diff --git a/src/typed_ast.ml b/src/typed_ast.ml
index ca8bbd7..43e9520 100644
--- a/src/typed_ast.ml
+++ b/src/typed_ast.ml
@@ -2,6 +2,8 @@
 open Core.Std
 open Sast
 
+exception Cant_infer_type of string
+
 (* environment *)
 type symbol_table = {
   parent: symbol_table option;
@@ -15,6 +17,10 @@ type environment = {
   types: Sast.tdefault list;
 }
 
+let rec get_top_scope scope = match scope.parent with
+  | None -> scope
+  | Some(scope) -> get_top_scope scope
+
 let rec has_cycle_rec nodes (self, children) seen =
   match List.find !seen ~f:(fun n -> n = self) with
     | Some(_) -> true
@@ -54,10 +60,10 @@ let rec find_field types t access_list =
 
 
 
-let unique_add l item = 
-  if List.mem !l item
-    then l := !l
-    else l := item :: !l
+let replace_add_fun l item =
+  let (Sast.FunDef(name, tparams, (_, _))) = item in
+  l := item :: List.filter !l
+    ~f:(fun (Sast.FunDef(n, tps, (_, _))) -> name <> n || tparams <> tps)
 
 let rec find_variable (scope: symbol_table) name =
   match List.find scope.variables ~f:(fun (s, _) -> s = name) with
@@ -68,6 +74,9 @@ let rec find_variable (scope: symbol_table) name =
     end
   | Some(x) -> x
 
+let find_seen_function functions name tparams =
+  List.find functions ~f:(fun (n,tps) -> name=n && tps=tparams)
+
 let find_function functions name num_args = match
   List.find functions ~f:(function (n, Ast.FunDef(fname,_,_)) -> name = fname && num_args = n)
   with
@@ -117,16 +126,16 @@ let chord_of sexpr =
     | _ -> failwith "This expression is not chordable"
   end, Ast.Type("chord")
 
-let rec sast_expr env tfuns_ref e =
-  let sast_expr_env = sast_expr env tfuns_ref in
+let rec sast_expr ?(seen_funs = []) ?(force = false) env tfuns_ref e =
+  let sast_expr_env = sast_expr ~seen_funs:seen_funs env tfuns_ref in
   match e with
   | Ast.LitBool(x) -> Sast.LitBool(x), Ast.Bool
   | Ast.LitInt(x) -> Sast.LitInt(x), Ast.Int
   | Ast.LitFloat(x) -> Sast.LitFloat(x), Ast.Float
   | Ast.LitStr(x) -> Sast.LitStr(x), Ast.String
   | Ast.Binop(lexpr, op, rexpr) ->
-    let lexprt = sast_expr env tfuns_ref lexpr in
-    let rexprt = sast_expr env tfuns_ref rexpr in
+    let lexprt = sast_expr_env lexpr in
+    let rexprt = sast_expr_env rexpr in
     let (_, lt) = lexprt in
     let (_, rt) = rexprt in
     let opfailwith constraint_str =
@@ -183,7 +192,7 @@ let rec sast_expr env tfuns_ref e =
             else failwith "left side expression of zip must of float or array of float"
     end
   | Ast.Uniop(op, expr) ->
-    let exprt = sast_expr env tfuns_ref expr in
+    let exprt = sast_expr_env expr in
     let (_, t) = exprt in
     begin match op with
       | Ast.Not when t = Ast.Bool -> Sast.Uniop(op, exprt), t
@@ -212,7 +221,7 @@ let rec sast_expr env tfuns_ref e =
   | Ast.FunApply(name, arg_exprs) ->
     (* Common code for all function calls *)
     (* get typed versions of input expressions *)
-    let arg_texprs = List.map arg_exprs ~f:(sast_expr env tfuns_ref) in
+    let arg_texprs = List.map arg_exprs ~f:(sast_expr_env) in
     (* get types of the typed arguments *)
     let arg_types = List.map arg_texprs ~f:(fun (_, t) -> t) in
     
