typechecking: try to solve goals of the form "a: A" where a is rigid*)
-fun typechk_tac ctxt =
-  let
-    val tac = SUBGOAL (fn (goal, i) =>
-      if Lib.rigid_typing_concl goal
-      then
-        let val net = Tactic.build_net
-          ((Named_Theorems.get ctxt \<^named_theorems>\<open>typechk\<close>)
-          @(Named_Theorems.get ctxt \<^named_theorems>\<open>intros\<close>)
-          @(map #1 (Elim.rules ctxt)))
-        in (resolve_from_net_tac ctxt net) i end
-      else no_tac)
-  in
-    REPEAT_ALL_NEW (known_tac ctxt ORELSE' tac)
-  end
-
-(*Many methods try to automatically discharge side conditions by typechecking.
-  Switch this flag off to discharge by non-unifying assumption instead.*)
-val auto_typechk = Attrib.setup_config_bool \<^binding>\<open>auto_typechk\<close> (K true)
-
-fun side_cond_tac ctxt = CHANGED o REPEAT o
-  (if Config.get ctxt auto_typechk then typechk_tac ctxt else known_tac ctxt)
-
-(*Combinator runs tactic and tries to discharge all new typing side conditions*)
-fun SIDE_CONDS tac ctxt = tac THEN_ALL_NEW (TRY o side_cond_tac ctxt)
-
-local
-fun mk_rules _ ths [] = ths
-  | mk_rules n ths ths' =
-      let val ths'' = foldr1 (op @)
-        (map (fn th => [rotate_prems n (th RS @{thm PiE})] handle THM _ => []) ths')
-      in
-        mk_rules n (ths @ ths') ths''
-      end
-in
-
-(*Resolves with given rules, discharging as many side conditions as possible*)
-fun rule_tac ths ctxt = resolve_tac ctxt (mk_rules 0 [] ths)
-
-(*Attempts destruct-resolution with the n-th premise of the given rules*)
-fun dest_tac opt_n ths ctxt = dresolve_tac ctxt
-  (mk_rules (case opt_n of NONE => 0 | SOME 0 => 0 | SOME n => n-1) [] ths)
-
-end
-
-(*Applies some introduction rule*)
-fun intro_tac ctxt = SUBGOAL (fn (_, i) => SIDE_CONDS
-  (resolve_tac ctxt (Named_Theorems.get ctxt \<^named_theorems>\<open>intros\<close>)) ctxt i)
-
-fun intros_tac ctxt = SUBGOAL (fn (_, i) =>
-  (CHANGED o REPEAT o CHANGED o intro_tac ctxt) i)
-
-(* Induction/elimination *)
-
-(*Pushes a context/goal premise typing t:T into a \<Prod>-type*)
-fun internalize_fact_tac t =
-  Subgoal.FOCUS_PARAMS (fn {context = ctxt, concl = raw_concl, ...} =>
-    let
-      val concl = Logic.strip_assums_concl (Thm.term_of raw_concl)
-      val C = Lib.type_of_typing concl
-      val B = Thm.cterm_of ctxt (Lib.lambda_var t C)
-      val a = Thm.cterm_of ctxt t
-      (*The resolvent is PiE[where ?B=B and ?a=a]*)
-      val resolvent =
-        Drule.infer_instantiate' ctxt [NONE, NONE, SOME B, SOME a] @{thm PiE}
-    in
-      HEADGOAL (resolve_tac ctxt [resolvent])
-      (*known_tac infers the correct type T inferred by unification*)
-      THEN SOMEGOAL (known_tac ctxt)
-    end)
-
-(*Premises that have already been pushed into the \<Prod>-type*)
-structure Inserts = Proof_Data (
-  type T = term Item_Net.T
-  val init = K (Item_Net.init Term.aconv_untyped single)
-)
-
-local
-
-fun elim_core_tac tms types ctxt = SUBGOAL (K (
-  let
-    val rule_insts = map ((Elim.lookup_rule ctxt) o Term.head_of) types
-    val rules = flat (map
-      (fn rule_inst => case rule_inst of
-          NONE => []
-        | SOME (rl, idxnames) => [Drule.infer_instantiate ctxt
-          (idxnames ~~ map (Thm.cterm_of ctxt) tms) rl])
-      rule_insts)
-  in
-    HEADGOAL (resolve_tac ctxt rules)
-    THEN RANGE (replicate (length tms) (typechk_tac ctxt)) 1
-  end handle Option => no_tac))
-
-in
-
-fun elim_context_tac tms ctxt = case tms of
-    [] => CONTEXT_SUBGOAL (K (Context_Tactic.CONTEXT_TACTIC (HEADGOAL (
-      SIDE_CONDS (eresolve_tac ctxt (map #1 (Elim.rules ctxt))) ctxt))))
-  | major::_  => CONTEXT_SUBGOAL (fn (goal, _) =>
-    let
-      val facts = Proof_Context.facts_of ctxt
-      val prems = Logic.strip_assums_hyp goal
-      val template = Lib.typing_of_term major
-      val types =
-        map (Thm.prop_of o #1) (Facts.could_unify facts template)
-        @ filter (fn prem => Term.could_unify (template, prem)) prems
-        |> map Lib.type_of_typing
-    in case types of
-        [] => Context_Tactic.CONTEXT_TACTIC no_tac
-      | _ =>
-        let
-          val inserts = map (Thm.prop_of o fst) (Facts.props facts) @ prems
-            |> filter Lib.is_typing
-            |> map Lib.dest_typing
-            |> filter_out (fn (t, _) =>
-              Term.aconv (t, major) orelse Item_Net.member (Inserts.get ctxt) t)
-            |> map (fn (t, T) => ((t, T), Lib.subterm_count_distinct tms T))
-            |> filter (fn (_, i) => i > 0)
-            (*`t1: T1` comes before `t2: T2` if T1 contains t2 as subterm.
-              If they are incomparable, then order by decreasing
-              `subterm_count [p, x, y] T`*)
-            |> sort (fn (((t1, _), i), ((_, T2), j)) =>
-                Lib.cond_order (Lib.subterm_order T2 t1) (int_ord (j, i)))
-            |> map (#1 o #1)
-          val record_inserts = Inserts.map (fold Item_Net.update inserts)
-          val tac =
-            (*Push premises having a subterm in `tms` into a \<Prod>*)
-            fold (fn t => fn tac =>
-              tac THEN HEADGOAL (internalize_fact_tac t ctxt))
-              inserts all_tac
-            (*Apply elimination rule*)
-            THEN (HEADGOAL (
-              elim_core_tac tms types ctxt
-              (*Pull pushed premises back out*)
-              THEN_ALL_NEW (SUBGOAL (fn (_, i) =>
-                REPEAT_DETERM_N (length inserts)
-                  (resolve_tac ctxt @{thms PiI} i)))
-            ))
-            (*Side conditions*)
-            THEN ALLGOALS (TRY o side_cond_tac ctxt)
-        in
-          fn (ctxt, st) => Context_Tactic.TACTIC_CONTEXT
-            (record_inserts ctxt) (tac st)
-        end
-    end)
-
-fun cases_tac tm ctxt = SUBGOAL (fn (goal, i) =>
-  let
-    val facts = Proof_Context.facts_of ctxt
-    val prems = Logic.strip_assums_hyp goal
-    val template = Lib.typing_of_term tm
-    val types =
-      map (Thm.prop_of o #1) (Facts.could_unify facts template)
-      @ filter (fn prem => Term.could_unify (template, prem)) prems
-      |> map Lib.type_of_typing
-    val res = (case types of
-        [typ] => Drule.infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt tm)]
-          (the (Case.lookup_rule ctxt (Term.head_of typ)))
-      | [] => raise Option
-      | _ => raise error (Syntax.string_of_term ctxt tm ^ "not uniquely typed"))
-      handle Option => error ("no case rule known for "
-        ^ (Syntax.string_of_term ctxt tm))
-  in
-    SIDE_CONDS (resolve_tac ctxt [res]) ctxt i
-  end)
-
-end
-
-end
-
-open Tactics
diff --git a/spartan/core/lib/types.ML b/spartan/core/lib/types.ML
deleted file mode 100644
index b0792fe..0000000
--- a/spartan/core/lib/types.ML
+++ /dev/null
@@ -1,18 +0,0 @@
-structure Types
-= struct
-
-structure Data = Generic_Data (
-  type T = thm Item_Net.T
-  val empty = Item_Net.init Thm.eq_thm
-    (single o Lib.term_of_typing o Thm.prop_of)
-  val extend = I
-  val merge = Item_Net.merge
-)
-
-fun put_type typing = Context.proof_map (Data.map (Item_Net.update typing))
-fun put_types typings = foldr1 (op o) (map put_type typings)
-
-fun get_types ctxt tm = Item_Net.retrieve (Data.get (Context.Proof ctxt)) tm
-
-
-end
diff --git a/spartan/core/ml/cases.ML b/spartan/core/ml/cases.ML
deleted file mode 100644
index 560a9f1..0000000
--- a/spartan/core/ml/cases.ML
+++ /dev/null
@@ -1,42 +0,0 @@
-(*  Title:      cases.ML
-    Author:     Joshua Chen
-
-Case reasoning.
-*)
-
-structure Case: sig
-
-val rules: Proof.context -> thm list
-val lookup_rule: Proof.context -> Termtab.key -> thm option
-val register_rule: thm -> Context.generic -> Context.generic
-
-end = struct
-
-(* Context data *)
-
-(*Stores elimination rules together with a list of the indexnames of the
-  variables each rule eliminates. Keyed by head of the type being eliminated.*)
-structure Rules = Generic_Data (
-  type T = thm Termtab.table
-  val empty = Termtab.empty
-  val extend = I
-  val merge = Termtab.merge Thm.eq_thm_prop
-)
-
-val rules = map #2 o Termtab.dest o Rules.get o Context.Proof
-fun lookup_rule ctxt = Termtab.lookup (Rules.get (Context.Proof ctxt))
-fun register_rule rl =
-  let val hd = Term.head_of (Lib.type_of_typing (Thm.major_prem_of rl))
-  in Rules.map (Termtab.update (hd, rl)) end
-
-
-(* [cases] attribute *)
-val _ = Theory.setup (
-  Attrib.setup \<^binding>\<open>cases\<close>
-    (Scan.succeed (Thm.declaration_attribute register_rule))
-    ""
-  #> Global_Theory.add_thms_dynamic (\<^binding>\<open>cases\<close>, rules o Context.proof_of)
-)
-
-
-end
diff --git a/spartan/core/ml/congruence.ML b/spartan/core/ml/congruence.ML
deleted file mode 100644
index d9f4ffa..0000000
--- a/spartan/core/ml/congruence.ML
+++ /dev/null
@@ -1,82 +0,0 @@
-structure Congruence = struct
-
-(* Congruence context data *)
-
-structure RHS = Generic_Data (
-  type T = (term * indexname) Termtab.table
-  val empty = Termtab.empty
-  val extend = I
-  val merge = Termtab.merge (Term.aconv o apply2 #1)
-)
-
-fun register_rhs t var =
-  let
-    val key = Term.head_of t
-    val idxname = #1 (dest_Var var)
-  in
-    RHS.map (Termtab.update (key, (t, idxname)))
-  end
-
-fun lookup_congruence ctxt t =
-  Termtab.lookup (RHS.get (Context.Proof ctxt)) (Term.head_of t)
-
-
-(* Congruence declarations *)
-
-local val Frees_to_Vars =
-  map_aterms (fn tm =>
-    case tm of
-      Free (name, T) => Var (("*!"^name, 0), T) (*Hacky naming!*)
-    | _ => tm)
-in
-
-(*Declare the "right-hand side" of types that are congruences.
