| V of var\r
| A of t * t\r
| L of t\r
- | B (* bottom *)\r
- | C of int\r
;;\r
\r
-let delta = L(A(V 0, V 0));;\r
-\r
-let eta_eq' =\r
- let rec aux l1 l2 t1 t2 = match t1, t2 with\r
- | L t1, L t2 -> aux l1 l2 t1 t2\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 eta_eq = eta_eq' 0 0;;\r
-\r
-(* is arg1 eta-subterm of arg2 ? *)\r
-let eta_subterm u =\r
- let rec aux lev t = eta_eq' lev 0 u t || match t with\r
- | L t -> aux (lev+1) t\r
- | A(t1, t2) -> aux lev t1 || aux lev t2\r
- | _ -> false\r
- in aux 0\r
-;;\r
-\r
-(* does NOT lift the argument *)\r
-let mk_lams = fold_nat (fun x _ -> L x) ;;\r
-\r
let string_of_t =\r
let string_of_bvar =\r
let bound_vars = ["x"; "y"; "z"; "w"; "q"] in\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
| A _\r
| L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"\r
- | B -> "BOT"\r
and string_of_term_no_pars_app level = function\r
| A(t1,t2) -> string_of_term_no_pars_app level t1 ^ " " ^ string_of_term_w_pars level t2\r
| _ as t -> string_of_term_w_pars level t\r
in string_of_term_no_pars 0\r
;;\r
\r
+\r
+let delta = L(A(V 0, V 0));;\r
+\r
+(* does NOT lift the argument *)\r
+let mk_lams = fold_nat (fun x _ -> L x) ;;\r
+\r
type problem = {\r
orig_freshno: int\r
; freshno : int\r
; div : t\r
; conv : t\r
; sigma : (var * t) list (* substitutions *)\r
- ; stepped : var list\r
; phase : [`One | `Two] (* :'( *)\r
}\r
\r
let string_of_problem p =\r
let lines = [\r
- "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);\r
"[DV] " ^ string_of_t p.div;\r
"[CV] " ^ string_of_t p.conv;\r
] in\r
String.concat "\n" lines\r
;;\r
\r
+exception B;;\r
exception Done of (var * t) list (* substitution *);;\r
exception Fail of int * string;;\r
\r
function\r
| A(t,_) -> is_inert t\r
| V _ -> true\r
- | C _\r
- | L _ | B -> false\r
+ | L _ -> 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
+;;\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
- | L t -> let t = subst (level + 1) delift sub t in if t = B then B else L t\r
+ | L t -> L (subst (level + 1) delift sub t)\r
| A (t1,t2) ->\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
-and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B\r
+and mk_app t1 t2 = if t1 = delta && t2 = delta then raise 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
and lift n =\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
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
- {p with\r
- div=subst sub p.div;\r
- conv=subst sub p.conv;\r
- stepped=(fst sub)::p.stepped;\r
- sigma=sub::p.sigma}\r
+let eta_eq =\r
+ let rec aux t1 t2 = match t1, t2 with\r
+ | L t1, L t2 -> aux t1 t2\r
+ | L t1, t2 -> aux t1 (A(lift 1 t2,V 0))\r
+ | t1, L t2 -> aux (A(lift 1 t1,V 0)) t2\r
+ | V a, V b -> a = b\r
+ | A(t1,t2), A(u1,u2) -> aux t1 u1 && aux t2 u2\r
+ | _, _ -> false\r
+ in aux ;;\r
+\r
+(* is arg1 eta-subterm of arg2 ? *)\r
+let eta_subterm u =\r
+ let rec aux lev t = eta_eq u (lift lev t) || match t with\r
+ | L t -> aux (lev+1) t\r
+ | A(t1, t2) -> aux lev t1 || aux lev t2\r
+ | _ -> false\r
+ in aux 0\r
+;;\r
+\r
+let subst_in_problem ((v, t) as sub) p =\r
+print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);\r
+ let sigma = sub::p.sigma in\r
+ let div = try subst sub p.div with B -> raise (Done sigma) in\r
+ let conv = try subst sub p.conv with B -> raise (Fail(-1,"p.conv diverged")) in\r
+ {p with div; conv; 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
+ | V _ -> 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
- | B -> Pure.B\r
;;\r
\r
let check p sigma =\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
let sanity p =\r
print_endline (string_of_problem p); (* non cancellare *)\r
- if p.conv = B then problem_fail p "p.conv diverged";\r
- if p.div = B then raise (Done p.sigma);\r
if p.phase = `Two && p.div = delta then raise (Done p.sigma);\r
if not (is_inert p.div) then problem_fail p "p.div converged";\r
p\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 _ -> None\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
- else aux t1 u1 (k-1)\r
+ (match aux t1 u1 (k-1) with\r
+ | None ->\r
+ if not (eta_eq t2 u2) then Some (k-1)\r
+ else None\r
+ | Some j -> Some j)\r
| _, _ -> assert false\r
- in aux p.div t n_args\r
+ in match aux p.div t argsno with\r
+ | None -> problem_fail p "no eta difference found (div subterm of conv?)"\r
+ | Some j -> j\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
- | _ -> assert false\r
in aux hd_var\r
;;\r
\r
print_cmd "EAT" "";\r
let var, k = get_inert p.div in\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, v = freshvar p in\r
p, A(t, V (v + k + 1))\r
) (p, V 0) n in\r
- let t = (* apply unused bound variables V_{k-1}..V_1 *)\r
- fold_nat (fun t m -> A(t, V (k-m+1))) t k in\r
+ let t = (* apply bound variables V_k..V_0 *)\r
+ fold_nat (fun t m -> A(t, V (k-m+1))) t (k+1) in\r
let t = mk_lams t (k+1) in (* make leading lambdas *)\r
let subst = var, t in\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 = function\r
+ | `Lam(_, t) -> L (aux t)\r
+ | `I ((v,_), args) -> Listx.fold_left (fun x y -> mk_app x (aux y)) (V v) args\r
+ | `Var(v,_) -> 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 (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 (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
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; phase=`One} in\r
(* initial sanity check *)\r
sanity p\r
;;\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