@@ -221,22 +230,58 @@ let rec sast_expr env tfuns_ref e =
     then
       (* find the function *)
       let num_args = List.length arg_exprs in
-      let (_,Ast.FunDef(_,params,expr)) = find_function env.functions name num_args in
+      let nh_fun_sig = find_function env.functions name num_args in
+      let (_,Ast.FunDef(_,params,expr)) = nh_fun_sig in
       (* zip params with input types *)
       let tparams = match List.zip params arg_types with
         | None -> failwith "Internal error: Mismatched lengths of types and arguments while type checking function call"
         | Some(x) -> x
       in
-      (* check if types of inputs can be used with this function and UPDATE tfuns_ref *)
-      let (sexpr, t) = try check_function_type tparams expr tfuns_ref env
-        with Failure(reason) ->
-          Log.info "Function template type check failed. Inner exception: %s" reason;
-          failwith ("Incorrect types passed into function "^name)
-      in begin
-      (* UPDATE tfuns_ref and return the sast node *)
-      ignore(unique_add tfuns_ref (Sast.FunDef(name, tparams, (sexpr, t))));
-      Sast.FunApply(NhFunction(name), arg_texprs), t
-      end
+      let has_seen_fun = (find_seen_function seen_funs name tparams) <> None in
+      (* check if function type already inferred *)
+      match List.find !tfuns_ref ~f:(fun (Sast.FunDef(n,tps,_)) -> name=n && tparams=tps) with
+        (* already know function signature and not forced to re-infer subexpression types
+          (or is forced but loop encountered, so need to use previous result anyway) *)
+        | Some(Sast.FunDef(_,_,(_,t))) when (force && has_seen_fun) || not force ->
+            Sast.FunApply(NhFunction(name), arg_texprs), t
+        (* don't know function signature, or do know signature but
+          forced to re-infer subexpression types *)
+        | _ ->
+          let seen_funs =
+            if has_seen_fun
+            (* if the function is already seen, we are in a loop - can't infer type;
+              roll back to most recent conditional and see what we can do there
+              (conditional catches Cant_infer_type exception) *)
+            then raise
+              (Cant_infer_type("Can't infer type of recursive call to nh function "^name))
+            (* function not seen yet; we need to infer subexpression types, so mark this function as seen *)
+            else (name,tparams):: seen_funs
+          in
+          let try_check_function_type force =
+            (* forcing type inference means that cached results in
+              tfuns_ref will be ignored unless a loop is encountered *)
+            try check_function_type tparams expr tfuns_ref env seen_funs force
+            with Failure(reason) ->
+              Log.info "Function template type check failed. Inner exception: %s" reason;
+              failwith ("Incorrect types passed into function "^name)
+          in
+          (* check if types of inputs can be used with this function *)
+          let (sexpr, t) = try_check_function_type force in
+          begin
+          (* UPDATE tfuns_ref *)
+          ignore(replace_add_fun tfuns_ref (Sast.FunDef(name, tparams, (sexpr, t))));
+          (* check if it is safe to re-infer all subexpression types (ie tfun_ref is fully updated)
+              and that we are not already trying to re-infer all subexpression types *)
+          if List.length seen_funs = 1 && not force
+            (* go back in to resolve all types; 
+              second pass guarantees no placeholder conditionals are in descendants *)
+            then let (sexpr, t) = try_check_function_type true in
+              ignore(replace_add_fun tfuns_ref (Sast.FunDef(name, tparams, (sexpr, t))));
+              Sast.FunApply(NhFunction(name), arg_texprs), t
+            (* pass sast back up the ast so higher expressions can infer type;
+              could still have placeholder conditionals in descendants *)
+            else Sast.FunApply(NhFunction(name), arg_texprs), t
+          end
     