-  Does not handle bound variables, so no dependent RHS in declarations!*)
-val _ = Outer_Syntax.local_theory \<^command_keyword>\<open>congruence\<close>
-  "declare right hand side of congruence"
-  (Parse.term -- (\<^keyword>\<open>rhs\<close> |-- Parse.term) >>
-    (fn (t_str, rhs_str) => fn lthy =>
-    let
-      val (t, rhs) = apply2 (Frees_to_Vars o Syntax.read_term lthy)
-        (t_str, rhs_str)
-    in lthy |>
-      Local_Theory.background_theory (
-        Context.theory_map (register_rhs t rhs))
-    end))
-
-end
-
-
-(* Calculational reasoning: ".." setup *)
-
-fun last_rhs ctxt = map_aterms (fn t =>
-  case t of
-    Const (\<^const_name>\<open>rhs\<close>, _) =>
-      let
-        val this_name = Name_Space.full_name (Proof_Context.naming_of ctxt)
-          (Binding.name Auto_Bind.thisN)
-        val this = #thms (the (Proof_Context.lookup_fact ctxt this_name))
-          handle Option => []
-        val rhs =
-          (case map Thm.prop_of this of
-            [prop] =>
-              (let
-                val typ = Lib.type_of_typing (Logic.strip_assums_concl prop)
-                val (cong_pttrn, varname) = the (lookup_congruence ctxt typ)
-                val unif_res = Pattern.unify (Context.Proof ctxt)
-                  (cong_pttrn, typ) Envir.init
-                val rhs = #2 (the
-                  (Vartab.lookup (Envir.term_env unif_res) varname))
-              in
-                rhs
-              end handle Option =>
-                error (".. can't match right-hand side of congruence"))
-          | _ => Term.dummy)
-      in rhs end
-  | _ => t)
-
-val _ = Context.>>
-  (Syntax_Phases.term_check 5 "" (fn ctxt => map (last_rhs ctxt)))
-
-
-end
diff --git a/spartan/core/ml/elimination.ML b/spartan/core/ml/elimination.ML
deleted file mode 100644
index 617f83e..0000000
--- a/spartan/core/ml/elimination.ML
+++ /dev/null
@@ -1,46 +0,0 @@
-(*  Title:      elimination.ML
-    Author:     Joshua Chen
-
-Type elimination setup.
-*)
-
-structure Elim: sig
-
-val rules: Proof.context -> (thm * indexname list) list
-val lookup_rule: Proof.context -> Termtab.key -> (thm * indexname list) option
-val register_rule: term list -> thm -> Context.generic -> Context.generic
-
-end = struct
-
-(** Context data **)
-
-(* Elimination rule data *)
-
-(*Stores elimination rules together with a list of the indexnames of the
-  variables each rule eliminates. Keyed by head of the type being eliminated.*)
-structure Rules = Generic_Data (
-  type T = (thm * indexname list) Termtab.table
-  val empty = Termtab.empty
-  val extend = I
-  val merge = Termtab.merge (eq_fst Thm.eq_thm_prop)
-)
-
-fun rules ctxt = map (op #2) (Termtab.dest (Rules.get (Context.Proof ctxt)))
-fun lookup_rule ctxt = Termtab.lookup (Rules.get (Context.Proof ctxt))
-fun register_rule tms rl =
-  let val hd = Term.head_of (Lib.type_of_typing (Thm.major_prem_of rl))
-  in Rules.map (Termtab.update (hd, (rl, map (#1 o dest_Var) tms))) end
-
-
-(* [elims] attribute *)
-val _ = Theory.setup (
-  Attrib.setup \<^binding>\<open>elims\<close>
-    (Scan.repeat Args.term_pattern >>
-      (Thm.declaration_attribute o register_rule))
-    ""
-  #> Global_Theory.add_thms_dynamic (\<^binding>\<open>elims\<close>,
-      fn context => (map #1 (rules (Context.proof_of context))))
-)
-
-
-end
diff --git a/spartan/core/ml/eqsubst.ML b/spartan/core/ml/eqsubst.ML
deleted file mode 100644
index ea6f098..0000000
--- a/spartan/core/ml/eqsubst.ML
+++ /dev/null
@@ -1,434 +0,0 @@
-(*  Title:      eqsubst.ML
-    Author:     Lucas Dixon, University of Edinburgh
-    Modified:   Joshua Chen, University of Innsbruck
-
-Perform a substitution using an equation.
-
-This code is slightly modified from the original at Tools/eqsubst..ML,
-to incorporate auto-typechecking for type theory.
-*)
-
-signature EQSUBST =
-sig
-  type match =
-    ((indexname * (sort * typ)) list (* type instantiations *)
-      * (indexname * (typ * term)) list) (* term instantiations *)
-    * (string * typ) list (* fake named type abs env *)
-    * (string * typ) list (* type abs env *)
-    * term (* outer term *)
-
-  type searchinfo =
-    Proof.context
-    * int (* maxidx *)
-    * Zipper.T (* focusterm to search under *)
-
-  datatype 'a skipseq = SkipMore of int | SkipSeq of 'a Seq.seq Seq.seq
-
-  val skip_first_asm_occs_search: ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> int -> 'b -> 'c skipseq
-  val skip_first_occs_search: int -> ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> 'b -> 'c Seq.seq
-  val skipto_skipseq: int -> 'a Seq.seq Seq.seq -> 'a skipseq
-
-  (* tactics *)
-  val eqsubst_asm_tac: Proof.context -> int list -> thm list -> int -> tactic
-  val eqsubst_asm_tac': Proof.context ->
-    (searchinfo -> int -> term -> match skipseq) -> int -> thm -> int -> tactic
-  val eqsubst_tac: Proof.context ->
-    int list -> (* list of occurrences to rewrite, use [0] for any *)
-    thm list -> int -> tactic
-  val eqsubst_tac': Proof.context ->
-    (searchinfo -> term -> match Seq.seq) (* search function *)
-    -> thm (* equation theorem to rewrite with *)
-    -> int (* subgoal number in goal theorem *)
-    -> thm (* goal theorem *)
-    -> thm Seq.seq (* rewritten goal theorem *)
-
-  (* search for substitutions *)
-  val valid_match_start: Zipper.T -> bool
-  val search_lr_all: Zipper.T -> Zipper.T Seq.seq
-  val search_lr_valid: (Zipper.T -> bool) -> Zipper.T -> Zipper.T Seq.seq
-  val searchf_lr_unify_all: searchinfo -> term -> match Seq.seq Seq.seq
-  val searchf_lr_unify_valid: searchinfo -> term -> match Seq.seq Seq.seq
-  val searchf_bt_unify_valid: searchinfo -> term -> match Seq.seq Seq.seq
-end;
-
-structure EqSubst: EQSUBST =
-struct
-
-(* changes object "=" to meta "==" which prepares a given rewrite rule *)
-fun prep_meta_eq ctxt =
-  Simplifier.mksimps ctxt #> map Drule.zero_var_indexes;
-
-(* make free vars into schematic vars with index zero *)
-fun unfix_frees frees =
-   fold (K (Thm.forall_elim_var 0)) frees o Drule.forall_intr_list frees;
-
-
-type match =
-  ((indexname * (sort * typ)) list (* type instantiations *)
-   * (indexname * (typ * term)) list) (* term instantiations *)
-  * (string * typ) list (* fake named type abs env *)
-  * (string * typ) list (* type abs env *)
-  * term; (* outer term *)
-
-type searchinfo =
-  Proof.context
-  * int (* maxidx *)
-  * Zipper.T; (* focusterm to search under *)
-
-
-(* skipping non-empty sub-sequences but when we reach the end
-   of the seq, remembering how much we have left to skip. *)
-datatype 'a skipseq =
-  SkipMore of int |
-  SkipSeq of 'a Seq.seq Seq.seq;
-
-(* given a seqseq, skip the first m non-empty seq's, note deficit *)
-fun skipto_skipseq m s =
-  let
-    fun skip_occs n sq =
-      (case Seq.pull sq of
-        NONE => SkipMore n
-      | SOME (h, t) =>
-        (case Seq.pull h of
-          NONE => skip_occs n t
-        | SOME _ => if n <= 1 then SkipSeq (Seq.cons h t) else skip_occs (n - 1) t))
-  in skip_occs m s end;
-
-(* note: outerterm is the taget with the match replaced by a bound
-   variable : ie: "P lhs" beocmes "%x. P x"
-   insts is the types of instantiations of vars in lhs
-   and typinsts is the type instantiations of types in the lhs
-   Note: Final rule is the rule lifted into the ontext of the
-   taget thm. *)
-fun mk_foo_match mkuptermfunc Ts t =
-  let
-    val ty = Term.type_of t
-    val bigtype = rev (map snd Ts) ---> ty
-    fun mk_foo 0 t = t
-      | mk_foo i t = mk_foo (i - 1) (t $ (Bound (i - 1)))
-    val num_of_bnds = length Ts
-    (* foo_term = "fooabs y0 ... yn" where y's are local bounds *)
-    val foo_term = mk_foo num_of_bnds (Bound num_of_bnds)
-  in Abs ("fooabs", bigtype, mkuptermfunc foo_term) end;
-
-(* T is outer bound vars, n is number of locally bound vars *)
-(* THINK: is order of Ts correct...? or reversed? *)
-fun mk_fake_bound_name n = ":b_" ^ n;
-fun fakefree_badbounds Ts t =
-  let val (FakeTs, Ts, newnames) =
-    fold_rev (fn (n, ty) => fn (FakeTs, Ts, usednames) =>
-      let
-        val newname = singleton (Name.variant_list usednames) n
-      in
-        ((mk_fake_bound_name newname, ty) :: FakeTs,
-          (newname, ty) :: Ts,
-          newname :: usednames)
-      end) Ts ([], [], [])
-  in (FakeTs, Ts, Term.subst_bounds (map Free FakeTs, t)) end;
-
-(* before matching we need to fake the bound vars that are missing an
-   abstraction. In this function we additionally construct the
-   abstraction environment, and an outer context term (with the focus
-   abstracted out) for use in rewriting with RW_Inst.rw *)
-fun prep_zipper_match z =
-  let
-    val t = Zipper.trm z
-    val c = Zipper.ctxt z
-    val Ts = Zipper.C.nty_ctxt c
-    val (FakeTs', Ts', t') = fakefree_badbounds Ts t
-    val absterm = mk_foo_match (Zipper.C.apply c) Ts' t'
-  in
-    (t', (FakeTs', Ts', absterm))
-  end;
-
-(* Unification with exception handled *)
-(* given context, max var index, pat, tgt; returns Seq of instantiations *)
-fun clean_unify ctxt ix (a as (pat, tgt)) =
-  let
-    (* type info will be re-derived, maybe this can be cached
-       for efficiency? *)
-    val pat_ty = Term.type_of pat;
-    val tgt_ty = Term.type_of tgt;
-    (* FIXME is it OK to ignore the type instantiation info?
