diff --git a/graph-lib/graph/graph-6-rich-returns-problem.scrbl b/graph-lib/graph/graph-6-rich-returns-problem.scrbl
new file mode 100644
index 00000000..60d0fb3b
--- /dev/null
+++ b/graph-lib/graph/graph-6-rich-returns-problem.scrbl
@@ -0,0 +1,93 @@
+#lang scribble/lp2
+
+@section{Problem 1}
+
+For the rich-returns graph, we want to detect nodes from the
+first step, and convert them to the appropriate value for
+the second step.
+
+The issue is that @racket[tmpl-replace-in-instance]
+requires us to provide a predicate which matches the types
+we should replace.
+
+Variants should all be subtypes of the global Tagged type,
+so that we can access their contents via the @racket[dot]
+operator without having to know the variant's tag (when
+accessing a node's content: nodes are tagged).
+
+@section{Problem 2}
+
+Graph subtyping: It seems reasonable to not allow arbitrary
+subtyping for graphs, as a pass might not be semantically
+correct if it ignores some of the nodes of the graph. For
+example, let's say we have a replace-arithmetic pass:
+
+@chunk[<replace-arithmetic-pass>
+       (define-pass replace-arithmetic
+         [(add a b) (arithmetic 'add a b)]
+         [(mul a b) (arithmetic 'mul a b)]
+         [(div a b) (arithmetic 'div a b)])]
+
+If the pass above is called on a graph @racket[g-div] where
+divisions are already marked as safe (@racket[b] is never 
+@racket[0]) or unsafe (@racket[b] can be @racket[0]), the
+resulting graph will have @racket[arithmetic] nodes
+@emph{and} @racket[div-unsafe] ones, whereas one would
+semantically expect the @racket[div-unsafe] nodes to have
+been merged too:
+
+@chunk[<g-div>
+       (define-graph (g-div)
+         (var [name : String])
+         (add [a : var] [b : var])
+         (mul [a : var] [b : var])
+         (div [a : var] [b : var])
+         (div-unsafe [a : var] [b : var] [on-error-message : String])
+         other-nodes …)]
+
+We do however wish to be able to test a pass without having
+to care about the irrelevant nodes. We could specify a union
+of graph types when writing the pass. The 
+@racket[replace-arithmetic] pass would then be declared as
+follows:
+
+@chunk[<replace-arithmetic-pass>
+       (define-pass (replace-arithmetic [x : (U g g-test)]) : g-arith
+         [(add a b) (arithmetic 'add a b)]
+         [(mul a b) (arithmetic 'mul a b)]
+         [(div a b) (arithmetic 'div a b)])]
+
+Where @racket[g] has been declared using:
+
+@chunk[<g>
+       (define-graph (g)
+         (var [name : String])
+         (add [a : var] [b : var])
+         (mul [a : var] [b : var])
+         (div [a : var] [b : var])
+         other-nodes …)]
+
+And @racket[g-test], which does not contain the 
+@racket[other-nodes] has been declared using:
+
+@chunk[<g-test>
+       (define-graph (g-test)
+         (var [name : String])
+         (add [a : var] [b : var])
+         (mul [a : var] [b : var])
+         (div [a : var] [b : var]))]
+
+The @racket[g-test] declaration could easily be derived
+from the pass declaration, by removing the node types not
+mentionned within.
+
+@subsection{Graph operations}
+
+The graph operations should not require specifying the type
+however: ideally, one should write the input graph type name
+only in the parameter list of the pass, and not have to
+refer to it within the pass body for common operations. Thes
+operations include:
+
+@chunk[<*>
+       (begin)]
\ No newline at end of file
diff --git a/graph-lib/graph/problems.rkt b/graph-lib/graph/problems.rkt
new file mode 100644
index 00000000..e1de9b71
--- /dev/null
+++ b/graph-lib/graph/problems.rkt
@@ -0,0 +1,151 @@
+#lang typed/racket
+
+(require typed/rackunit)
+
+;; tagged
+(begin
+  ;; Base struct for all tagged values
+  (struct (A B) tagged ([tag : A] [value : B]))
+  
+  ;; (define-tagged a T)
+  ;; Use tag-a just for match and (get …)
+  (struct tag-a ()) ;; "remember" this one
+  (define-type (tagged-a T) (tagged tag-a T))
+  ;; (define-tagged #:uninterned a T)
+  (struct tag-a-1 tag-a ()) ;; do not "rembmer" the #:uninterned ones
+  (define-type (tagged-a-1 T) (tagged tag-a-1 T))
+  ;; (define-tagged #:uninterned a T)
+  (struct tag-a-2 tag-a ())
+  (define-type (tagged-a-2 T) (tagged tag-a-2 T))
+  ;; (define-tagged #:uninterned a T)
+  (struct tag-a-3 tag-a ())
+  (define-type (tagged-a-3 T) (tagged tag-a-3 T))
+  ;; (define-tagged b T)
+  (struct tag-b ())
+  (define-type (tagged-b T) (tagged tag-b T))
+  
+  ;; instanciation:
+  (tagged (tag-a) "ice")
+  
+  (define-syntax-rule (define-pred name? tag)
+    (define-match-expander name?
