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264 lines
9.6 KiB
264 lines
9.6 KiB
open Unification |
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(* ======================================== |
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Definitions |
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======================================== *) |
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type pol = Pos | Neg | Npol |
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type ray = Var of id | Func of (id * pol * ray list) |
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(* alternative ray definition using terms *) |
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(* type ray = PR of id * pol * ray | NR of term *) |
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type star = ray list |
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type constellation = star list |
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type graph = (int * int) * (ray * ray) list |
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(* List monad *) |
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let return x = [x] (*plongement dans la monade de liste*) |
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let (>>=) xs k = List.flatten (List.map k xs) |
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let guard c x = if c then return x else [] |
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(* ======================================== |
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Useful functions |
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======================================== *) |
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(* Convert a pol and an id to a string, adding + or - before the id *) |
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let pol_to_string pol id = |
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if pol = Pos then "+" ^ id |
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else if pol = Neg then "-" ^ id |
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else id |
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(* Convert a ray (which is polarized) to a term *) |
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let rec ray_to_term r = |
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match r with |
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| Var id -> (Var(id) : term) |
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| Func(id, pol, raylist) -> (Func(pol_to_string pol id, List.map ray_to_term raylist) : term) |
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(* Invert polarization of a pol*) |
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let inv_pol pol = |
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if pol = Pos then Neg |
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else if pol = Neg then Pos |
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else pol |
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(* Invert the polarization of a ray to allow an easier Unification writing *) |
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let rec inv_pol_ray ray = |
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match ray with |
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| Func(id, pol, raylist) -> Func(id, inv_pol pol, List.map inv_pol_ray raylist) |
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| _ -> ray |
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(* Checks if a ray is polarised *) |
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let rec is_polarised r = |
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match r with |
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| Var id -> false |
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| Func(_, p, r) -> (p <> Npol) || (List.fold_left (fun acc b -> (is_polarised b) || acc) false r) |
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(* Checks if two rays are dual, meaning that after inverting polarization of one ray, the two rays can be unified *) |
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let dual_check r1 r2 = |
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if (is_polarised r1 && is_polarised r2) then |
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(solve [(extends_varname (ray_to_term (inv_pol_ray r1)) "0"), (extends_varname ((ray_to_term r2)) "1")] []) |
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else None |
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(* Create an index for a constellation *) |
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let index_constellation const = |
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List.combine (List.init (List.length const) (fun a -> a)) const |
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(* apply_ray applies a substitution to a var of a ray*) |
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let apply_ray id sub = |
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let (_,s) = try List.find (fun (a,_) -> a = id ) sub with Not_found -> (id,Var(id)) in (s :ray) |
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(* substit_ray applies all possible substition from an environment to a ray *) |
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let rec substit_ray ray sub = |
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match ray with |
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| Var id -> apply_ray id sub |
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| Func(f, p, tl) -> Func(f, p, List.map (fun a -> substit_ray a sub) tl) |
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(* substit_star applies all possible substition from an environment to a star *) |
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let substit_star star sub = |
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List.map (fun a -> substit_ray a sub) star |
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(* substit_const applies all possible substition from an environment to a constellation *) |
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let substit_const const sub = |
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List.map (fun a -> substit_star a sub) const |
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(* extends_varname adds suffix to all var names of a ray *) |
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let rec extends_varname_ray t ext = |
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match t with |
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| Var id -> Var(id ^ ext) |
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| Func(f, p, tl) -> Func(f, p, List.map (fun a -> extends_varname_ray a ext) tl) |
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(* extends_varname adds suffix to all var names of a star *) |
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let extends_varname_star const ext = |
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List.map (fun a -> extends_varname_ray a ext) const |
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(* extends_varname adds suffix to all var names of a constellation based on each star number after being indexed *) |
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let extends_varname_const const = |
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List.map (fun (i,a) -> extends_varname_star a (string_of_int i)) (index_constellation const) |
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(* convert a term to a ray *) |
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let rec term_to_ray (term : term) = |
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match term with |
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| Var id -> (Var(id) : ray) |
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| Func(f, r) -> Func(f, Npol, List.map (fun a -> term_to_ray a) r) |
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(* ======================================== |
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Constellation graph |
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======================================== *) |
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(* Makes a dgraph from a constellation *) |
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let dgraph const = |
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let indexed_const = index_constellation const in |
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indexed_const >>= fun (i, il) -> |
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indexed_const >>= fun (j, jl) -> |
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il >>= fun r1 -> |
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jl >>= fun r2 -> |
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guard (j >= i) ( let uni = dual_check r1 r2 in |
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if Option.is_some uni then [((i,j),(r1,r2))] |
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else []) |
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(* Convert a link to a string to be printable *) |
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let link_to_string dg = |
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let rec aux dgl = |
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match dgl with |
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| [] -> "" |
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| ((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) ^ ")") |
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| ((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) |
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in aux dg ;; |
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(* Print a dgraph *) |
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let print_dgraph dg = |
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let rec aux dgl = |
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match dgl with |
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| [] -> "" |
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| h::[] -> (link_to_string h) |
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| h::t -> (link_to_string h) ^ "\n" ^ aux t |