-       or should I be using it? *)
-    val typs_unify =
-      SOME (Sign.typ_unify (Proof_Context.theory_of ctxt) (pat_ty, tgt_ty) (Vartab.empty, ix))
-        handle Type.TUNIFY => NONE;
-  in
-    (case typs_unify of
-      SOME (typinsttab, ix2) =>
-        let
-          (* FIXME is it right to throw away the flexes?
-             or should I be using them somehow? *)
-          fun mk_insts env =
-            (Vartab.dest (Envir.type_env env),
-             Vartab.dest (Envir.term_env env));
-          val initenv =
-            Envir.Envir {maxidx = ix2, tenv = Vartab.empty, tyenv = typinsttab};
-          val useq = Unify.smash_unifiers (Context.Proof ctxt) [a] initenv
-            handle ListPair.UnequalLengths => Seq.empty
-              | Term.TERM _ => Seq.empty;
-          fun clean_unify' useq () =
-            (case (Seq.pull useq) of
-               NONE => NONE
-             | SOME (h, t) => SOME (mk_insts h, Seq.make (clean_unify' t)))
-            handle ListPair.UnequalLengths => NONE
-              | Term.TERM _ => NONE;
-        in
-          (Seq.make (clean_unify' useq))
-        end
-    | NONE => Seq.empty)
-  end;
-
-(* Unification for zippers *)
-(* Note: Ts is a modified version of the original names of the outer
-   bound variables. New names have been introduced to make sure they are
-   unique w.r.t all names in the term and each other. usednames' is
-   oldnames + new names. *)
-fun clean_unify_z ctxt maxidx pat z =
-  let val (t, (FakeTs, Ts, absterm)) = prep_zipper_match z in
-    Seq.map (fn insts => (insts, FakeTs, Ts, absterm))
-      (clean_unify ctxt maxidx (t, pat))
-  end;
-
-
-fun bot_left_leaf_of (l $ _) = bot_left_leaf_of l
-  | bot_left_leaf_of (Abs (_, _, t)) = bot_left_leaf_of t
-  | bot_left_leaf_of x = x;
-
-(* Avoid considering replacing terms which have a var at the head as
-   they always succeed trivially, and uninterestingly. *)
-fun valid_match_start z =
-  (case bot_left_leaf_of (Zipper.trm z) of
-    Var _ => false
-  | _ => true);
-
-(* search from top, left to right, then down *)
-val search_lr_all = ZipperSearch.all_bl_ur;
-
-(* search from top, left to right, then down *)
-fun search_lr_valid validf =
-  let
-    fun sf_valid_td_lr z =
-      let val here = if validf z then [Zipper.Here z] else [] in
-        (case Zipper.trm z of
-          _ $ _ =>
-            [Zipper.LookIn (Zipper.move_down_left z)] @ here @
-            [Zipper.LookIn (Zipper.move_down_right z)]
-        | Abs _ => here @ [Zipper.LookIn (Zipper.move_down_abs z)]
-        | _ => here)
-      end;
-  in Zipper.lzy_search sf_valid_td_lr end;
-
-(* search from bottom to top, left to right *)
-fun search_bt_valid validf =
-  let
-    fun sf_valid_td_lr z =
-      let val here = if validf z then [Zipper.Here z] else [] in
-        (case Zipper.trm z of
-          _ $ _ =>
-            [Zipper.LookIn (Zipper.move_down_left z),
-             Zipper.LookIn (Zipper.move_down_right z)] @ here
-        | Abs _ => [Zipper.LookIn (Zipper.move_down_abs z)] @ here
-        | _ => here)
-      end;
-  in Zipper.lzy_search sf_valid_td_lr end;
-
-fun searchf_unify_gen f (ctxt, maxidx, z) lhs =
-  Seq.map (clean_unify_z ctxt maxidx lhs) (Zipper.limit_apply f z);
-
-(* search all unifications *)
-val searchf_lr_unify_all = searchf_unify_gen search_lr_all;
-
-(* search only for 'valid' unifiers (non abs subterms and non vars) *)
-val searchf_lr_unify_valid = searchf_unify_gen (search_lr_valid valid_match_start);
-
-val searchf_bt_unify_valid = searchf_unify_gen (search_bt_valid valid_match_start);
-
-(* apply a substitution in the conclusion of the theorem *)
-(* cfvs are certified free var placeholders for goal params *)
-(* conclthm is a theorem of for just the conclusion *)
-(* m is instantiation/match information *)
-(* rule is the equation for substitution *)
-fun apply_subst_in_concl ctxt i st (cfvs, conclthm) rule m =
-  RW_Inst.rw ctxt m rule conclthm
-  |> unfix_frees cfvs
-  |> Conv.fconv_rule Drule.beta_eta_conversion
-  |> (fn r => resolve_tac ctxt [r] i st);
-
-(* substitute within the conclusion of goal i of gth, using a meta
-equation rule. Note that we assume rule has var indicies zero'd *)
-fun prep_concl_subst ctxt i gth =
-  let
-    val th = Thm.incr_indexes 1 gth;
-    val tgt_term = Thm.prop_of th;
-
-    val (fixedbody, fvs) = IsaND.fix_alls_term ctxt i tgt_term;
-    val cfvs = rev (map (Thm.cterm_of ctxt) fvs);
-
-    val conclterm = Logic.strip_imp_concl fixedbody;
-    val conclthm = Thm.trivial (Thm.cterm_of ctxt conclterm);
-    val maxidx = Thm.maxidx_of th;
-    val ft =
-      (Zipper.move_down_right (* ==> *)
-       o Zipper.move_down_left (* Trueprop *)
-       o Zipper.mktop
-       o Thm.prop_of) conclthm
-  in
-    ((cfvs, conclthm), (ctxt, maxidx, ft))
-  end;
-
-(* substitute using an object or meta level equality *)
-fun eqsubst_tac' ctxt searchf instepthm i st =
-  let
-    val (cvfsconclthm, searchinfo) = prep_concl_subst ctxt i st;
-    val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
-    fun rewrite_with_thm r =
-      let val (lhs,_) = Logic.dest_equals (Thm.concl_of r) in
-        searchf searchinfo lhs
-        |> Seq.maps (apply_subst_in_concl ctxt i st cvfsconclthm r)
-      end;
-  in stepthms |> Seq.maps rewrite_with_thm end;
-
-
-(* General substitution of multiple occurrences using one of
-   the given theorems *)
-
-fun skip_first_occs_search occ srchf sinfo lhs =
-  (case skipto_skipseq occ (srchf sinfo lhs) of
-    SkipMore _ => Seq.empty
-  | SkipSeq ss => Seq.flat ss);
-
-(* The "occs" argument is a list of integers indicating which occurrence
-w.r.t. the search order, to rewrite. Backtracking will also find later
-occurrences, but all earlier ones are skipped. Thus you can use [0] to
-just find all rewrites. *)
-
-fun eqsubst_tac ctxt occs thms i st =
-  let val nprems = Thm.nprems_of st in
-    if nprems < i then Seq.empty else
-    let
-      val thmseq = Seq.of_list thms;
-      fun apply_occ occ st =
-        thmseq |> Seq.maps (fn r =>
-          eqsubst_tac' ctxt
-            (skip_first_occs_search occ searchf_lr_unify_valid) r
-            (i + (Thm.nprems_of st - nprems)) st);
-      val sorted_occs = Library.sort (rev_order o int_ord) occs;
-    in
-      Seq.maps distinct_subgoals_tac (Seq.EVERY (map apply_occ sorted_occs) st)
-    end
-  end;
-
-
-(* apply a substitution inside assumption j, keeps asm in the same place *)
-fun apply_subst_in_asm ctxt i st rule ((cfvs, j, _, pth),m) =
-  let
-    val st2 = Thm.rotate_rule (j - 1) i st; (* put premice first *)
-    val preelimrule =
-      RW_Inst.rw ctxt m rule pth
-      |> (Seq.hd o prune_params_tac ctxt)
-      |> Thm.permute_prems 0 ~1 (* put old asm first *)
-      |> unfix_frees cfvs (* unfix any global params *)
-      |> Conv.fconv_rule Drule.beta_eta_conversion; (* normal form *)
-  in
-    (* ~j because new asm starts at back, thus we subtract 1 *)
-    Seq.map (Thm.rotate_rule (~ j) (Thm.nprems_of rule + i))
-      (dresolve_tac ctxt [preelimrule] i st2)
-  end;
-
-
-(* prepare to substitute within the j'th premise of subgoal i of gth,
-using a meta-level equation. Note that we assume rule has var indicies
-zero'd. Note that we also assume that premt is the j'th premice of
-subgoal i of gth. Note the repetition of work done for each
-assumption, i.e. this can be made more efficient for search over
-multiple assumptions.  *)
-fun prep_subst_in_asm ctxt i gth j =
-  let
-    val th = Thm.incr_indexes 1 gth;
-    val tgt_term = Thm.prop_of th;
-
-    val (fixedbody, fvs) = IsaND.fix_alls_term ctxt i tgt_term;
-    val cfvs = rev (map (Thm.cterm_of ctxt) fvs);
-
-    val asmt = nth (Logic.strip_imp_prems fixedbody) (j - 1);
-    val asm_nprems = length (Logic.strip_imp_prems asmt);
-
-    val pth = Thm.trivial ((Thm.cterm_of ctxt) asmt);
-    val maxidx = Thm.maxidx_of th;
-
-    val ft =
-      (Zipper.move_down_right (* trueprop *)
-         o Zipper.mktop
-         o Thm.prop_of) pth
-  in ((cfvs, j, asm_nprems, pth), (ctxt, maxidx, ft)) end;
-
-(* prepare subst in every possible assumption *)
-fun prep_subst_in_asms ctxt i gth =
-  map (prep_subst_in_asm ctxt i gth)
-    ((fn l => Library.upto (1, length l))
-      (Logic.prems_of_goal (Thm.prop_of gth) i));
-
-
-(* substitute in an assumption using an object or meta level equality *)
-fun eqsubst_asm_tac' ctxt searchf skipocc instepthm i st =
-  let
-    val asmpreps = prep_subst_in_asms ctxt i st;
-    val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
-    fun rewrite_with_thm r =
-      let
-        val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
-        fun occ_search occ [] = Seq.empty
-          | occ_search occ ((asminfo, searchinfo)::moreasms) =
-              (case searchf searchinfo occ lhs of
-                SkipMore i => occ_search i moreasms
-              | SkipSeq ss =>
-                  Seq.append (Seq.map (Library.pair asminfo) (Seq.flat ss))
-                    (occ_search 1 moreasms)) (* find later substs also *)
-      in
-        occ_search skipocc asmpreps |> Seq.maps (apply_subst_in_asm ctxt i st r)
-      end;
-  in stepthms |> Seq.maps rewrite_with_thm end;
-
-
-fun skip_first_asm_occs_search searchf sinfo occ lhs =
-  skipto_skipseq occ (searchf sinfo lhs);
-
-fun eqsubst_asm_tac ctxt occs thms i st =
-  let val nprems = Thm.nprems_of st in
-    if nprems < i then Seq.empty
-    else
-      let
-        val thmseq = Seq.of_list thms;
-        fun apply_occ occ st =
-          thmseq |> Seq.maps (fn r =>
-            eqsubst_asm_tac' ctxt
-              (skip_first_asm_occs_search searchf_lr_unify_valid) occ r