     (* C++ function calls *)
     else
@@ -266,7 +311,7 @@ let rec sast_expr env tfuns_ref e =
                       extern_functions=env.extern_functions; types=env.types; }
                 | _ -> env
               end
-        in let texpr = sast_expr env tfuns_ref expr in
+        in let texpr = sast_expr ~seen_funs:seen_funs env tfuns_ref expr in
         (texpr :: texprs, env)
       )
     in
@@ -301,12 +346,46 @@ let rec sast_expr env tfuns_ref e =
       let (condition, condition_t) = sast_expr_env condition in
       if condition_t <> Ast.Bool then
         failwith (sprintf "Condition must be a bool expression (%s found)" (Ast.string_of_type condition_t)) else
-      let (case_true, case_true_t) = sast_expr_env case_true
-      and (case_false, case_false_t) = sast_expr_env case_false in
-      if case_true_t <> case_false_t then
-        failwith (sprintf "Both expressions in a conditional must have the same type (%s and %s found)"
-          (Ast.string_of_type case_true_t) (Ast.string_of_type case_false_t)) else
-      Sast.Conditional( (condition, condition_t), (case_true, case_true_t), (case_false, case_false_t) ), case_true_t
+
+      let try_sast_expr_env expr =
+        try Some(sast_expr_env expr)
+        (* Note that Cant_infer_type is raised when an nh function has already
+          been seen higher up in the ast and it's not in tfuns_ref either *)
+        (* Also note that this case won't trigger if force was set to true (from FunApply) *)
+        with Cant_infer_type(_) -> None
+      in
+      (* try to infer type of true branch *)
+      begin match try_sast_expr_env case_true with
+        (* true branch type inference failed,
+          ie tfuns_ref is missing an nh function that has been used higher up in the ast *)
+        | None ->
+            (* see if other case can infer type *)
+            begin match try_sast_expr_env case_false with
+              (* neither branch terminates *)
+              | None -> failwith "Couldn't infer type of either branch of conditional"
+              (* only false branch terminates, assume entire conditional is of that type;
+                return fake sast with correct type so that tfuns_ref can be updated *)
+              | Some((_,t)) ->
+                  let fake_sexpr = (Sast.LitUnit, t) in
+                  Sast.Conditional((condition, condition_t), fake_sexpr, fake_sexpr), t
+            end
+        (* true branch type inference successful, now check false branch *)
+        | Some((case_true, case_true_t)) ->
+            (* see if other case can infer type *)
+            begin match try_sast_expr_env case_false with
+              (* both branch types have been inferred, check if types are the same *)
+              | Some((case_false, case_false_t)) -> if case_true_t <> case_false_t
+                  then failwith (sprintf "Both expressions in a conditional must have the same type (%s and %s found)"
+                    (Ast.string_of_type case_true_t) (Ast.string_of_type case_false_t))
+                  else Sast.Conditional( (condition, condition_t), (case_true, case_true_t), (case_false, case_false_t) ), case_true_t
+              (* false branch type inference failed, ie tfuns_ref is missing an nh function that
+                  has been used higher up in the ast;
+                true branch terminates, assume entire conditional is of that type;
+                return fake sast with correct type so that tfuns_ref can be updated *)
+              | None -> let fake_sexpr = (Sast.LitUnit, case_true_t) in
+                  Sast.Conditional((condition, condition_t), fake_sexpr, fake_sexpr), case_true_t
+            end
+      end
   
   | For(loop_var_name, items, body) ->
     ignore (loop_var_name, items, body); failwith "Type checking not implemented for For"
@@ -315,7 +394,7 @@ let rec sast_expr env tfuns_ref e =
     ignore msg; failwith "Type checking not implemented for Throw"
   
   | Assign(names, expr) ->
-      let (value, tvalue) = sast_expr env tfuns_ref expr in
+      let (value, tvalue) = sast_expr_env expr in
       begin match names with
         | [] -> failwith "Internal error: Assign(names, _) had empty string list"
         | name :: fields -> try begin
@@ -341,7 +420,7 @@ let rec sast_expr env tfuns_ref e =
         | None -> failwith ("type "^typename^" not found")
       in
       let fields = List.map defaults ~f:(fun (n,(_,t)) -> (n,t)) in
-      let sexprs = List.map init_list ~f:(sast_expr env tfuns_ref) in
+      let sexprs = List.map init_list ~f:(sast_expr_env) in
       let varname = function
         | Init(name,(_,t)),_
             when begin match List.find fields ~f:(fun (n,_) -> n = name) with
@@ -380,14 +459,15 @@ let rec sast_expr env tfuns_ref e =
 
 
 
-and check_function_type tparams expr tfuns_ref env = 
+and check_function_type tparams expr tfuns_ref env seen_funs force = 
   let env' = {
-    scope = { variables = tparams; parent = env.scope.parent };
+    (* allow global scope *)
+    scope = { variables = tparams; parent = Some(get_top_scope env.scope) };
     functions = env.functions;
     extern_functions = env.extern_functions;
     types = env.types;
   } in
-  sast_expr env' tfuns_ref expr
+  sast_expr ~seen_funs:seen_funs ~force:force env' tfuns_ref expr
 
