diff --git a/src/analyses/ai.cpp b/src/analyses/ai.cpp
index d2aa0c14bbb..c12c1f4d0a3 100644
--- a/src/analyses/ai.cpp
+++ b/src/analyses/ai.cpp
@@ -15,8 +15,9 @@ Author: Daniel Kroening, kroening@kroening.com
 #include <memory>
 #include <sstream>
 
-#include <util/std_expr.h>
+#include <util/invariant.h>
 #include <util/std_code.h>
+#include <util/std_expr.h>
 
 #include "is_threaded.h"
 
@@ -50,7 +51,7 @@ void ai_baset::output(
     out << "**** " << i_it->location_number << " "
         << i_it->source_location << "\n";
 
-    find_state(i_it).output(out, *this, ns);
+    abstract_state_before(i_it)->output(out, *this, ns);
     out << "\n";
     #if 1
     goto_program.output_instruction(ns, identifier, out, *i_it);
@@ -101,7 +102,8 @@ jsont ai_baset::output_json(
       json_numbert(std::to_string(i_it->location_number));
     location["sourceLocation"]=
       json_stringt(i_it->source_location.as_string());
-    location["abstractState"]=find_state(i_it).output_json(*this, ns);
+    location["abstractState"] =
+      abstract_state_before(i_it)->output_json(*this, ns);
 
     // Ideally we need output_instruction_json
     std::ostringstream out;
@@ -162,7 +164,7 @@ xmlt ai_baset::output_xml(
       "source_location",
       i_it->source_location.as_string());
 
-    location.new_element(find_state(i_it).output_xml(*this, ns));
+    location.new_element(abstract_state_before(i_it)->output_xml(*this, ns));
 
     // Ideally we need output_instruction_xml
     std::ostringstream out;
@@ -219,7 +221,7 @@ void ai_baset::finalize()
 ai_baset::locationt ai_baset::get_next(
   working_sett &working_set)
 {
-  assert(!working_set.empty());
+  PRECONDITION(!working_set.empty());
 
   working_sett::iterator i=working_set.begin();
   locationt l=i->second;
@@ -247,6 +249,7 @@ bool ai_baset::fixedpoint(
   {
     locationt l=get_next(working_set);
 
+    // goto_program is really only needed for iterator manipulation
     if(visit(l, working_set, goto_program, goto_functions, ns))
       new_data=true;
   }
@@ -322,6 +325,8 @@ bool ai_baset::do_function_call(
   // initialize state, if necessary
   get_state(l_return);
 
+  PRECONDITION(l_call->is_function_call());
+
   const goto_functionst::goto_functiont &goto_function=
     f_it->second;
 
@@ -387,69 +392,27 @@ bool ai_baset::do_function_call_rec(
   const goto_functionst &goto_functions,
   const namespacet &ns)
 {
-  assert(!goto_functions.function_map.empty());
+  PRECONDITION(!goto_functions.function_map.empty());
+
+  // This is quite a strong assumption on the well-formedness of the program.
+  // It means function pointers must be removed before use.
+  DATA_INVARIANT(
+    function.id() == ID_symbol,
+    "Function pointers and indirect calls must be removed before analysis.");
 
   bool new_data=false;
 
-  if(function.id()==ID_symbol)
-  {
-    const irep_idt &identifier = to_symbol_expr(function).get_identifier();
+  const irep_idt &identifier = to_symbol_expr(function).get_identifier();
 
-    goto_functionst::function_mapt::const_iterator it=
-      goto_functions.function_map.find(identifier);
+  goto_functionst::function_mapt::const_iterator it =
+    goto_functions.function_map.find(identifier);
 
-    if(it==goto_functions.function_map.end())
-      throw "failed to find function "+id2string(identifier);
+  DATA_INVARIANT(
+    it != goto_functions.function_map.end(),
+    "Function " + id2string(identifier) + "not in function map");
 