-              (i + (Thm.nprems_of st - nprems)) st);
-        val sorted_occs = Library.sort (rev_order o int_ord) occs;
-      in
-        Seq.maps distinct_subgoals_tac (Seq.EVERY (map apply_occ sorted_occs) st)
-      end
-  end;
-
-(* combination method that takes a flag (true indicates that subst
-   should be done to an assumption, false = apply to the conclusion of
-   the goal) as well as the theorems to use *)
-val _ =
-  Theory.setup
-    (Method.setup \<^binding>\<open>sub\<close>
-      (Scan.lift (Args.mode "asm" -- Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) --
-        Attrib.thms >> (fn ((asm, occs), inthms) => fn ctxt =>
-          SIMPLE_METHOD' ((if asm then eqsubst_asm_tac else eqsubst_tac) ctxt occs inthms)))
-      "single-step substitution"
-    #>
-    (Method.setup \<^binding>\<open>subst\<close>
-      (Scan.lift (Args.mode "asm" -- Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) --
-        Attrib.thms >> (fn ((asm, occs), inthms) => fn ctxt =>
-          SIMPLE_METHOD' (SIDE_CONDS
-            ((if asm then eqsubst_asm_tac else eqsubst_tac) ctxt occs inthms)
-            ctxt)))
-      "single-step substitution with auto-typechecking"))
-
-end;
diff --git a/spartan/core/ml/equality.ML b/spartan/core/ml/equality.ML
deleted file mode 100644
index 023147b..0000000
--- a/spartan/core/ml/equality.ML
+++ /dev/null
@@ -1,90 +0,0 @@
-(*  Title:      equality.ML
-    Author:     Joshua Chen
-
-Equality reasoning with identity types.
-*)
-
-structure Equality:
-sig
-
-val dest_Id: term -> term * term * term
-
-val push_hyp_tac: term * term -> Proof.context -> int -> tactic
-val induction_tac: term -> term -> term -> term -> Proof.context -> tactic
-val equality_context_tac: Facts.ref -> Proof.context -> context_tactic
-
-end = struct
-
-fun dest_Id tm = case tm of
-    Const (\<^const_name>\<open>Id\<close>, _) $ A $ x $ y => (A, x, y)
-  | _ => error "dest_Id"
-
-(*Context assumptions that have already been pushed into the type family*)
-structure Inserts = Proof_Data (
-  type T = term Item_Net.T
-  val init = K (Item_Net.init Term.aconv_untyped single)
-)
-
-fun push_hyp_tac (t, _) =
-  Subgoal.FOCUS_PARAMS (fn {context = ctxt, concl, ...} =>
-    let
-      val (_, C) = Lib.dest_typing (Thm.term_of concl)
-      val B = Thm.cterm_of ctxt (Lib.lambda_var t C)
-      val a = Thm.cterm_of ctxt t
-      (*The resolvent is PiE[where ?B=B and ?a=a]*)
-      val resolvent =
-        Drule.infer_instantiate' ctxt [NONE, NONE, SOME B, SOME a] @{thm PiE}
-    in
-      HEADGOAL (resolve_tac ctxt [resolvent])
-      THEN SOMEGOAL (known_tac ctxt)
-    end)
-
-fun induction_tac p A x y ctxt =
-  let
-    val [p, A, x, y] = map (Thm.cterm_of ctxt) [p, A, x, y]
-  in
-    HEADGOAL (resolve_tac ctxt
-      [Drule.infer_instantiate' ctxt [SOME p, SOME A, SOME x, SOME y] @{thm IdE}])
-  end
-
-val side_conds_tac = TRY oo typechk_tac
-
-fun equality_context_tac fact ctxt =
-  let
-    val eq_th = Proof_Context.get_fact_single ctxt fact
-    val (p, (A, x, y)) = (Lib.dest_typing ##> dest_Id) (Thm.prop_of eq_th)
-
-    val hyps =
-      Facts.props (Proof_Context.facts_of ctxt)
-      |> filter (fn (th, _) => Lib.is_typing (Thm.prop_of th))
-      |> map (Lib.dest_typing o Thm.prop_of o fst)
-      |> filter_out (fn (t, _) =>
-          Term.aconv (t, p) orelse Item_Net.member (Inserts.get ctxt) t)
-      |> map (fn (t, T) => ((t, T), Lib.subterm_count_distinct [p, x, y] T))
-      |> filter (fn (_, i) => i > 0)
-      (*`t1: T1` comes before `t2: T2` if T1 contains t2 as subterm.
-        If they are incomparable, then order by decreasing
-        `subterm_count [p, x, y] T`*)
-      |> sort (fn (((t1, _), i), ((_, T2), j)) =>
-          Lib.cond_order (Lib.subterm_order T2 t1) (int_ord (j, i)))
-      |> map #1
-
-    val record_inserts =
-      Inserts.map (fold (fn (t, _) => fn net => Item_Net.update t net) hyps)
-
-    val tac =
-      fold (fn hyp => fn tac => tac THEN HEADGOAL (push_hyp_tac hyp ctxt))
-        hyps all_tac
-      THEN (
-        induction_tac p A x y ctxt
-        THEN RANGE (replicate 3 (typechk_tac ctxt) @ [side_conds_tac ctxt]) 1
-      )
-      THEN (
-        REPEAT_DETERM_N (length hyps) (SOMEGOAL (resolve_tac ctxt @{thms PiI}))
-        THEN ALLGOALS (side_conds_tac ctxt)
-      )
-  in
-    fn (ctxt, st) => Context_Tactic.TACTIC_CONTEXT (record_inserts ctxt) (tac st)
-  end
-
-end
diff --git a/spartan/core/ml/focus.ML b/spartan/core/ml/focus.ML
deleted file mode 100644
index 1d8de78..0000000
--- a/spartan/core/ml/focus.ML
+++ /dev/null
@@ -1,125 +0,0 @@
-(*  Title:      focus.ML
-    Author:     Makarius Wenzel, Joshua Chen
-
-A modified version of the Isar `subgoal` command
-that keeps schematic variables in the goal state.
-
-Modified from code originally written by Makarius Wenzel.
-*)
-
-local
-
-fun param_bindings ctxt (param_suffix, raw_param_specs) st =
-  let
-    val _ = if Thm.no_prems st then error "No subgoals!" else ()
-    val subgoal = #1 (Logic.dest_implies (Thm.prop_of st))
-    val subgoal_params =
-      map (apfst (Name.internal o Name.clean)) (Term.strip_all_vars subgoal)
-      |> Term.variant_frees subgoal |> map #1
-
-    val n = length subgoal_params
-    val m = length raw_param_specs
-    val _ =
-      m <= n orelse
-        error ("Excessive subgoal parameter specification" ^
-          Position.here_list (map snd (drop n raw_param_specs)))
-
-    val param_specs =
-      raw_param_specs |> map
-        (fn (NONE, _) => NONE
-          | (SOME x, pos) =>
-              let
-                val b = #1 (#1 (Proof_Context.cert_var (Binding.make (x, pos), NONE, NoSyn) ctxt))
-                val _ = Variable.check_name b
-              in SOME b end)
-      |> param_suffix ? append (replicate (n - m) NONE)
-
-    fun bindings (SOME x :: xs) (_ :: ys) = x :: bindings xs ys
-      | bindings (NONE :: xs) (y :: ys) = Binding.name y :: bindings xs ys
-      | bindings _ ys = map Binding.name ys
-  in bindings param_specs subgoal_params end
-
-fun gen_schematic_subgoal prep_atts raw_result_binding raw_prems_binding param_specs state =
-  let
-    val _ = Proof.assert_backward state
-
-    val state1 = state
-      |> Proof.map_context (Proof_Context.set_mode Proof_Context.mode_schematic)
-      |> Proof.refine_insert []
-
-    val {context = ctxt, facts = facts, goal = st} = Proof.raw_goal state1
-
-    val result_binding = apsnd (map (prep_atts ctxt)) raw_result_binding
-    val (prems_binding, do_prems) =
-      (case raw_prems_binding of
-        SOME (b, raw_atts) => ((b, map (prep_atts ctxt) raw_atts), true)
-      | NONE => (Binding.empty_atts, false))
-
-    val (subgoal_focus, _) =
-      (if do_prems then Subgoal.focus_prems else Subgoal.focus_params) ctxt
-        1 (SOME (param_bindings ctxt param_specs st)) st
-
-    fun after_qed (ctxt'', [[result]]) =
-      Proof.end_block #> (fn state' =>
-        let
-          val ctxt' = Proof.context_of state'
-          val results' =
-            Proof_Context.export ctxt'' ctxt' (Conjunction.elim_conjunctions result)
-        in
-          state'
-          |> Proof.refine_primitive (fn _ => fn _ =>
-            Subgoal.retrofit ctxt'' ctxt' (#params subgoal_focus) (#asms subgoal_focus) 1
-              (Goal.protect 0 result) st
-            |> Seq.hd)
-          |> Proof.map_context
-            (#2 o Proof_Context.note_thmss "" [(result_binding, [(results', [])])])
-        end)
-      #> Proof.reset_facts
-      #> Proof.enter_backward
-  in
-    state1
-    |> Proof.enter_forward
-    |> Proof.using_facts []
-    |> Proof.begin_block
-    |> Proof.map_context (fn _ =>
-      #context subgoal_focus
-      |> Proof_Context.note_thmss "" [(prems_binding, [(#prems subgoal_focus, [])])] |> #2)
-    |> Proof.internal_goal (K (K ())) (Proof_Context.get_mode ctxt) true "subgoal"
-        NONE after_qed [] [] [(Binding.empty_atts, [(Thm.term_of (#concl subgoal_focus), [])])] |> #2
-    |> Proof.using_facts facts
-    |> pair subgoal_focus
-  end
-
-val opt_fact_binding =
-  Scan.optional (Parse.binding -- Parse.opt_attribs || Parse.attribs >> pair Binding.empty)
-    Binding.empty_atts
-
-val for_params =
-  Scan.optional
-    (\<^keyword>\<open>vars\<close> |--
-      Parse.!!! ((Scan.option Parse.dots >> is_some) --
-        (Scan.repeat1 (Parse.maybe_position Parse.name_position))))
-    (false, [])
-
-val schematic_subgoal_cmd = gen_schematic_subgoal Attrib.attribute_cmd
-
-val parser =
-  opt_fact_binding
-  -- (Scan.option (\<^keyword>\<open>prems\<close> |-- Parse.!!! opt_fact_binding))
-  -- for_params >> (fn ((a, b), c) =>
-    Toplevel.proofs (Seq.make_results o Seq.single o #2 o schematic_subgoal_cmd a b c))
-
-in
-
-(** Outer syntax commands **)
-
-val _ = Outer_Syntax.command \<^command_keyword>\<open>focus\<close>
-  "focus on first subgoal within backward refinement, without instantiating schematic vars"
-  parser
-
-val _ = Outer_Syntax.command \<^command_keyword>\<open>\<guillemotright>\<close> "focus bullet" parser
-val _ = Outer_Syntax.command \<^command_keyword>\<open>\<^item>\<close> "focus bullet" parser
-val _ = Outer_Syntax.command \<^command_keyword>\<open>\<^enum>\<close> "focus bullet" parser
-val _ = Outer_Syntax.command \<^command_keyword>\<open>~\<close> "focus bullet" parser
-
-end
diff --git a/spartan/core/ml/goals.ML b/spartan/core/ml/goals.ML
deleted file mode 100644
index 9f394f0..0000000
--- a/spartan/core/ml/goals.ML
+++ /dev/null
@@ -1,214 +0,0 @@
-(*  Title:      goals.ML
-    Author:     Makarius Wenzel, Joshua Chen
-
-Goal statements and proof term export.
