package alba
Alba compiler
Install
Dune Dependency
Authors
Maintainers
Sources
0.4.3.tar.gz
sha256=062f33c55ef39706c4290dff67d5a00bf009051fd757f9352be527f629ae21fc
md5=eb4edc4d6b7e15b83d6397bd34994153
doc/src/alba.core/gamma_holes.ml.html
Source file gamma_holes.ml
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open Fmlib open Common type term_n = Term.t * int module Entry = struct type t = | Hole of term_n option * Int_set.t (* Users *) | Bound of int (* number of bound variable (counting upwards) *) let hole: t = Hole (None, Int_set.empty) let make_bound (n: int): t = Bound n let is_hole (loc: t): bool = match loc with | Hole _ -> true | Bound _ -> false let is_unfilled (loc: t): bool = match loc with | Hole (None, _ ) -> true | _ -> false let is_bound (loc: t): bool = not (is_hole loc) let value (loc: t): term_n option = match loc with | Hole (value, _) -> value | _ -> None let users (loc: t): Int_set.t = match loc with | Hole (_, users) -> users | _ -> assert false (* Illegal call! *) let add_users (user: int) (users: Int_set.t) (loc: t): t = match loc with | Hole (value, users0) -> let set = Int_set.add user (Int_set.union users0 users) in Hole (value, set) | _ -> assert false (* Illegal call! *) let set_value (term_n: term_n) (loc: t): t = match loc with | Hole (_, users) -> Hole (Some term_n, users) | _ -> assert false (* Illegal call! *) let bound_number (loc: t): int = match loc with | Bound n -> n | _ -> assert false (* Illegal call! *) end type t = { base0: Gamma.t; base: Gamma.t; entries: Entry.t array; bounds: (int * bool) array; (* level of bound, is typed? *) nholes: int; } let make (base: Gamma.t): t = { base0 = base; base; entries = [||]; bounds = [||]; nholes = 0; } let string_of_term (term: Term.t) (gh: t): string = Term_printer.string_of_term term gh.base let _ = string_of_term let count (gh: t): int = Gamma.count gh.base let count_base (gh: t): int = Gamma.count gh.base0 let count_bounds (gh: t): int = Array.length gh.bounds let count_entries (gh: t): int = Array.length gh.entries let context (gh: t): Gamma.t = gh.base let base_context (gh: t): Gamma.t = gh.base0 let is_valid_index (idx: int) (gh: t): bool = Gamma.is_valid_index idx gh.base let name_of_index (idx: int) (gh: t): string = Gamma.name_of_index idx gh.base let index_of_level (level: int) (gh: t): int = Gamma.index_of_level level gh.base let level_of_index (idx: int) (gh: t): int = Gamma.level_of_index idx gh.base let is_entry (idx: int) (gh: t): bool = idx < count_entries gh let entry_of_index (idx: int) (gh: t): Entry.t = assert (is_entry idx gh); let level = level_of_index idx gh in gh.entries.(level - count_base gh) let is_hole (idx: int) (gh: t): bool = is_entry idx gh && Entry.is_hole (entry_of_index idx gh) let is_unfilled (idx: int) (gh: t): bool = is_entry idx gh && Entry.is_unfilled (entry_of_index idx gh) let is_bound (idx: int) (gh: t): bool = is_entry idx gh && Entry.is_bound (entry_of_index idx gh) let bound_number (idx: int) (gh: t): int = assert (is_bound idx gh); Entry.bound_number (entry_of_index idx gh) let variable_of_bound (i: int) (gh: t): Term.t = assert (i < count_bounds gh); Term.Variable (index_of_level (fst gh.bounds.(i)) gh) let value (idx: int) (gh: t): Term.t option = if is_entry idx gh then Option.map (fun (term, n) -> assert (n <= count gh); Term.up (count gh - n) term) (Entry.value (entry_of_index idx gh)) else None let has_value (idx: int) (gh: t): bool = Option.has (value idx gh) let collect_holes (cnt0: int) (filled: bool) (term: Term.t) (gh: t) : Int_set.t = (* collect filled or unfilled holes in [term] starting from [cnt0]. *) let cntbase =count_base gh in let delta = max (cnt0 - cntbase) 0 in let idx_beyond = count_entries gh - delta in Term.fold_free (fun idx set -> if idx < idx_beyond then let entry = entry_of_index idx gh in if Entry.is_hole entry && ((Entry.value entry <> None) = filled) then Int_set.add (Gamma.level_of_index idx gh.base) set else set else set) term Int_set.empty let unfilled_holes (cnt0: int) (term: Term.t) (gh: t): Int_set.t = collect_holes cnt0 false term gh let expand (term: Term.t) (gh: t): Term.t = Term.substitute_with_beta (fun i -> match value i gh with | None -> Variable i | Some term -> term) term let is_expanded (term: Term.t) (gh: t): bool = Int_set.is_empty (collect_holes 0 true term gh) let term_of_term_n ((term,n): Term.t_n) (gh: t): Term.t = expand (Term.up (count gh - n) term) gh let name_at_level (level: int) (gh: t): string = Gamma.name_at_level level gh.base let type_at_level (level: int) (gh: t): Term.typ = let typ = Gamma.type_at_level level gh.base in if count_base gh <= level then expand typ gh else typ let type_of_variable (idx: int) (gh: t): Term.typ = type_at_level (Gamma.level_of_index idx gh.base) gh let type_of_literal (value: Term.Value.t) (gh: t): Term.typ = Gamma.type_of_literal value gh.base let definition_term (idx: int) (gh: t): Term.t option = Gamma.definition_term idx gh.base let fold_entries (f: int -> int -> string -> Term.typ -> bool -> Term.t option -> 'a -> 'a) (gh: t) (a: 'a): 'a = let cnt0 = count_base gh in Array.foldi_left (fun a k entry -> let level = cnt0 + k in let idx = index_of_level level gh in f level idx (name_at_level level gh) (type_at_level level gh) (Entry.is_hole entry) (value idx gh) a ) a gh.entries let push_bound (name: string) (typed: bool) (typ: Term.typ) (gh: t): t = {gh with base = Gamma.push_local name typ gh.base; entries = Array.push (Entry.make_bound (Array.length gh.bounds)) gh.entries; bounds = Array.push (count gh, typed) gh.bounds; } let remove_bounds (n: int) (gh: t): t = assert (n <= count_bounds gh); {gh with bounds = Array.remove_last n gh.bounds} let push_local (name: string) (typ: Term.typ) (gh: t): t = push_bound name true typ gh let push_named_hole (name: string) (typ: Term.typ) (gh: t): t = {gh with base = Gamma.push_local name typ gh.base; entries = Array.push Entry.hole gh.entries; nholes = gh.nholes + 1; } let push_hole (typ: Term.typ) (gh: t): t = push_named_hole ("<" ^ string_of_int gh.nholes ^ ">") typ gh let fill_hole0 (idx: int) (value: Term.t) (beta_reduce: bool) (gh: t): t = assert (is_unfilled idx gh); assert (not (Term.has_variable idx value)); let value = expand value gh and cnt = count gh and nentries = count_entries gh and entries = Array.copy gh.entries in let cnt0 = cnt - nentries and loc_level = Term.bruijn_convert idx nentries in let gh_new = {gh with entries} in (* fill the hole *) entries.(loc_level) <- Entry.set_value (value, cnt) entries.(loc_level); (* [idx] and users of [idx] also become users of all unfilled holes in [value] *) let users = Entry.users entries.(loc_level) in Int_set.iter (fun unfilled -> let iloc = unfilled - cnt0 in entries.(iloc) <- Entry.add_users (cnt0 + loc_level) users entries.(iloc)) (unfilled_holes cnt0 value gh); (* Substitute in all users of [idx] the variable [idx] by value. *) Int_set.iter (fun user -> let i = user - cnt0 in match Entry.value entries.(i) with | Some (term,n) -> let term = Term.up (count gh - n) term in let term = Term.substitute0 (fun k -> if k = idx then value else Term.Variable k) beta_reduce term in entries.(i) <- Entry.set_value (term, cnt) entries.(i) | _ -> assert false (* Illegal, all users must have a substitution, otherwise they would not be users. *)) users; gh_new let fill_hole (idx: int) (value: Term.t) (gh: t): t = fill_hole0 idx value false gh let into_binder (bnd0: int) (nb: int) (term: Term.t) (gh: t) : Term.typ = (* Put [term] into a context with additional [nb] bound variables. The bound variables [bnd0, bnd0+1, ..., bnd0+nb-1] become the new bound variables [0,1,...,nb-1]. *) assert (bnd0 <= count_bounds gh); let nentries = count_entries gh in Term.substitute (fun idx -> if nentries <= idx then Variable (idx + nb) else let entry = entry_of_index idx gh in if Entry.is_bound entry then let i = Entry.bound_number entry in if bnd0 <= i then ( assert (i < bnd0 + nb); Variable (Term.bruijn_convert (i - bnd0) nb) ) else Variable (idx + nb) else Variable (idx + nb)) term let pi_lambda (mk: string -> bool -> Term.typ -> Term.t -> Term.t) (nbounds: int) (inner: Term.t) (gh: t) : Term.t = assert (nbounds <= count_bounds gh); let bnd0 = count_bounds gh - nbounds in let into = into_binder bnd0 in let rec make i exp = if i = 0 then exp else let i = i - 1 in let name, typed, arg_tp = let level, typed = gh.bounds.(bnd0 + i) in name_at_level level gh, typed, into i (type_at_level level gh) gh in make i (mk name typed arg_tp exp) in make nbounds (into nbounds inner gh) let pi (nargs: int) (res_tp: Term.typ) (gh: t): Term.typ = assert (0 < nargs); assert (nargs <= count_bounds gh); pi_lambda Term.product0 nargs res_tp gh let lambda (nargs: int) (exp: Term.t) (gh: t): Term.t = assert (0 < nargs); assert (nargs <= count_bounds gh); pi_lambda Term.lambda0 nargs exp gh
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