| A of t * t\r
| L of t\r
| B (* bottom *)\r
- | C of int\r
+ | C (* constant *)\r
;;\r
\r
let delta = L(A(V 0, V 0));;\r
| L t1, t2 -> aux l1 (l2+1) t1 t2\r
| t1, L t2 -> aux (l1+1) l2 t1 t2\r
| V a, V b -> a + l1 = b + l2\r
- | C a, C b -> a = b\r
| A(t1,t2), A(u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2\r
| _, _ -> false\r
in aux ;;\r
let rec string_of_term_w_pars level = function\r
| V v -> if v >= level then "`" ^ string_of_int (v-level) else\r
string_of_bvar (level - v-1)\r
- | C n -> "c" ^ string_of_int n\r
+ | C -> "C"\r
| A _\r
| L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"\r
| B -> "BOT"\r
function\r
| A(t,_) -> is_inert t\r
| V _ -> true\r
- | C _\r
+ | C\r
| L _ | B -> false\r
;;\r
\r
-let is_var = function V _ -> true | _ -> false;;\r
-let is_lambda = function L _ -> true | _ -> false;;\r
-\r
-let rec no_leading_lambdas = function\r
- | L t -> 1 + no_leading_lambdas t\r
- | _ -> 0\r
-;;\r
-\r
let rec get_inert = function\r
| V n -> (n,0)\r
| A(t, _) -> let hd,args = get_inert t in hd,args+1\r
| _ -> assert false\r
;;\r
\r
+(* precomputes the number of leading lambdas in a term,\r
+ after replacing _v_ w/ a term starting with n lambdas *)\r
+let rec no_leading_lambdas v n = function\r
+ | L t -> 1 + no_leading_lambdas (v+1) n t\r
+ | A _ as t -> let v', m = get_inert t in if v = v' then max 0 (n - m) else 0\r
+ | V v' -> if v = v' then n else 0\r
+ | B | C -> 0\r
+;;\r
+\r
let rec subst level delift sub =\r
function\r
| V v -> if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)\r
let t1 = subst level delift sub t1 in\r
let t2 = subst level delift sub t2 in\r
mk_app t1 t2\r
- | C _ as t -> t\r
- | B -> B\r
+ | C | B as t -> t\r
and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B\r
else match t1 with\r
- | C _ as t -> t\r
| B -> B\r
| L t1 -> subst 0 true (0, t2) t1\r
| _ -> A (t1, t2)\r
| V m -> V (if m >= lev then m + n else m)\r
| L t -> L (aux (lev+1) t)\r
| A (t1, t2) -> A (aux lev t1, aux lev t2)\r
- | C _ as t -> t\r
- | B -> B\r
+ | C | B as t -> t\r
in aux 0\r
;;\r
let subst = subst 0 false;;\r
\r
-let subst_in_problem (sub: var * t) (p: problem) =\r
-print_endline ("-- SUBST " ^ string_of_t (V (fst sub)) ^ " |-> " ^ string_of_t (snd sub));\r
+let subst_in_problem ((v, t) as sub) p =\r
+print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);\r
{p with\r
div=subst sub p.div;\r
conv=subst sub p.conv;\r
- stepped=(fst sub)::p.stepped;\r
+ stepped=v::p.stepped;\r
sigma=sub::p.sigma}\r
;;\r
\r
let get_subterm_with_head_and_args hd_var n_args =\r
let rec aux lev = function\r
- | C _\r
- | V _ | B -> None\r
+ | C | V _ | B -> None\r
| L t -> aux (lev+1) t\r
| A(t1,t2) as t ->\r
let hd_var', n_args' = get_inert t1 in\r
if hd_var' = hd_var + lev && n_args <= 1 + n_args'\r
+ (* the `+1` above is because of t2 *)\r
then Some (lift ~-lev t)\r
else match aux lev t2 with\r
| None -> aux lev t1\r
| L t -> Pure.L (purify t)\r