-
-Modified from code originally written by Makarius Wenzel.
-*)
-
-local
-
-val long_keyword =
-  Parse_Spec.includes >> K "" ||
-  Parse_Spec.long_statement_keyword
-
-val long_statement =
-  Scan.optional
-    (Parse_Spec.opt_thm_name ":" --| Scan.ahead long_keyword)
-    Binding.empty_atts --
-  Scan.optional Parse_Spec.includes [] -- Parse_Spec.long_statement
-    >> (fn ((binding, includes), (elems, concl)) =>
-        (true, binding, includes, elems, concl))
-
-val short_statement =
-  Parse_Spec.statement -- Parse_Spec.if_statement -- Parse.for_fixes
-    >> (fn ((shows, assumes), fixes) =>
-      (false, Binding.empty_atts, [],
-        [Element.Fixes fixes, Element.Assumes assumes],
-        Element.Shows shows))
-
-fun prep_statement prep_att prep_stmt raw_elems raw_stmt ctxt =
-  let
-    val (stmt, elems_ctxt) = prep_stmt raw_elems raw_stmt ctxt
-    val prems = Assumption.local_prems_of elems_ctxt ctxt
-    val stmt_ctxt = fold (fold (Proof_Context.augment o fst) o snd)
-      stmt elems_ctxt
-  in
-    case raw_stmt of
-      Element.Shows _ =>
-        let val stmt' = Attrib.map_specs (map prep_att) stmt
-        in (([], prems, stmt', NONE), stmt_ctxt) end
-    | Element.Obtains raw_obtains =>
-        let
-          val asms_ctxt = stmt_ctxt
-            |> fold (fn ((name, _), asm) =>
-                snd o Proof_Context.add_assms Assumption.assume_export
-                  [((name, [Context_Rules.intro_query NONE]), asm)]) stmt
-          val that = Assumption.local_prems_of asms_ctxt stmt_ctxt
-          val ([(_, that')], that_ctxt) = asms_ctxt
-            |> Proof_Context.set_stmt true
-            |> Proof_Context.note_thmss ""
-                [((Binding.name Auto_Bind.thatN, []), [(that, [])])]
-            ||> Proof_Context.restore_stmt asms_ctxt
-
-          val stmt' = [
-              (Binding.empty_atts,
-              [(#2 (#1 (Obtain.obtain_thesis ctxt)), [])])
-            ]
-        in
-          ((Obtain.obtains_attribs raw_obtains, prems, stmt', SOME that'),
-          that_ctxt)
-        end
-  end
-
-fun define_proof_term name (local_name, [th]) lthy =
-      let
-        fun make_name_binding suffix local_name =
-          let val base_local_name = Long_Name.base_name local_name
-          in
-            Binding.qualified_name
-              ((case base_local_name of
-                  "" => name
-                | _ => base_local_name)
-              ^(case suffix of
-                  SOME "prf" => "_prf"
-                | SOME "def" => "_def"
-                | _ => ""))
-          end
-
-        val (prems, concl) =
-          (Logic.strip_assums_hyp (Thm.prop_of th),
-          Logic.strip_assums_concl (Thm.prop_of th))
-      in
-        if not (Lib.is_typing concl) then
-          ([], lthy)
-        else let
-          val prems_vars = distinct Term.aconv (flat
-            (map (Lib.collect_subterms is_Var) prems))
-
-          val concl_vars = Lib.collect_subterms is_Var
-            (Lib.term_of_typing concl)
-
-          val params = inter Term.aconv concl_vars prems_vars
-
-          val prf_tm =
-            fold_rev lambda params (Lib.term_of_typing concl)
-
-          val ((_, (_, raw_def)), lthy') = Local_Theory.define
-            ((make_name_binding NONE local_name, Mixfix.NoSyn),
-            ((make_name_binding (SOME "prf") local_name, []), prf_tm)) lthy
-
-          val def =
-            fold
-              (fn th1 => fn th2 => Thm.combination th2 th1)
-              (map (Thm.reflexive o Thm.cterm_of lthy) params)
-              raw_def
-
-          val ((_, def'), lthy'') = Local_Theory.note
-            ((make_name_binding (SOME "def") local_name, []), [def])
-            lthy'
-        in
-          (def', lthy'')
-        end
-      end
-  | define_proof_term _ _ _ = error
-      ("Unimplemented: handling proof terms of multiple facts in"
-      ^" single result")
-
-fun gen_schematic_theorem
-      bundle_includes prep_att prep_stmt
-      gen_prf long kind before_qed after_qed (name, raw_atts)
-      raw_includes raw_elems raw_concl int lthy =
-  let
-    val _ = Local_Theory.assert lthy;
-
-    val elems = raw_elems |> map (Element.map_ctxt_attrib (prep_att lthy))
-    val ((more_atts, prems, stmt, facts), goal_ctxt) = lthy
-      |> bundle_includes raw_includes
-      |> prep_statement (prep_att lthy) prep_stmt elems raw_concl
-    val atts = more_atts @ map (prep_att lthy) raw_atts
-    val pos = Position.thread_data ()
-
-    val prems_name = if long then Auto_Bind.assmsN else Auto_Bind.thatN
-
-    fun after_qed' results goal_ctxt' =
-      let
-        val results' = burrow
-          (map (Goal.norm_result lthy) o Proof_Context.export goal_ctxt' lthy)
-          results
-
-        val ((res, lthy'), substmts) =
-          if forall (Binding.is_empty_atts o fst) stmt
-          then ((map (pair "") results', lthy), false)
-          else
-            (Local_Theory.notes_kind kind
-              (map2 (fn (b, _) => fn ths => (b, [(ths, [])])) stmt results')
-              lthy,
-            true)
-
-        val (res', lthy'') =
-          if gen_prf
-          then
-            let
-              val (prf_tm_defs, lthy'') =
-                fold
-                  (fn result => fn (defs, lthy) =>
-                    apfst (fn new_defs => defs @ new_defs)
-                      (define_proof_term (Binding.name_of name) result lthy))
-                  res ([], lthy')
-  
-              val res_folded =
-                map (apsnd (map (Local_Defs.fold lthy'' prf_tm_defs))) res
-            in
-              Local_Theory.notes_kind kind
-                [((name, @{attributes [typechk]} @ atts),
-                  [(maps #2 res_folded, [])])]
-                lthy''
-            end
-          else
-            Local_Theory.notes_kind kind
-              [((name, atts), [(maps #2 res, [])])]
-              lthy'
-
-        val _ = Proof_Display.print_results int pos lthy''
-            ((kind, Binding.name_of name), map (fn (_, ths) => ("", ths)) res')
-
-        val _ =
-          if substmts then map
-            (fn (name, ths) => Proof_Display.print_results int pos lthy''
-              (("and", name), [("", ths)]))
-            res
-          else []
-      in
-        after_qed results' lthy''
-      end
-  in
-    goal_ctxt
-    |> not (null prems) ?