 and typed_typedefs env tfuns_ref typedefs =
   (* Assuming the users have defined the types in the correct order *)
diff --git a/test/fundef_mutual_rec.nh b/test/fundef_mutual_rec.nh
new file mode 100644
index 0000000..fe50a76
--- /dev/null
+++ b/test/fundef_mutual_rec.nh
@@ -0,0 +1,11 @@
+
+fun First x = (
+  Print (StringOfInt x)
+  if x > 1 then (Print "s"; Second x; "not") else "done"
+)
+
+fun Second x = (
+  Print (First (x-1))
+)
+
+Print (First 5)
diff --git a/test/fundef_mutual_rec.out b/test/fundef_mutual_rec.out
new file mode 100644
index 0000000..ff441e6
--- /dev/null
+++ b/test/fundef_mutual_rec.out
@@ -0,0 +1 @@
+5s4s3s2s1donenotnotnotnot
\ No newline at end of file
diff --git a/test/fundef_rec.nh b/test/fundef_rec.nh
new file mode 100644
index 0000000..b103617
--- /dev/null
+++ b/test/fundef_rec.nh
@@ -0,0 +1,5 @@
+
+fun Factorial x = if x <= 1 then 1 else x * Factorial (x-1)
+
+x = Factorial 3
+Print (StringOfInt x)
diff --git a/test/fundef_rec.out b/test/fundef_rec.out
new file mode 100644
index 0000000..62f9457
--- /dev/null
+++ b/test/fundef_rec.out
@@ -0,0 +1 @@
+6
\ No newline at end of file
diff --git a/test/fundef_rec_notail.nh b/test/fundef_rec_notail.nh
new file mode 100644
index 0000000..f072df8
--- /dev/null
+++ b/test/fundef_rec_notail.nh
@@ -0,0 +1,5 @@
+
+fun Factorial x = if x > 1 then x * Factorial (x-1) else 1
+
+x = Factorial 3
+Print (StringOfInt x)
diff --git a/test/fundef_rec_notail.out b/test/fundef_rec_notail.out
new file mode 100644
index 0000000..62f9457
--- /dev/null
+++ b/test/fundef_rec_notail.out
@@ -0,0 +1 @@
+6
\ No newline at end of file
diff --git a/test/fundef_simple.nh b/test/fundef_simple.nh
new file mode 100644
index 0000000..a2c397e
--- /dev/null
+++ b/test/fundef_simple.nh
@@ -0,0 +1,5 @@
+
+fun Hello x = x
+
+PrintEndline (Hello "what")
+PrintEndline (StringOfInt (Hello 1))
diff --git a/test/fundef_simple.out b/test/fundef_simple.out
new file mode 100644
index 0000000..acb2571
--- /dev/null
+++ b/test/fundef_simple.out
@@ -0,0 +1,2 @@
+what
+1
diff --git a/test/simple_assign.nh b/test/simple_assign.nh
index 94faedd..47d8638 100644
--- a/test/simple_assign.nh
+++ b/test/simple_assign.nh
@@ -1,7 +1,7 @@
 
-x = 5
+x = "x"
 y = 10
 
-Print (StringOfInt x)
+Print x
 Print "\n"
 Print (StringOfInt y)
diff --git a/test/simple_assign.out b/test/simple_assign.out
index 81882f0..63cf67f 100644
--- a/test/simple_assign.out
+++ b/test/simple_assign.out
@@ -1,2 +1,2 @@
-5
+x
 10
\ No newline at end of file
diff --git a/test/simple_varref.nh b/test/simple_varref.nh
new file mode 100644
index 0000000..461a23f
--- /dev/null
+++ b/test/simple_varref.nh
@@ -0,0 +1,3 @@
+
+x = 5
+x
diff --git a/test/simple_varref.out b/test/simple_varref.out
new file mode 100644
index 0000000..e69de29
diff --git a/test/typedef_chained.nh b/test/typedef_chained.nh
new file mode 100644
index 0000000..8c8eac8
--- /dev/null
+++ b/test/typedef_chained.nh
@@ -0,0 +1,16 @@
+
+type first = {
+  f = "hello"
+}
+
+type second = {
+  s = init first
+}
+
+type third = {
+  t = init second
+}
+
+x = init third
+
+Print x$t$s$f
diff --git a/test/typedef_chained.out b/test/typedef_chained.out
new file mode 100644
index 0000000..b6fc4c6
--- /dev/null
+++ b/test/typedef_chained.out
@@ -0,0 +1 @@
+hello
\ No newline at end of file