-    new_data=do_function_call(
-      l_call, l_return,
-      goto_functions,
-      it,
-      arguments,
-      ns);
-  }
-  else if(function.id()==ID_if)
-  {
-    if(function.operands().size()!=3)
-      throw "if has three operands";
-
-    bool new_data1=
-      do_function_call_rec(
-        l_call, l_return,
-        function.op1(),
-        arguments,
-        goto_functions,
-        ns);
-
-    bool new_data2=
-      do_function_call_rec(
-        l_call, l_return,
-        function.op2(),
-        arguments,
-        goto_functions,
-        ns);
-
-    if(new_data1 || new_data2)
-      new_data=true;
-  }
-  else if(function.id()==ID_dereference)
-  {
-    // We can't really do this here -- we rely on
-    // these being removed by some previous analysis.
-  }
-  else if(function.id() == ID_null_object)
-  {
-    // ignore, can't be a function
-  }
-  else if(function.id()==ID_member || function.id()==ID_index)
-  {
-    // ignore, can't be a function
-  }
-  else
-  {
-    throw "unexpected function_call argument: "+
-      function.id_string();
-  }
+  new_data =
+    do_function_call(l_call, l_return, goto_functions, it, arguments, ns);
 
   return new_data;
 }
diff --git a/src/analyses/ai.h b/src/analyses/ai.h
index aea76ea7480..e2f3a4d83a4 100644
--- a/src/analyses/ai.h
+++ b/src/analyses/ai.h
@@ -25,6 +25,8 @@ Author: Daniel Kroening, kroening@kroening.com
 
 #include "ai_domain.h"
 
+/// The basic interface of an abstract interpreter.  This should be enough
+/// to create, run and query an abstract interpreter.
 // don't use me -- I am just a base class
 // use ait instead
 class ai_baset
@@ -41,6 +43,7 @@ class ai_baset
   {
   }
 
+  /// Running the interpreter
   void operator()(
     const goto_programt &goto_program,
     const namespacet &ns)
@@ -82,17 +85,26 @@ class ai_baset
     finalize();
   }
 
+  /// Accessing individual domains at particular locations
+  /// (without needing to know what kind of domain or history is used)
+  /// A pointer to a copy as the method should be const and
+  /// there are some non-trivial cases including merging domains, etc.
+  /// Intended for users of the abstract interpreter; don't use internally.
+
   /// Returns the abstract state before the given instruction
-  virtual const ai_domain_baset & abstract_state_before(
-    goto_programt::const_targett t) const = 0;
+  /// PRECONDITION(l is dereferenceable)
+  virtual std::unique_ptr<statet> abstract_state_before(locationt l) const = 0;
 
   /// Returns the abstract state after the given instruction
-  virtual const ai_domain_baset & abstract_state_after(
-    goto_programt::const_targett t) const
+  virtual std::unique_ptr<statet> abstract_state_after(locationt l) const
   {
-    return abstract_state_before(std::next(t));
+    /// PRECONDITION(l is dereferenceable && std::next(l) is dereferenceable)
+    /// Check relies on a DATA_INVARIANT of goto_programs
+    INVARIANT(!l->is_end_function(), "No state after the last instruction");
+    return abstract_state_before(std::next(l));
   }
 
+  /// Resets the domain
   virtual void clear()
   {
   }
@@ -237,6 +249,9 @@ class ai_baset
     const goto_functionst &goto_functions,
     const namespacet &ns);
 
+  // Visit performs one step of abstract interpretation from location l
+  // Depending on the instruction type it may compute a number of "edges"
+  // or applications of the abstract transformer
   // true = found something new
   bool visit(
     locationt l,
@@ -304,10 +319,17 @@ class ait:public ai_baset
     return it->second;
   }
 
-  const ai_domain_baset & abstract_state_before(
-    goto_programt::const_targett t) const override
+  std::unique_ptr<statet> abstract_state_before(locationt t) const override
   {
-    return (*this)[t];
+    typename state_mapt::const_iterator it = state_map.find(t);
+    if(it == state_map.end())
+    {
+      std::unique_ptr<statet> d = util_make_unique<domainT>();
+      CHECK_RETURN(d->is_bottom());
+      return d;
+    }
+
+    return util_make_unique<domainT>(it->second);
   }
 
   void clear() override
diff --git a/src/analyses/constant_propagator.cpp b/src/analyses/constant_propagator.cpp
index 57b854a52ee..b6bb6688f62 100644
--- a/src/analyses/constant_propagator.cpp
+++ b/src/analyses/constant_propagator.cpp
@@ -592,43 +592,45 @@ void constant_propagator_ait::replace(
 {
   Forall_goto_program_instructions(it, goto_function.body)
   {
-    state_mapt::iterator s_it=state_map.find(it);
+    // Works because this is a location (but not history) sensitive domain
+    const constant_propagator_domaint &d = (*this)[it];
 
-    if(s_it==state_map.end())
+    if(d.is_bottom())
       continue;
 
