dgraph ocaml

ocaml/Resolution.ml

@@ -0,0 +1,128 @@
+open Unification
+
+(* ========================================
+     Definitions
+   ======================================== *)
+
+type pol = Pos | Neg | Npol
+type ray = Var of id | Func of (id * pol * ray list)
+type star = ray list
+type constellation = star list
+type graph = (int * int) * (ray * ray) list
+
+(* List monad *)
+let return x = [x] (*plongement dans la monade de liste*)
+let (>>=) xs k = List.flatten (List.map k xs)
+let guard c x = if c then return x else []
+
+(* ========================================
+     Useful functions
+   ======================================== *)
+
+(* Convert a pol and an id to a string, adding + or - before the id *)
+
+let pol_to_string pol id =
+    if pol = Pos then "+" ^ id 
+    else if pol = Neg then "-" ^ id 
+    else id
+
+(* Convert a ray (which is polarized) to a term *)
+
+let rec ray_to_term r =
+  match r with
+  | Var id -> (Var(id) : term)
+  | Func(id, pol, raylist) -> (Func(pol_to_string pol id, List.map ray_to_term raylist) : term)
+
+(* Invert polarization of a pol*)
+
+let inv_pol pol = 
+    if pol = Pos then Neg
+    else if pol = Neg then Pos 
+    else pol
+
+(* Invert the polarization of a ray to allow an easier Unification writing *)
+
+let rec inv_pol_ray ray = 
+    match ray with
+    | Func(id, pol, raylist) -> Func(id, inv_pol pol, List.map inv_pol_ray raylist)
+    | _ -> ray
+
+(* Checks if a ray is polarised *)
+
+let rec is_polarised r =
+    match r with
+    | Var id -> false
+    | Func(_, p, r) -> (p <> Npol) || (List.fold_left (fun acc b -> (is_polarised b) || acc) false r)
+
+(* Checks if two rays are dual, meaning that after inverting polarization of one ray, the two rays can be unified *)
+
+let dual_check r1 r2 =
+  if (is_polarised r1 && is_polarised r2) then 
+  (solve [(extends_varname (ray_to_term (inv_pol_ray r1)) "0"), (extends_varname ((ray_to_term r2)) "1")] []) 
+  else None
+
+(* Create an index for a constellation *)
+
+let index_constellation const = 
+    List.combine (List.init (List.length const) (fun a -> a)) const
+
+(* Make a list of links between two stars using their indexes*)
+
+let are_linked (i, il) (j, jl) =
+  List.fold_left (fun link_list ray -> 
+      List.fold_left (fun rl rs -> 
+          let uni = dual_check ray rs in 
+          if Option.is_some uni then ((i,j),(ray,rs))::rl else rl
+        ) [] jl ) [] il
+
+(* ========================================
+     Constellation graph
+   ======================================== *)
+
+(* Makes a dgraph from a constellation *)
+let dgraph const =
+  let indexed_const = index_constellation const in 
+  indexed_const >>= fun (i, il) ->
+  indexed_const >>= fun (j, jl) -> 
+  guard (j >= i) (are_linked (i, il) (j, jl))
+
+(* Convert a link to a string to be printable *)
+
+let link_to_string dg = 
+  let rec aux dgl =
+    match dgl with
+    | [] -> ""
+    | ((i,j),(r1, r2))::[] -> ("(" ^ string_of_int i ^ ", " ^ string_of_int j ^ ")" ^ "," ^ "(" ^ term_to_string (ray_to_term r1) ^ ", " ^ term_to_string (ray_to_term r2) ^ ")")
+    | ((i,j),(r1, r2))::t -> ("(" ^ string_of_int i ^ ", " ^ string_of_int j ^ ")" ^ "," ^ "(" ^ term_to_string (ray_to_term r1) ^ ", " ^ term_to_string (ray_to_term r2) ^ ")") ^ "+" ^ (aux t)
+  in aux dg ;;
+
+(* Print a dgraph *)
+
+let print_dgraph dg =
+  let rec aux dgl =
+    match dgl with
+    | [] -> ""
+    | h::[] -> (link_to_string h)
+    | h::t -> (link_to_string h) ^ "\n" ^ aux t 
+  in print_string (aux dg);;
+
+(* _________ Examples _________ *)
+let y = Var("y")
+let x = Var("x")
+let z = Var("z")
+let r = Var("r")
+let zero = Func("0", Npol, [])
+let s x = Func("s", Npol, [x])
+let add p x y z = Func("add", p, [x;y;z])
+
+(* Convert int to term *)
+let rec enat i = 
+  if i = 0 then Func("0", Npol, []) else s (enat (i-1))
+
+(* makes the constellation corresponding to an addition *)
+let make_const_add n m = 
+  [[add Pos zero y y]; [add Neg x y z; add Pos (s x) y (s z)]; [add Neg (enat n) (enat m) r; r]] 
+
+let constellation = make_const_add 3 1 ;;
+
+print_dgraph (dgraph constellation) ;;

ocaml/Unification.ml

@@ -1,8 +1,7 @@
 open List
 (* ========================================
      Definitions
-   ========================================
+   ======================================== *)
- *)
 
 type id = string
 type term = Var of id | Func of (id * term list)
@@ -10,9 +9,7 @@ type term = Var of id | Func of (id * term list)
 type subst = id * term list
 type equation = term * term
 