-      (Proof_Context.note_thmss "" [((Binding.name prems_name, []), [(prems, [])])] #> snd)
-    |> Proof.theorem before_qed after_qed' (map snd stmt)
-    |> (case facts of NONE => I | SOME ths => Proof.refine_insert ths)
-  end
-
-val schematic_theorem_cmd =
-  gen_schematic_theorem
-    Bundle.includes_cmd
-    Attrib.check_src
-    Expression.read_statement
-
-fun theorem spec descr =
-  Outer_Syntax.local_theory_to_proof' spec ("state " ^ descr)
-    (Scan.option (Args.parens (Args.$$$ "derive"))
-    -- (long_statement || short_statement) >>
-      (fn (opt_derive, (long, binding, includes, elems, concl)) =>
-        schematic_theorem_cmd
-          (case opt_derive of SOME "derive" => true | _ => false)
-          long descr NONE (K I) binding includes elems concl))
-in
-
-val _ = theorem \<^command_keyword>\<open>Theorem\<close> "Theorem"
-val _ = theorem \<^command_keyword>\<open>Lemma\<close> "Lemma"
-val _ = theorem \<^command_keyword>\<open>Corollary\<close> "Corollary"
-val _ = theorem \<^command_keyword>\<open>Proposition\<close> "Proposition"
-
-end
diff --git a/spartan/core/ml/implicits.ML b/spartan/core/ml/implicits.ML
deleted file mode 100644
index 4d73c8d..0000000
--- a/spartan/core/ml/implicits.ML
+++ /dev/null
@@ -1,78 +0,0 @@
-structure Implicits :
-sig
-
-val implicit_defs: Proof.context -> (term * term) Symtab.table
-val implicit_defs_attr: attribute
-val make_holes: Proof.context -> term -> term
-
-end = struct
-
-structure Defs = Generic_Data (
-  type T = (term * term) Symtab.table
-  val empty = Symtab.empty
-  val extend = I
-  val merge = Symtab.merge (Term.aconv o apply2 #1)
-)
-
-val implicit_defs = Defs.get o Context.Proof
-
-val implicit_defs_attr = Thm.declaration_attribute (fn th =>
-  let
-    val (t, def) = Lib.dest_eq (Thm.prop_of th)
-    val (head, args) = Term.strip_comb t
-    val def' = fold_rev lambda args def
-  in
-    Defs.map (Symtab.update (Term.term_name head, (head, def')))
-  end)
-
-fun make_holes ctxt =
-  let
-    fun iarg_to_hole (Const (\<^const_name>\<open>iarg\<close>, T)) =
-          Const (\<^const_name>\<open>hole\<close>, T)
-      | iarg_to_hole t = t
-
-    fun expand head args =
-      let
-        fun betapplys (head', args') =
-          Term.betapplys (map_aterms iarg_to_hole head', args')
-      in
-        case head of
-          Abs (x, T, t) =>
-            list_comb (Abs (x, T, Lib.traverse_term expand t), args)
-        | _ =>
-            case Symtab.lookup (implicit_defs ctxt) (Term.term_name head) of
-              SOME (t, def) => betapplys
-                (Envir.expand_atom
-                  (Term.fastype_of head)
-                  (Term.fastype_of t, def),
-                args)
-            | NONE => list_comb (head, args)
-      end
-
-    fun holes_to_vars t =
-      let
-        val count = Lib.subterm_count (Const (\<^const_name>\<open>hole\<close>, dummyT))
-
-        fun subst (Const (\<^const_name>\<open>hole\<close>, T)) (Var (idx, _)::_) Ts =
-              let
-                val bounds = map Bound (0 upto (length Ts - 1))
-                val T' = foldr1 (op -->) (Ts @ [T])
-              in
-                foldl1 (op $) (Var (idx, T')::bounds)
-              end
-          | subst (Abs (x, T, t)) vs Ts = Abs (x, T, subst t vs (T::Ts))
-          | subst (t $ u) vs Ts =
-              let val n = count t
-              in subst t (take n vs) Ts $ subst u (drop n vs) Ts end
-          | subst t _ _ = t
-
-        val vars = map (fn n => Var ((n, 0), dummyT))
-          (Name.invent (Variable.names_of ctxt) "*" (count t))
-      in
-        subst t vars []
-      end
-  in
-    Lib.traverse_term expand #> holes_to_vars
-  end
-
-end
diff --git a/spartan/core/ml/lib.ML b/spartan/core/ml/lib.ML
deleted file mode 100644
index 615f601..0000000
--- a/spartan/core/ml/lib.ML
+++ /dev/null
@@ -1,145 +0,0 @@
-structure Lib :
-sig
-
-(*Lists*)
-val max: ('a * 'a -> bool) -> 'a list -> 'a
-val maxint: int list -> int
-
-(*Terms*)
-val is_rigid: term -> bool
-val dest_eq: term -> term * term
-val mk_Var: string -> int -> typ -> term
-val lambda_var: term -> term -> term
-
-val is_typing: term -> bool
-val dest_typing: term -> term * term
-val term_of_typing: term -> term
-val type_of_typing: term -> term
-val mk_Pi: term -> term -> term -> term
-
-val typing_of_term: term -> term
-
-(*Goals*)
-val rigid_typing_concl: term -> bool
-
-(*Subterms*)
-val has_subterm: term list -> term -> bool
-val subterm_count: term -> term -> int
-val subterm_count_distinct: term list -> term -> int
-val traverse_term: (term -> term list -> term) -> term -> term
-val collect_subterms: (term -> bool) -> term -> term list
-
-(*Orderings*)
-val subterm_order: term -> term -> order
-val cond_order: order -> order -> order
-
-end = struct
-
-
-(** Lists **)
-
-fun max gt (x::xs) = fold (fn a => fn b => if gt (a, b) then a else b) xs x
-  | max _ [] = error "max of empty list"
-
-val maxint = max (op >)
-
-
-(** Terms **)
-
-(* Meta *)
-
-val is_rigid = not o is_Var o head_of
-
-fun dest_eq (Const (\<^const_name>\<open>Pure.eq\<close>, _) $ t $ def) = (t, def)
-  | dest_eq _ = error "dest_eq"
-
-fun mk_Var name idx T = Var ((name, idx), T)
-
-fun lambda_var x tm =
-  let
-    fun var_args (Var (idx, T)) = Var (idx, \<^typ>\<open>o\<close> --> T) $ x
-      | var_args t = t
-  in
-    tm |> map_aterms var_args
-       |> lambda x
-  end
-
-(* Object *)
-
-fun is_typing (Const (\<^const_name>\<open>has_type\<close>, _) $ _ $ _) = true
-  | is_typing _ = false
-
-fun dest_typing (Const (\<^const_name>\<open>has_type\<close>, _) $ t $ T) = (t, T)
-  | dest_typing _ = error "dest_typing"
-
-val term_of_typing = #1 o dest_typing
-val type_of_typing = #2 o dest_typing
-
-fun mk_Pi v typ body = Const (\<^const_name>\<open>Pi\<close>, dummyT) $ typ $ lambda v body
-
-fun typing_of_term tm = \<^const>\<open>has_type\<close> $ tm $ Var (("*?", 0), \<^typ>\<open>o\<close>)
-(*The above is a bit hacky; basically we need to guarantee that the schematic
-  var is fresh*)
-
-
-(** Goals **)
-
-fun rigid_typing_concl goal =
-  let val concl = Logic.strip_assums_concl goal
-  in is_typing concl andalso is_rigid (term_of_typing concl) end
-
-
-(** Subterms **)
-
-fun has_subterm tms =
-  Term.exists_subterm
-    (foldl1 (op orf) (map (fn t => fn s => Term.aconv_untyped (s, t)) tms))
-
-fun subterm_count s t =
-  let
-    fun count (t1 $ t2) i = i + count t1 0 + count t2 0
-      | count (Abs (_, _, t)) i = i + count t 0
-      | count t i = if Term.aconv_untyped (s, t) then i + 1 else i
-  in
-    count t 0
-  end
-
-(*Number of distinct subterms in `tms` that appear in `tm`*)
-fun subterm_count_distinct tms tm =
-  length (filter I (map (fn t => has_subterm [t] tm) tms))
-
-(*
-  "Folds" a function f over the term structure of t by traversing t from child
-  nodes upwards through parents. At each node n in the term syntax tree, f is
-  additionally passed a list of the results of f at all children of n.
-*)
-fun traverse_term f t =
-  let
-    fun map_aux (Abs (x, T, t)) = Abs (x, T, map_aux t)
-      | map_aux t =
-          let
-            val (head, args) = Term.strip_comb t
-            val args' = map map_aux args
-          in
-            f head args'
-          end
-  in
-    map_aux t
-  end
-
-fun collect_subterms f (t $ u) = collect_subterms f t @ collect_subterms f u
-  | collect_subterms f (Abs (_, _, t)) = collect_subterms f t
-  | collect_subterms f t = if f t then [t] else []
-
-
-(** Orderings **)
-
-fun subterm_order t1 t2 =
-  if has_subterm [t1] t2 then LESS
-  else if has_subterm [t2] t1 then GREATER
-  else EQUAL
-
-fun cond_order o1 o2 = case o1 of EQUAL => o2 | _ => o1
-
-
-end
diff --git a/spartan/core/ml/rewrite.ML b/spartan/core/ml/rewrite.ML
deleted file mode 100644
index f9c5d8e..0000000
--- a/spartan/core/ml/rewrite.ML
+++ /dev/null
@@ -1,465 +0,0 @@
-(*  Title:      rewrite.ML
-    Author:     Christoph Traut, Lars Noschinski, TU Muenchen
-    Modified:   Joshua Chen, University of Innsbruck
-
-This is a rewrite method that supports subterm-selection based on patterns.
-
-The patterns accepted by rewrite are of the following form:
-  <atom>    ::= <term> | "concl" | "asm" | "for" "(" <names> ")"
-  <pattern> ::= (in <atom> | at <atom>) [<pattern>]
-  <args>    ::= [<pattern>] ("to" <term>) <thms>
-
-This syntax was clearly inspired by Gonthier's and Tassi's language of
-patterns but has diverged significantly during its development.
-
-We also allow introduction of identifiers for bound variables,
-which can then be used to match arbitrary subterms inside abstractions.
-
-This code is slightly modified from the original at HOL/Library/rewrite.ML,
-to incorporate auto-typechecking for type theory.
