let rec fact =
  \lambda x:nat.
    [\lambda x:nat. nat]
    match x:nat with
    [ O \Rightarrow 1
    | (S (x: nat)) \Rightarrow (mult (S x) (fact x)) ]
in
(fact 4)
###### INTERPRETATION NUMBER 1 ######
### (* disambiguation environment  *)
alias id S = cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)
alias id mult = cic:/Coq/Init/Peano/mult.con
alias id nat = cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)
alias num (instance 0) = "natural number"
### (* METASENV after disambiguation  *)

### (* TERM after disambiguation      *)
[fact:=
Fix fact {
fact / 0 : (nat->nat) := 
[x:nat]
<[x:nat]nat>Cases x of 
 O => (S O)
 S => [x:nat](mult (S x) (fact x))
end}
](fact (S (S (S (S O)))))
### (* TYPE_OF the disambiguated term *)
nat
### (* REDUCED disambiguated term     *)
(S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) O)))))) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) O)))))) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) O)))))) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 (S (
Fix plus {
plus / 0 : (nat->(nat->nat)) := 
[n:nat][m:nat]
<[n0:nat]nat>Cases n of 
 O => m
 S => [p:nat](S (plus p m))
end}
 O O)) O)))))) O))))))))