+      (λ (stx)
+        (syntax-case stx ()
+          [(_ v)
+           #'(and (? name?) (app tagged-value v))]))
+      (λ (stx)
+        (syntax-case stx ()
+          [(_ v)
+           #'(let ([v-cache v])
+               ;; make-predicate works for polymorphic structs when
+               ;; instantiating them with Any.
+               (and ((make-predicate (tagged Any Any)) v-cache)
+                    ((make-predicate tag) (tagged-tag v-cache))))]))))
+  
+  (define-pred tagged-a-1? tag-a-1)
+  (define-pred tagged-a-2? tag-a-2)
+  (define-pred tagged-a? tag-a)
+  (define-pred tagged-b? tag-b)
+  
+  (check-true (tagged-a? (tagged (tag-a) "water")))
+  (check-true (tagged-a-1? (tagged (tag-a-1) "fire")))
+  (check-true (tagged-a-1? (tagged (tag-a-1) "air")))
+  (check-false (tagged-a-1? (tagged (tag-a-2) "earth")))
+  (check-false (tagged-a-1? (tagged (tag-a) "salt")))
+  (check-false (tagged-b? (tagged (tag-a) "mercury")))
+  (check-false (tagged-b? (tagged (tag-a-1) "alchemy")))
+  
+  (λ ([x : (U (tagged-a-1 String)
+              (tagged-a-2 Number)
+              (tagged-b Symbol))])
+    : (U Number String)
+    ;; Match should expand to this:
+    (match x
+      [(tagged-a? v) v]
+      [(tagged-b? v) (symbol->string v)]))
+  
+  (λ ([x : (U (tagged-a-1 String)
+              (tagged-a-2 String)
+              (tagged tag-a String)
+              (tagged-b Symbol))])
+    : String
+    ;; Match should expand to this
+    (match x
+      [(tagged-a-1? v) (string-append v "-1")]
+      [(tagged-a-2? v) (string-append v "-2")]
+      [(tagged-a? v) (string-append v "-base")]
+      [(tagged-b? v) (symbol->string v)])))
+
+;; struct
+(begin
+  ;; The structs seem to work well the way they are currently defined (using
+  ;; "remember" to know all the structs with a given field).
+  
+  ;; (define-struct [x : Number] [y : String])
+  (struct (X Y) structure+x+y ([x : X] [y : Y])) ;; "remember"
+  (define-type structure+x=number+y=string (structure+x+y Number String))
+  
+  ;; (define-struct [x : Number] [y : String] [z : Symbol])
+  (struct (X Y Z) structure+x+y+z ([x : X] [y : Y] [z : Z])) ;; "remember"
+  (define-type structure+x=number+y=string+z=symbol
+    (structure+x+y+z Number String Symbol))
+  
+  ;; (define-struct [z : Symbol])
+  (struct (Z) structure+z ([z : Z])) ;; "remember"
+  (define-type structure+z=symbol (structure+z Symbol))
+  
+  ;; (define-struct [x : Symbol])
+  (struct (X) structure+x ([x : X])) ;; "remember"
+  (define-type structure+x=symbol (structure+x Symbol))
+  
+  ;; (has-get [x Number])
+  (define-type (has-get+x X) (U (structure+x X)
+                                (structure+x+y X Any)
+                                (structure+x+y+z X Any Any)))
+  (define-type has-get+x=number (has-get+x Number))
+  
+  ;; (has-get [y Number])
+  (define-type (has-get+y Y) (U (structure+x+y Any Y)
+                                (structure+x+y+z Any Y Any)))
+  (define-type has-get+y=number (has-get+y Number))
+  
+  ;; (has-get [z Number])
+  (define-type (has-get+z Z) (U (structure+z Z)
+                                (structure+x+y+z Any Any Z)))
+  (define-type has-get+z=number (has-get+z Number))
+  
+  ;; (get v x)
+  (define get-x
+    (λ #:∀ (X) ([s : (has-get+x X)]) : X
+      (cond
+        [(structure+x? s) (structure+x-x s)]
+        [(structure+x+y? s) (structure+x+y-x s)]
+        [(structure+x+y+z? s) (structure+x+y+z-x s)])))
+  
+  ;; (get v y)
+  (define get-y
+    (λ #:∀ (Y) ([s : (has-get+y Y)]) : Y
+      (cond
+        [(structure+x+y? s) (structure+x+y-y s)]
+        [(structure+x+y+z? s) (structure+x+y+z-y s)])))
+  
+  ;; (get v z)
+  (define get-z
+    (λ #:∀ (Z) ([s : (has-get+z Z)]) : Z
+      (cond
+        [(structure+z? s) (structure+z-z s)]
+        [(structure+x+y+z? s) (structure+x+y+z-z s)]))))
+
+;; graph
+(begin
+  ;; define-graph
+  (define-type g-test (tagged-a-1 (structure+x+y String g-test)))
+  (define-type g (tagged-a-2 (structure+x+y+z String g Number)))
+  ;; pass:
+  (λ ([root-node : (U g g-test)])
+    (ann (match root-node
+           [(tagged-a-1? s) (string-length (get-x s))]
+           [(tagged-a-2? s) (get-z s)])
+         Number)
+    (cons (get-x (tagged-value root-node))
+          (get-y (tagged-value root-node)))))