-    replace_types_rec(s_it->second.values.replace_const, it->code);
-    replace_types_rec(s_it->second.values.replace_const, it->guard);
+    replace_types_rec(d.values.replace_const, it->code);
+    replace_types_rec(d.values.replace_const, it->guard);
 
     if(it->is_goto() || it->is_assume() || it->is_assert())
     {
-      s_it->second.partial_evaluate(it->guard, ns);
+      d.partial_evaluate(it->guard, ns);
     }
     else if(it->is_assign())
     {
       exprt &rhs=to_code_assign(it->code).rhs();
-      s_it->second.partial_evaluate(rhs, ns);
+      d.partial_evaluate(rhs, ns);
+
       if(rhs.id()==ID_constant)
         rhs.add_source_location()=it->code.op0().source_location();
     }
     else if(it->is_function_call())
     {
       exprt &function = to_code_function_call(it->code).function();
-      s_it->second.partial_evaluate(function, ns);
+      d.partial_evaluate(function, ns);
 
       exprt::operandst &args=
         to_code_function_call(it->code).arguments();
 
       for(auto &arg : args)
       {
-        s_it->second.partial_evaluate(arg, ns);
+        d.partial_evaluate(arg, ns);
       }
     }
     else if(it->is_other())
     {
       if(it->code.get_statement()==ID_expression)
       {
-        s_it->second.partial_evaluate(it->code, ns);
+        d.partial_evaluate(it->code, ns);
       }
     }
   }
diff --git a/src/analyses/dependence_graph.cpp b/src/analyses/dependence_graph.cpp
index 95ae2de10ae..24c0320af66 100644
--- a/src/analyses/dependence_graph.cpp
+++ b/src/analyses/dependence_graph.cpp
@@ -307,9 +307,9 @@ void dependence_grapht::add_dep(
   goto_programt::const_targett from,
   goto_programt::const_targett to)
 {
-  const node_indext n_from=state_map[from].get_node_id();
+  const node_indext n_from = (*this)[from].get_node_id();
   assert(n_from<size());
-  const node_indext n_to=state_map[to].get_node_id();
+  const node_indext n_to = (*this)[to].get_node_id();
   assert(n_to<size());
 
   // add_edge is redundant as the subsequent operations also insert
diff --git a/src/analyses/invariant_propagation.cpp b/src/analyses/invariant_propagation.cpp
index 9ef31e4f962..e89a21529e7 100644
--- a/src/analyses/invariant_propagation.cpp
+++ b/src/analyses/invariant_propagation.cpp
@@ -206,7 +206,7 @@ void invariant_propagationt::initialize(const goto_programt &goto_program)
 
   forall_goto_program_instructions(it, goto_program)
   {
-    invariant_sett &s=state_map[it].invariant_set;
+    invariant_sett &s = (*this)[it].invariant_set;
 
     if(it==goto_program.instructions.begin())
       s.make_true();
@@ -243,11 +243,11 @@ void invariant_propagationt::simplify(goto_programt &goto_program)
       continue;
 
     // find invariant set
-    state_mapt::const_iterator s_it=state_map.find(i_it);
-    if(s_it==state_map.end())
+    const auto &d = (*this)[i_it];
+    if(d.is_bottom())
       continue;
 
-    const invariant_sett &invariant_set=s_it->second.invariant_set;
+    const invariant_sett &invariant_set = d.invariant_set;
 
     exprt simplified_guard(i_it->guard);
 
diff --git a/src/goto-analyzer/static_simplifier.cpp b/src/goto-analyzer/static_simplifier.cpp
index d83026698a4..7bf82c7723d 100644
--- a/src/goto-analyzer/static_simplifier.cpp
+++ b/src/goto-analyzer/static_simplifier.cpp
@@ -65,8 +65,8 @@ bool static_simplifier(
 
       if(i_it->is_assert())
       {
-        bool unchanged=
-          ai.abstract_state_before(i_it).ai_simplify(i_it->guard, ns);
+        bool unchanged =
+          ai.abstract_state_before(i_it)->ai_simplify(i_it->guard, ns);
 
         if(unchanged)
           unmodified.asserts++;
@@ -75,8 +75,8 @@ bool static_simplifier(
       }
       else if(i_it->is_assume())
       {
-        bool unchanged=
-          ai.abstract_state_before(i_it).ai_simplify(i_it->guard, ns);
+        bool unchanged =
+          ai.abstract_state_before(i_it)->ai_simplify(i_it->guard, ns);
 
         if(unchanged)
           unmodified.assumes++;
@@ -85,8 +85,8 @@ bool static_simplifier(
       }
       else if(i_it->is_goto())
       {
-        bool unchanged=
-          ai.abstract_state_before(i_it).ai_simplify(i_it->guard, ns);
+        bool unchanged =
+          ai.abstract_state_before(i_it)->ai_simplify(i_it->guard, ns);
 
         if(unchanged)
           unmodified.gotos++;
@@ -102,11 +102,11 @@ bool static_simplifier(
         // <i=0, j=1>  i=j
         // should simplify to i=1, not to 0=1.
 