-*)
-
-infix 1 then_pconv;
-infix 0 else_pconv;
-
-signature REWRITE =
-sig
-  type patconv = Proof.context -> Type.tyenv * (string * term) list -> cconv
-  val then_pconv: patconv * patconv -> patconv
-  val else_pconv: patconv * patconv -> patconv
-  val abs_pconv:  patconv -> string option * typ -> patconv (*XXX*)
-  val fun_pconv: patconv -> patconv
-  val arg_pconv: patconv -> patconv
-  val imp_pconv: patconv -> patconv
-  val params_pconv: patconv -> patconv
-  val forall_pconv: patconv -> string option * typ option -> patconv
-  val all_pconv: patconv
-  val for_pconv: patconv -> (string option * typ option) list -> patconv
-  val concl_pconv: patconv -> patconv
-  val asm_pconv: patconv -> patconv
-  val asms_pconv: patconv -> patconv
-  val judgment_pconv: patconv -> patconv
-  val in_pconv: patconv -> patconv
-  val match_pconv: patconv -> term * (string option * typ) list -> patconv
-  val rewrs_pconv: term option -> thm list -> patconv
-
-  datatype ('a, 'b) pattern = At | In | Term of 'a | Concl | Asm | For of 'b list
-
-  val mk_hole: int -> typ -> term
-
-  val rewrite_conv: Proof.context
-    -> (term * (string * typ) list, string * typ option) pattern list * term option
-    -> thm list
-    -> conv
-end
-
-structure Rewrite : REWRITE =
-struct
-
-datatype ('a, 'b) pattern = At | In | Term of 'a | Concl | Asm | For of 'b list
-
-exception NO_TO_MATCH
-
-val holeN = Name.internal "_hole"
-
-fun prep_meta_eq ctxt = Simplifier.mksimps ctxt #> map Drule.zero_var_indexes
-
-
-(* holes *)
-
-fun mk_hole i T = Var ((holeN, i), T)
-
-fun is_hole (Var ((name, _), _)) = (name = holeN)
-  | is_hole _ = false
-
-fun is_hole_const (Const (\<^const_name>\<open>rewrite_HOLE\<close>, _)) = true
-  | is_hole_const _ = false
-
-val hole_syntax =
-  let
-    (* Modified variant of Term.replace_hole *)
-    fun replace_hole Ts (Const (\<^const_name>\<open>rewrite_HOLE\<close>, T)) i =
-          (list_comb (mk_hole i (Ts ---> T), map_range Bound (length Ts)), i + 1)
-      | replace_hole Ts (Abs (x, T, t)) i =
-          let val (t', i') = replace_hole (T :: Ts) t i
-          in (Abs (x, T, t'), i') end
-      | replace_hole Ts (t $ u) i =
-          let
-            val (t', i') = replace_hole Ts t i
-            val (u', i'') = replace_hole Ts u i'
-          in (t' $ u', i'') end
-      | replace_hole _ a i = (a, i)
-    fun prep_holes ts = #1 (fold_map (replace_hole []) ts 1)
-  in
-    Context.proof_map (Syntax_Phases.term_check 101 "hole_expansion" (K prep_holes))
-    #> Proof_Context.set_mode Proof_Context.mode_pattern
-  end
-
-
-(* pattern conversions *)
-
-type patconv = Proof.context -> Type.tyenv * (string * term) list -> cterm -> thm
-
-fun (cv1 then_pconv cv2) ctxt tytenv ct = (cv1 ctxt tytenv then_conv cv2 ctxt tytenv) ct
-
-fun (cv1 else_pconv cv2) ctxt tytenv ct = (cv1 ctxt tytenv else_conv cv2 ctxt tytenv) ct
-
-fun raw_abs_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    Abs _ => CConv.abs_cconv (fn (x, ctxt') => cv x ctxt' tytenv) ctxt ct
-  | t => raise TERM ("raw_abs_pconv", [t])
-
-fun raw_fun_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    _ $ _ => CConv.fun_cconv (cv ctxt tytenv) ct
-  | t => raise TERM ("raw_fun_pconv", [t])
-
-fun raw_arg_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    _ $ _ => CConv.arg_cconv (cv ctxt tytenv) ct
-  | t => raise TERM ("raw_arg_pconv", [t])
-
-fun abs_pconv cv (s,T) ctxt (tyenv, ts) ct =
-  let val u = Thm.term_of ct
-  in
-    case try (fastype_of #> dest_funT) u of
-      NONE => raise TERM ("abs_pconv: no function type", [u])
-    | SOME (U, _) =>
-        let
-          val tyenv' =
-            if T = dummyT then tyenv
-            else Sign.typ_match (Proof_Context.theory_of ctxt) (T, U) tyenv
-          val eta_expand_cconv =
-            case u of
-              Abs _=> Thm.reflexive
-            | _ => CConv.rewr_cconv @{thm eta_expand}
-          fun add_ident NONE _ l = l
-            | add_ident (SOME name) ct l = (name, Thm.term_of ct) :: l
-          val abs_cv = CConv.abs_cconv (fn (ct, ctxt) => cv ctxt (tyenv', add_ident s ct ts)) ctxt
-        in (eta_expand_cconv then_conv abs_cv) ct end
-        handle Pattern.MATCH => raise TYPE ("abs_pconv: types don't match", [T,U], [u])
-  end
-
-fun fun_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    _ $ _ => CConv.fun_cconv (cv ctxt tytenv) ct
-  | Abs (_, T, _ $ Bound 0) => abs_pconv (fun_pconv cv) (NONE, T) ctxt tytenv ct
-  | t => raise TERM ("fun_pconv", [t])
-
-local
-
-fun arg_pconv_gen cv0 cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    _ $ _ => cv0 (cv ctxt tytenv) ct
-  | Abs (_, T, _ $ Bound 0) => abs_pconv (arg_pconv_gen cv0 cv) (NONE, T) ctxt tytenv ct
-  | t => raise TERM ("arg_pconv_gen", [t])
-
-in
-
-fun arg_pconv ctxt = arg_pconv_gen CConv.arg_cconv ctxt
-fun imp_pconv ctxt = arg_pconv_gen (CConv.concl_cconv 1) ctxt
-
-end
-
-(* Move to B in !!x_1 ... x_n. B. Do not eta-expand *)
-fun params_pconv cv ctxt tytenv ct =
-  let val pconv =
-    case Thm.term_of ct of
-      Const (\<^const_name>\<open>Pure.all\<close>, _) $ Abs _ => (raw_arg_pconv o raw_abs_pconv) (fn _ => params_pconv cv)
-    | Const (\<^const_name>\<open>Pure.all\<close>, _) => raw_arg_pconv (params_pconv cv)
-    | _ => cv
-  in pconv ctxt tytenv ct end
-
-fun forall_pconv cv ident ctxt tytenv ct =
-  case Thm.term_of ct of
-    Const (\<^const_name>\<open>Pure.all\<close>, T) $ _ =>
-      let
-        val def_U = T |> dest_funT |> fst |> dest_funT |> fst
-        val ident' = apsnd (the_default (def_U)) ident
-      in arg_pconv (abs_pconv cv ident') ctxt tytenv ct end
-  | t => raise TERM ("forall_pconv", [t])
-
-fun all_pconv _ _ = Thm.reflexive
-
-fun for_pconv cv idents ctxt tytenv ct =
-  let
-    fun f rev_idents (Const (\<^const_name>\<open>Pure.all\<close>, _) $ t) =
-        let val (rev_idents', cv') = f rev_idents (case t of Abs (_,_,u) => u | _ => t)
-        in
-          case rev_idents' of
-            [] => ([], forall_pconv cv' (NONE, NONE))
-          | (x :: xs) => (xs, forall_pconv cv' x)
-        end
-      | f rev_idents _ = (rev_idents, cv)
-  in
-    case f (rev idents) (Thm.term_of ct) of
-      ([], cv') => cv' ctxt tytenv ct
-    | _ => raise CTERM ("for_pconv", [ct])
-  end
-
-fun concl_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ _) $ _ => imp_pconv (concl_pconv cv) ctxt tytenv ct
-  | _ => cv ctxt tytenv ct
-
-fun asm_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ _) $ _ => CConv.with_prems_cconv ~1 (cv ctxt tytenv) ct
-  | t => raise TERM ("asm_pconv", [t])
-
-fun asms_pconv cv ctxt tytenv ct =
-  case Thm.term_of ct of
-    (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ _) $ _ =>
-      ((CConv.with_prems_cconv ~1 oo cv) else_pconv imp_pconv (asms_pconv cv)) ctxt tytenv ct
-  | t => raise TERM ("asms_pconv", [t])
-
-fun judgment_pconv cv ctxt tytenv ct =
-  if Object_Logic.is_judgment ctxt (Thm.term_of ct)
-  then arg_pconv cv ctxt tytenv ct
-  else cv ctxt tytenv ct
-
-fun in_pconv cv ctxt tytenv ct =
-  (cv else_pconv 
-   raw_fun_pconv (in_pconv cv) else_pconv
-   raw_arg_pconv (in_pconv cv) else_pconv
-   raw_abs_pconv (fn _  => in_pconv cv))
-  ctxt tytenv ct
-
-fun replace_idents idents t =
-  let
-    fun subst ((n1, s)::ss) (t as Free (n2, _)) = if n1 = n2 then s else subst ss t
-      | subst _ t = t
-  in Term.map_aterms (subst idents) t end
-
-fun match_pconv cv (t,fixes) ctxt (tyenv, env_ts) ct =
-  let
-    val t' = replace_idents env_ts t
-    val thy = Proof_Context.theory_of ctxt
-    val u = Thm.term_of ct
-
-    fun descend_hole fixes (Abs (_, _, t)) =
-        (case descend_hole fixes t of
-          NONE => NONE
-        | SOME (fix :: fixes', pos) => SOME (fixes', abs_pconv pos fix)
-        | SOME ([], _) => raise Match (* less fixes than abstractions on path to hole *))
-      | descend_hole fixes (t as l $ r) =
-        let val (f, _) = strip_comb t
-        in
-          if is_hole f
-          then SOME (fixes, cv)
-          else
-            (case descend_hole fixes l of
-              SOME (fixes', pos) => SOME (fixes', fun_pconv pos)
-            | NONE =>
-              (case descend_hole fixes r of
-                SOME (fixes', pos) => SOME (fixes', arg_pconv pos)
-              | NONE => NONE))
-        end
-      | descend_hole fixes t =
-        if is_hole t then SOME (fixes, cv) else NONE
-
-    val to_hole = descend_hole (rev fixes) #> the_default ([], cv) #> snd
-  in
-    case try (Pattern.match thy (apply2 Logic.mk_term (t',u))) (tyenv, Vartab.empty) of
-      NONE => raise TERM ("match_pconv: Does not match pattern", [t, t',u])
-    | SOME (tyenv', _) => to_hole t ctxt (tyenv', env_ts) ct
-  end
-
-fun rewrs_pconv to thms ctxt (tyenv, env_ts) =
-  let
-    fun instantiate_normalize_env ctxt env thm =
-      let
-        val prop = Thm.prop_of thm
-        val norm_type = Envir.norm_type o Envir.type_env
-        val insts = Term.add_vars prop []
-          |> map (fn x as (s, T) =>
-              ((s, norm_type env T), Thm.cterm_of ctxt (Envir.norm_term env (Var x))))
-        val tyinsts = Term.add_tvars prop []
-          |> map (fn x => (x, Thm.ctyp_of ctxt (norm_type env (TVar x))))
-      in Drule.instantiate_normalize (tyinsts, insts) thm end
-    
-    fun unify_with_rhs context to env thm =
-      let
-        val (_, rhs) = thm |> Thm.concl_of |> Logic.dest_equals
-        val env' = Pattern.unify context (Logic.mk_term to, Logic.mk_term rhs) env
-          handle Pattern.Unif => raise NO_TO_MATCH