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in print_string (aux dg);; |
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let clean_dgraph g = |
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List.filter (fun a -> a <> []) g |
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(* _________ Examples _________ *) |
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let make_const_pol pol c = Func (c, pol, []) |
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let make_const c = make_const_pol Npol c |
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let y = Var("y") |
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let x = Var("x") |
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let z = Var("z") |
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let r = Var("r") |
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let zero = make_const "0" |
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let s x = Func("s", Npol, [x]) |
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let add p x y z = Func("add", p, [x;y;z]) |
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(* Convert int to term *) |
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let rec enat i = |
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if i = 0 then zero else s (enat (i-1)) |
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(* makes the constellation corresponding to an addition *) |
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let make_const_add n m = |
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[[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]] |
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let constellation = make_const_add 1 3 ;; |
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print_dgraph (dgraph constellation) ;; |
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(* former try |
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let exec graph const = |
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let rec aux graph sol = |
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match graph with |
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| [] -> Some sol |
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| h::tail -> |
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let rec aux2 glink sol = |
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match glink, sol with |
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| [], _ -> aux tail sol |
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| ((i,j),(ri, rj))::t,(Some sola, solb) -> |
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aux2 t (solve [(substit (ray_to_term ri) sola,substit (ray_to_term rj) sola)] sola, (List.filter (fun a -> a <> ri) (List.nth const i))@solb ) |
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| (_,(None,_)) -> None |
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in aux2 h sol |
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in aux graph (Some [],[]) ;; |
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former try |
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let exec2 graph const = |
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let rec aux graph sol = |
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match graph with |
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| [] -> Some sol |
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| h::tail -> |
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let rec aux2 glink sol = |
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match glink, sol with |
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| [], _ -> aux tail sol |
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| ((i,j),(ri, rj))::t,(Some sola, solb) -> |
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aux2 t (let eq = ((ray_to_term ri),(ray_to_term rj))::sola in |
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if (solve eq []) = None then |
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failwith "marchpo" |
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else Some eq, |
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(List.filter (fun a -> a <> ri) (List.nth const i))@solb ) |
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| (_,(None,_)) -> None |
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in aux2 h sol |
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in aux graph (Some [],[]) ;; |
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*) |
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(* token is a couple of a family number and a star number in the constellation *) |
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type token = int * int |
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type process = token list |
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(* get a star using its number in the list from a constellation *) |
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let get_star const i = |
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List.nth const i |
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(* Takes a constellation, a ray and a (ray,ray) list and extracts rays from stars number i (respectively j) that are not ri (respectively rj) when ri (respectively rj) isn't in the prob list *) |
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let star_filter const ((i, j),(ri,rj)) prob = |
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let (prob_a, prob_b) = List.split prob in |
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(if List.mem ri prob_a then [] |
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else (List.filter (fun a -> a <> ri) (get_star const i)) |
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)@( |
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if List.mem rj prob_b then [] |
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else (List.filter (fun a -> a <> rj) (get_star const j)) |
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) |
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(* convert the (ray,ray) list part of a link to an equation, converting its rays to terms *) |
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let link_to_eq prob = |
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List.map (fun (ra, rb) -> (ray_to_term (inv_pol_ray ra)), ray_to_term rb) prob |
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(* removes prob rays from stars *) |
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let star_postfilter star prob = |
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let (prob_a, prob_b) = List.split prob in |
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List.filter (fun a -> Not(List.mem a prob_a || List.mem a prob_b )) star |
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(* takes a token, a graph and a constellation and returns the list of tokens to check next and a list of solvable equation *) |
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let divide_token (fam, n_star) graph const = |
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let rec aux g toklist prob fstar = |
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match g with |
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| [] -> Some (toklist,prob,fstar) |
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| h::t -> let links = List.filter (fun ((i, _),(_, _)) -> i = n_star) h in |
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let rec aux2 l tokl prob2 star2 = |
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match l with |
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| [] -> Some (toklist,prob2,star2) |
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| ((i, j),(ri,rj))::tl -> |
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if Option.is_some (solve (link_to_eq (( ri, rj)::prob2)) []) then |
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aux2 tl ((fam, j)::tokl) ((ri, rj)::prob2) ( ( star_filter const ((i, j),(ri,rj)) prob2 )@star2 ) |
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else None |
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in if links = [] then aux t toklist prob fstar else aux2 links toklist prob fstar |
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in aux graph [] [] [] |
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(* should be deterministic exec, graph shouldn't be empty *) |
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let exec const = |
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let const_ext = extends_varname_const const in |
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let graph = clean_dgraph (dgraph const_ext) in |
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let rec aux (toklist,prob,star) = |
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begin match toklist with |
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| [] -> star,prob |
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| h::t -> aux (Option.get (divide_token h graph const_ext)) |
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end |
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in let ((i,_),(_,_)) = (List.hd (List.hd graph)) in let (starf, probf) = aux ([(0,i)],[],[]) in substit_star (star_postfilter starf probf) (List.map (fun (i,b) -> (i,term_to_ray b)) (Option.get (solve (link_to_eq probf) []))) |
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(* test constellation cyclique déterministe *) |
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let test = [ [Func("c", Neg, [x]); x] ; [Func("c", Pos, [Func("f", Npol, [y])]) ; Func("c", Npol, [x]) ] ] ;; |
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print_dgraph (dgraph test);; |
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exec test ;; |
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(* TODO : |
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faire un filtre post application, const_filter |
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corriger la substitution qui ne fonctionne pas dans exec |
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*) |
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(* prob : |
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let fgraph = List.flatten graph in *) |