-        bool unchanged_lhs=
-          ai.abstract_state_before(i_it).ai_simplify_lhs(assign.lhs(), ns);
+        bool unchanged_lhs =
+          ai.abstract_state_before(i_it)->ai_simplify_lhs(assign.lhs(), ns);
 
-        bool unchanged_rhs=
-          ai.abstract_state_before(i_it).ai_simplify(assign.rhs(), ns);
+        bool unchanged_rhs =
+          ai.abstract_state_before(i_it)->ai_simplify(assign.rhs(), ns);
 
         if(unchanged_lhs && unchanged_rhs)
           unmodified.assigns++;
@@ -117,13 +117,13 @@ bool static_simplifier(
       {
         code_function_callt &fcall=to_code_function_call(i_it->code);
 
-        bool unchanged=
-          ai.abstract_state_before(i_it).ai_simplify(fcall.function(), ns);
+        bool unchanged =
+          ai.abstract_state_before(i_it)->ai_simplify(fcall.function(), ns);
 
         exprt::operandst &args=fcall.arguments();
 
         for(auto &o : args)
-          unchanged&=ai.abstract_state_before(i_it).ai_simplify(o, ns);
+          unchanged &= ai.abstract_state_before(i_it)->ai_simplify(o, ns);
 
         if(unchanged)
           unmodified.function_calls++;
diff --git a/src/goto-analyzer/static_verifier.cpp b/src/goto-analyzer/static_verifier.cpp
index f4fbc6320b7..70789e4ca5c 100644
--- a/src/goto-analyzer/static_verifier.cpp
+++ b/src/goto-analyzer/static_verifier.cpp
@@ -55,7 +55,8 @@ bool static_verifier(
           continue;
 
         exprt e(i_it->guard);
-        const ai_domain_baset &domain(ai.abstract_state_before(i_it));
+        auto dp = ai.abstract_state_before(i_it);
+        const ai_domain_baset &domain(*dp);
         domain.ai_simplify(e, ns);
 
         json_objectt &j=json_result.push_back().make_object();
@@ -104,7 +105,8 @@ bool static_verifier(
           continue;
 
         exprt e(i_it->guard);
-        const ai_domain_baset &domain(ai.abstract_state_before(i_it));
+        auto dp = ai.abstract_state_before(i_it);
+        const ai_domain_baset &domain(*dp);
         domain.ai_simplify(e, ns);
 
         xmlt &x=xml_result.new_element("result");
@@ -160,7 +162,8 @@ bool static_verifier(
           continue;
 
         exprt e(i_it->guard);
-        const ai_domain_baset &domain(ai.abstract_state_before(i_it));
+        auto dp = ai.abstract_state_before(i_it);
+        const ai_domain_baset &domain(*dp);
         domain.ai_simplify(e, ns);
 
         out << '[' << i_it->source_location.get_property_id()
diff --git a/src/goto-analyzer/unreachable_instructions.cpp b/src/goto-analyzer/unreachable_instructions.cpp
index 7f2c42a34a5..0c7ef1a4581 100644
--- a/src/goto-analyzer/unreachable_instructions.cpp
+++ b/src/goto-analyzer/unreachable_instructions.cpp
@@ -59,7 +59,7 @@ static void build_dead_map_from_ai(
   dead_mapt &dest)
 {
   forall_goto_program_instructions(it, goto_program)
-    if(ai.abstract_state_before(it).is_bottom())
+    if(ai.abstract_state_before(it)->is_bottom())
       dest.insert(std::make_pair(it->location_number, it));
 }
 
@@ -418,7 +418,7 @@ std::unordered_set<irep_idt> compute_called_functions_from_ai(
 
     const goto_programt &p = f_it->second.body;
 
-    if(!ai.abstract_state_before(p.instructions.begin()).is_bottom())
+    if(!ai.abstract_state_before(p.instructions.begin())->is_bottom())
       called.insert(f_it->first);
   }