-      in env' end
-    
-    fun inst_thm_to _ (NONE, _) thm = thm
-      | inst_thm_to (ctxt : Proof.context) (SOME to, env) thm =
-          instantiate_normalize_env ctxt (unify_with_rhs (Context.Proof ctxt) to env thm) thm
-    
-    fun inst_thm ctxt idents (to, tyenv) thm =
-      let
-        (* Replace any identifiers with their corresponding bound variables. *)
-        val maxidx = Term.maxidx_typs (map (snd o snd) (Vartab.dest tyenv)) 0
-        val env = Envir.Envir {maxidx = maxidx, tenv = Vartab.empty, tyenv = tyenv}
-        val maxidx = Envir.maxidx_of env |> fold Term.maxidx_term (the_list to)
-        val thm' = Thm.incr_indexes (maxidx + 1) thm
-      in SOME (inst_thm_to ctxt (Option.map (replace_idents idents) to, env) thm') end
-      handle NO_TO_MATCH => NONE
-    
-  in CConv.rewrs_cconv (map_filter (inst_thm ctxt env_ts (to, tyenv)) thms) end
-
-fun rewrite_conv ctxt (pattern, to) thms ct =
-  let
-    fun apply_pat At = judgment_pconv
-      | apply_pat In = in_pconv
-      | apply_pat Asm = params_pconv o asms_pconv
-      | apply_pat Concl = params_pconv o concl_pconv
-      | apply_pat (For idents) = (fn cv => for_pconv cv (map (apfst SOME) idents))
-      | apply_pat (Term x) = (fn cv => match_pconv cv (apsnd (map (apfst SOME)) x))
-
-    val cv = fold_rev apply_pat pattern
-
-    fun distinct_prems th =
-      case Seq.pull (distinct_subgoals_tac th) of
-        NONE => th
-      | SOME (th', _) => th'
-
-    val rewrite = rewrs_pconv to (maps (prep_meta_eq ctxt) thms)
-  in cv rewrite ctxt (Vartab.empty, []) ct |> distinct_prems end
-
-fun rewrite_export_tac ctxt (pat, pat_ctxt) thms =
-  let
-    val export = case pat_ctxt of
-        NONE => I
-      | SOME inner => singleton (Proof_Context.export inner ctxt)
-  in CCONVERSION (export o rewrite_conv ctxt pat thms) end
-
-val _ =
-  Theory.setup
-  let
-    fun mk_fix s = (Binding.name s, NONE, NoSyn)
-
-    val raw_pattern : (string, binding * string option * mixfix) pattern list parser =
-      let
-        val sep = (Args.$$$ "at" >> K At) || (Args.$$$ "in" >> K In)
-        val atom =  (Args.$$$ "asm" >> K Asm) ||
-          (Args.$$$ "concl" >> K Concl) ||
-          (Args.$$$ "for" |-- Args.parens (Scan.optional Parse.vars []) >> For) ||
-          (Parse.term >> Term)
-        val sep_atom = sep -- atom >> (fn (s,a) => [s,a])
-
-        fun append_default [] = [Concl, In]
-          | append_default (ps as Term _ :: _) = Concl :: In :: ps
-          | append_default [For x, In] = [For x, Concl, In]
-          | append_default (For x :: (ps as In :: Term _:: _)) = For x :: Concl :: ps
-          | append_default ps = ps
-
-      in Scan.repeats sep_atom >> (rev #> append_default) end
-
-    fun context_lift (scan : 'a parser) f = fn (context : Context.generic, toks) =>
-      let
-        val (r, toks') = scan toks
-        val (r', context') = Context.map_proof_result (fn ctxt => f ctxt r) context
-      in (r', (context', toks' : Token.T list)) end
-
-    fun read_fixes fixes ctxt =
-      let fun read_typ (b, rawT, mx) = (b, Option.map (Syntax.read_typ ctxt) rawT, mx)
-      in Proof_Context.add_fixes (map read_typ fixes) ctxt end
-
-    fun prep_pats ctxt (ps : (string, binding * string option * mixfix) pattern list) =
-      let
-        fun add_constrs ctxt n (Abs (x, T, t)) =
-            let
-              val (x', ctxt') = yield_singleton Proof_Context.add_fixes (mk_fix x) ctxt
-            in
-              (case add_constrs ctxt' (n+1) t of
-                NONE => NONE
-              | SOME ((ctxt'', n', xs), t') =>
-                  let
-                    val U = Type_Infer.mk_param n []
-                    val u = Type.constraint (U --> dummyT) (Abs (x, T, t'))
-                  in SOME ((ctxt'', n', (x', U) :: xs), u) end)
-            end
-          | add_constrs ctxt n (l $ r) =
-            (case add_constrs ctxt n l of
-              SOME (c, l') => SOME (c, l' $ r)
-            | NONE =>
-              (case add_constrs ctxt n r of
-                SOME (c, r') => SOME (c, l $ r')
-              | NONE => NONE))
-          | add_constrs ctxt n t =
-            if is_hole_const t then SOME ((ctxt, n, []), t) else NONE
-
-        fun prep (Term s) (n, ctxt) =
-            let
-              val t = Syntax.parse_term ctxt s
-              val ((ctxt', n', bs), t') =
-                the_default ((ctxt, n, []), t) (add_constrs ctxt (n+1) t)
-            in (Term (t', bs), (n', ctxt')) end
-          | prep (For ss) (n, ctxt) =
-            let val (ns, ctxt') = read_fixes ss ctxt
-            in (For ns, (n, ctxt')) end
-          | prep At (n,ctxt) = (At, (n, ctxt))
-          | prep In (n,ctxt) = (In, (n, ctxt))
-          | prep Concl (n,ctxt) = (Concl, (n, ctxt))
-          | prep Asm (n,ctxt) = (Asm, (n, ctxt))
-
-        val (xs, (_, ctxt')) = fold_map prep ps (0, ctxt)
-
-      in (xs, ctxt') end
-
-    fun prep_args ctxt (((raw_pats, raw_to), raw_ths)) =
-      let
-
-        fun check_terms ctxt ps to =
-          let
-            fun safe_chop (0: int) xs = ([], xs)
-              | safe_chop n (x :: xs) = chop (n - 1) xs |>> cons x
-              | safe_chop _ _ = raise Match
-
-            fun reinsert_pat _ (Term (_, cs)) (t :: ts) =
-                let val (cs', ts') = safe_chop (length cs) ts
-                in (Term (t, map dest_Free cs'), ts') end
-              | reinsert_pat _ (Term _) [] = raise Match
-              | reinsert_pat ctxt (For ss) ts =
-                let val fixes = map (fn s => (s, Variable.default_type ctxt s)) ss
-                in (For fixes, ts) end
-              | reinsert_pat _ At ts = (At, ts)
-              | reinsert_pat _ In ts = (In, ts)
-              | reinsert_pat _ Concl ts = (Concl, ts)
-              | reinsert_pat _ Asm ts = (Asm, ts)
-
-            fun free_constr (s,T) = Type.constraint T (Free (s, dummyT))
-            fun mk_free_constrs (Term (t, cs)) = t :: map free_constr cs
-              | mk_free_constrs _ = []
-
-            val ts = maps mk_free_constrs ps @ the_list to
-              |> Syntax.check_terms (hole_syntax ctxt)
-            val ctxt' = fold Variable.declare_term ts ctxt
-            val (ps', (to', ts')) = fold_map (reinsert_pat ctxt') ps ts
-              ||> (fn xs => case to of NONE => (NONE, xs) | SOME _ => (SOME (hd xs), tl xs))
-            val _ = case ts' of (_ :: _) => raise Match | [] => ()
-          in ((ps', to'), ctxt') end
-
-        val (pats, ctxt') = prep_pats ctxt raw_pats
-
-        val ths = Attrib.eval_thms ctxt' raw_ths
-        val to = Option.map (Syntax.parse_term ctxt') raw_to
-
-        val ((pats', to'), ctxt'') = check_terms ctxt' pats to
-
-      in ((pats', ths, (to', ctxt)), ctxt'') end
-
-    val to_parser = Scan.option ((Args.$$$ "to") |-- Parse.term)
-
-    val subst_parser =
-      let val scan = raw_pattern -- to_parser -- Parse.thms1
-      in context_lift scan prep_args end
-  in
-    Method.setup \<^binding>\<open>rewr\<close> (subst_parser >>
-      (fn (pattern, inthms, (to, pat_ctxt)) => fn orig_ctxt =>
-        SIMPLE_METHOD'
-          (rewrite_export_tac orig_ctxt ((pattern, to), SOME pat_ctxt) inthms)))
-      "single-step rewriting, allowing subterm selection via patterns"
-    #>
-    (Method.setup \<^binding>\<open>rewrite\<close> (subst_parser >>
-      (fn (pattern, inthms, (to, pat_ctxt)) => fn orig_ctxt =>
-        SIMPLE_METHOD' (SIDE_CONDS
-          (rewrite_export_tac orig_ctxt ((pattern, to), SOME pat_ctxt) inthms)
-          orig_ctxt)))
-      "single-step rewriting with auto-typechecking")
-  end
-end
diff --git a/spartan/core/ml/types.ML b/spartan/core/ml/types.ML
deleted file mode 100644
index b0792fe..0000000
--- a/spartan/core/ml/types.ML
+++ /dev/null
@@ -1,18 +0,0 @@
-structure Types
-= struct
-
-structure Data = Generic_Data (
-  type T = thm Item_Net.T
-  val empty = Item_Net.init Thm.eq_thm
-    (single o Lib.term_of_typing o Thm.prop_of)
-  val extend = I
-  val merge = Item_Net.merge
-)
-
-fun put_type typing = Context.proof_map (Data.map (Item_Net.update typing))
-fun put_types typings = foldr1 (op o) (map put_type typings)
-
-fun get_types ctxt tm = Item_Net.retrieve (Data.get (Context.Proof ctxt)) tm
-
-
-end
diff --git a/spartan/core/lib/rewrite.ML b/spartan/core/rewrite.ML
index f9c5d8e..f9c5d8e 100644
--- a/spartan/core/lib/rewrite.ML
+++ b/spartan/core/rewrite.ML
diff --git a/spartan/core/ml/tactics.ML b/spartan/core/tactics.ML
index 0c71665..0c71665 100644
--- a/spartan/core/ml/tactics.ML
+++ b/spartan/core/tactics.ML
diff --git a/spartan/core/types.ML b/spartan/core/types.ML
new file mode 100644
index 0000000..1eaf60b
--- /dev/null
+++ b/spartan/core/types.ML
@@ -0,0 +1,29 @@
+(*  Title:      types.ML
+    Author:     Joshua Chen
+
+Type information storage.
+*)
+
+structure Types: sig
+
+val Data: Proof.context -> thm Item_Net.T
+val types: Proof.context -> term -> thm list
+val put_type: thm -> Proof.context -> Proof.context
+val put_types: thm list -> Proof.context -> Proof.context
+
+end = struct
+
+structure Data = Generic_Data (
+  type T = thm Item_Net.T
+  val empty = Item_Net.init Thm.eq_thm
+    (single o Lib.term_of_typing o Thm.prop_of)
+  val extend = I
+  val merge = Item_Net.merge
+)
+
+val Data = Data.get o Context.Proof
+fun types ctxt tm = Item_Net.retrieve (Data ctxt) tm
+fun put_type typing = Context.proof_map (Data.map (Item_Net.update typing))
+fun put_types typings = foldr1 (op o) (map put_type typings)
+
+end