| A (t1,t2) -> Pure.A (purify t1, purify t2)\r
| V n -> Pure.V n\r
- | C _ -> Pure.V max_int (* FIXME *)\r
+ | C -> Pure.V (min_int/2)\r
| B -> Pure.B\r
;;\r
\r
let div = purify p.div in\r
let conv = purify p.conv in\r
let sigma = List.map (fun (v,t) -> v, purify t) sigma in\r
- let freshno = List.fold_right (fun (x,_) -> max x) sigma 0 in\r
+ let freshno = List.fold_right (max ++ fst) sigma 0 in\r
let env = Pure.env_of_sigma freshno sigma in\r
assert (Pure.diverged (Pure.mwhd (env,div,[])));\r
print_endline " D diverged.";\r
;;\r
\r
(* drops the arguments of t after the n-th *)\r
+(* FIXME! E' usato in modo improprio contando sul fatto\r
+ errato che ritorna un inerte lungo esattamente n *)\r
let inert_cut_at n t =\r
let rec aux t =\r
match t with\r
in snd (aux t)\r
;;\r
\r
-let find_eta_difference p t n_args =\r
- let t = inert_cut_at n_args t in\r
+(* return the index of the first argument with a difference\r
+ (the first argument is 0)\r
+ precondition: p.div and t have n+1 arguments\r
+ *)\r
+let find_eta_difference p t argsno =\r
+ let t = inert_cut_at argsno t in\r
let rec aux t u k = match t, u with\r
- | V _, V _ -> assert false (* div subterm of conv *)\r
+ | V _, V _ -> problem_fail p "no eta difference found (div subterm of conv?)"\r
| A(t1,t2), A(u1,u2) ->\r
- if not (eta_eq t2 u2) then ((*print_endline((string_of_t t2) ^ " <> " ^ (string_of_t u2));*) k)\r
+ if not (eta_eq t2 u2) then (k-1)\r
else aux t1 u1 (k-1)\r
| _, _ -> assert false\r
- in aux p.div t n_args\r
+ in aux p.div t argsno\r
;;\r
\r
let compute_max_lambdas_at hd_var j =\r
then max ( (*FIXME*)\r
if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd\r
then let hd', j' = get_inert t2 in j - j'\r
- else no_leading_lambdas t2)\r
+ else no_leading_lambdas hd_var j t2)\r
else id) (max (aux hd t1) (aux hd t2))\r
| L t -> aux (hd+1) t\r
- | V _ -> 0\r
+ | V _ | C -> 0\r
| _ -> assert false\r
in aux hd_var\r
;;\r
let eat p =\r
print_cmd "EAT" "";\r
let var, k = get_inert p.div in\r
+ match var with\r
+ | C | L _ | B | A _ -> assert false\r
+ | V var ->\r
let phase = p.phase in\r
- let p, t =\r
+ let p =\r
match phase with\r
| `One ->\r
let n = 1 + max\r
- (compute_max_lambdas_at var k p.div)\r
- (compute_max_lambdas_at var k p.conv) in\r
+ (compute_max_lambdas_at var (k-1) p.div)\r
+ (compute_max_lambdas_at var (k-1) p.conv) in\r
(* apply fresh vars *)\r
let p, t = fold_nat (fun (p, t) _ ->\r
let p, v = freshvar p in\r
p, A(t, V (v + k))\r
) (p, V 0) n in\r
- let p = {p with phase=`Two} in p, A(t, delta)\r
- | `Two -> p, delta in\r
- let subst = var, mk_lams t k in\r
- let p = subst_in_problem subst p in\r
- sanity p;\r
- let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in\r
+ let p = {p with phase=`Two} in\r
+ let t = A(t, delta) in\r
+ let t = fold_nat (fun t m -> A(t, V (k-m))) t (k-1) in\r
+ let subst = var, mk_lams t k in\r
+ let p = subst_in_problem subst p in\r
