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128 lines
4.0 KiB
128 lines
4.0 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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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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(* Make a list of links between two stars using their indexes*) |
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let are_linked (i, il) (j, jl) = |
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List.fold_left (fun link_list ray -> |
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List.fold_left (fun rl rs -> |
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let uni = dual_check ray rs in |
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if Option.is_some uni then ((i,j),(ray,rs))::rl else rl |
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) [] jl ) [] il |
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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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guard (j >= i) (are_linked (i, il) (j, jl)) |
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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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(* _________ Examples _________ *) |
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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 = Func("0", Npol, []) |
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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 Func("0", Npol, []) 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 3 1 ;; |
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print_dgraph (dgraph constellation) ;; |