-(*
+(* Affiche un term *)
-Affiche un term
-*)
 
 let print_term t =
    let rec aux t =
@@ -27,9 +24,7 @@ let print_term t =
       in (aux2 tl) ^ ")"
    in print_string (aux t)
 
-(*
+(* Fonction de comparaison entre deux termes sur l'ordre lexicographique *)
-Fonction de comparaison entre deux termes sur l'ordre lexicographique
-*)
 
 let rec compare_term t1 t2 =
    match t1, t2 with
@@ -40,27 +35,21 @@ let rec compare_term t1 t2 =
    else if comp < 0 then -1 
    else List.compare compare_term fs gs
 
-(*
+(* indom regarde si une variable est dans le domaine d'une substitution *)
-indom regarde si une variable est dans le domaine d'une substitution
-*)
 
 let rec indom t sl = 
   match t with
   | Var id -> List.exists (fun (a,_) -> a = id ) sl
   | Func(_, tl) -> List.exists (fun a -> indom a sl) tl
 
-(*
+(* occurs regarde si une variable apparaît dans un term *)
-occurs regarde si une variable apparaît dans un term
- *)
 
 let rec occurs id t =
   match t with
   | Var i -> i = id 
   | Func(_, tl) -> List.exists (fun a -> occurs id a) tl
 
-(*
+(* extends_varname ajoute un suffixe à toutes les variables *)
-extends_varname ajoute un suffixe à toutes les variables
-*)
 
 let rec extends_varname t ext =
   match t with
@@ -68,9 +57,7 @@ let rec extends_varname t ext =
   | Func(f, tl) -> Func(f, List.map (fun a -> extends_varname a ext) tl)
 
 
-(*
+(* vars renvoie la liste de toutes les variables d'un term *)
-vars renvoie la liste de toutes les variables d'un term
-*)
 
 let rec vars t =
   match t with
@@ -81,21 +68,36 @@ let rec vars t =
       Substitution
      ======================================== *)
 
-(*
+(* apply applique une substitution à une variable *)
-apply applique une substitution à une variable
-*)
 
 let apply id sub = let (_,s) = try List.find (fun (a,_) -> a = id ) sub with Not_found -> (id,Var(id)) in s
 
-(*
+(* subst applique une substitution sur un terme *)
-subst applique une substitution sur un terme
- *)
 
 let rec substit trm sub =
   match trm with
   | Var id -> apply id sub
   | Func(f,tl) -> Func(f,List.map (fun a -> substit a sub) tl)  
 
+  (* ========================================
+      Unification
+     ======================================== *)
+
+(* Résout une liste d'équations *)
+
+let rec solve eq sub = 
+  match eq with
+  | [] -> Some sub
+  | (Var(x), term)::t -> if Var(x) = term then Some (solve t sub) else Some (elim x term t sub) (* Si x = x c'est une équation inutile, on passe donc à la suite *)
+  | (term, Var(x))::t -> Some (elim x term t sub) (*Inutile de vérifier si term = Var(x) ici car c'est déjà vérifié à la ligne ci-dessus*)
+  | (Func(f, fs), Func(g, gs))::t -> if f = g then Some (solve ((List.combine fs gs)@t) sub) else None (*si f et g ne sont pas égaux, on ne peut pas résoudre l'équation*)
+
+and elim id term eq sub =
+  if eq = [] then Some sub
+  else if occurs id term then None (* l'équation n'est pas soluble, car on aurait quelque chose de la forme x = f(x) *)
+  else let sigma_xy = [(id, term)] in
+  Some (solve (List.map (fun (a,b) -> (substit a sigma_xy, substit b sigma_xy)) eq) (sigma_xy@sub)) (* On substitue toutes les occurences d'id dans le système d'équation et on ajoute cette solution au système *)
+
   (* ========================================
       Tests
      ======================================== *)
@@ -130,31 +132,11 @@ apply "x" subd ;;
 print_term terme ;;
 print_term (substit terme subd) ;;
 
-  (* ========================================
-      Unification
-     ======================================== *)
-
-(*Résout une liste d'équations, à modifier avec option*)
-
-let rec solve eq sub = 
-  match eq with
-  | [] -> sub
-  | (Var(x), term)::t -> if Var(x) = term then solve t sub else elim x term t sub
-  | (term, Var(x))::t -> elim x term t sub
-  | (Func(f, fs), Func(g, gs))::t -> if f = g then solve ((List.combine fs gs)@t) sub else []
-
-and elim id term eq sub =
-  if eq = [] then sub
-  else if occurs id term then []
-  else let sigma_xy = [(id, term)] in
-  solve (List.map (fun (a,b) -> (substit a sigma_xy, substit b sigma_xy)) eq) (sigma_xy@sub) 
-
 let melina = Var("Melina")
 let sieg = Var("Sieg")
 let hyetta = Var("Hyetta")
 let adeline = Var("Adeline")
 
-let terme = Func("f",[x; v; Func("g",[z; y])]) ;;
 let terme3 = Func("f",[ melina ; sieg; Func("g",[Func("h",[hyetta]); adeline])]) ;;
 
 solve [(terme,terme3)] [] ;;