+ let _, args = get_inert p.div in\r
+ {p with div = inert_cut_at (args-k) p.div}\r
+ | `Two ->\r
+ let subst = var, mk_lams delta k in\r
+ subst_in_problem subst p in\r
sanity p\r
;;\r
\r
let p = subst_in_problem subst p in\r
sanity p\r
;;\r
-;;\r
-\r
-let parse strs =\r
- let rec aux level = function\r
- | Parser_andrea.Lam t -> L (aux (level + 1) t)\r
- | Parser_andrea.App (t1, t2) ->\r
- if level = 0 then mk_app (aux level t1) (aux level t2)\r
- else A(aux level t1, aux level t2)\r
- | Parser_andrea.Var v -> V v in\r
- let (tms, free) = Parser_andrea.parse_many strs in\r
- (List.map (aux 0) tms, free)\r
-;;\r
\r
let rec auto p =\r
let hd_var, n_args = get_inert p.div in\r
else auto p\r
with Done sigma -> sigma)\r
| Some t ->\r
- let j = find_eta_difference p t n_args - 1 in\r
+ let j = find_eta_difference p t n_args in\r
let k = 1 + max\r
(compute_max_lambdas_at hd_var j p.div)\r
(compute_max_lambdas_at hd_var j p.conv) in\r
auto p\r
;;\r
\r
-let problem_of div convs =\r
- let rec conv_join = function\r
- | [] -> "@"\r
- | x::xs -> conv_join xs ^ " ("^ x ^")" in\r
+let problem_of (label, div, convs, ps, var_names) =\r
print_hline ();\r
- let conv = conv_join convs in\r
- let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) in\r
+ let rec aux lev = function\r
+ | `Lam(_, t) -> L (aux (lev+1) t)\r
+ | `I (v, args) -> Listx.fold_left (fun x y -> mk_app x (aux lev y)) (aux lev (`Var v)) args\r
+ | `Var(v,_) -> if v >= lev && List.nth var_names (v-lev) = "C" then C else V v\r
+ | `N _ | `Match _ -> assert false in\r
+ assert (List.length ps = 0);\r
+ let convs = List.rev convs in\r
+ let conv = List.fold_left (fun x y -> mk_app x (aux 0 (y :> Num.nf))) (V (List.length var_names)) convs in\r
+ let var_names = "@" :: var_names in\r
+ let div = match div with\r
+ | Some div -> aux 0 (div :> Num.nf)\r
+ | None -> assert false in\r
let varno = List.length var_names in\r
let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]; phase=`One} in\r
(* initial sanity check *)\r
else check p (auto p)\r
;;\r
\r
-let run x y = solve (problem_of x y);;\r
+Problems.main (solve ++ problem_of);\r
\r
(* Example usage of interactive: *)\r
\r
(* interactive "x y"\r
"@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]\r
;; *)\r
-\r
-run "x x" ["x y"; "y y"; "y x"] ;;\r
-run "x y" ["x (_. x)"; "y z"; "y x"] ;;\r
-run "a (x. x b) (x. x c)" ["a (x. b b) @"; "a @ c"; "a (x. x x) a"; "a (a a a) (a c c)"] ;;\r
-\r
-run "x (y. x y y)" ["x (y. x y x)"] ;;\r
-\r
-run "x a a a a" [\r
- "x b a a a";\r
- "x a b a a";\r
- "x a a b a";\r
- "x a a a b";\r
-] ;;\r
-\r
-(* Controesempio ad usare un conto dei lambda che non considere le permutazioni *)\r
-run "x a a a a (x (x. x x) @ @ (_._.x. x x) x) b b b" [\r
- "x a a a a (_. a) b b b";\r
- "x a a a a (_. _. _. _. x. y. x y)";\r
-] ;;\r
-\r
-print_hline();\r
-print_endline ">>> EXAMPLES IN simple.ml FINISHED <<<"\r
projects / fireball-separation.git / blobdiff