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Add support for Reason (#3336)
This commit is contained in:
committed by
Brandon Black
parent
a4d12cc8e4
commit
7867b946b9
344
samples/Reason/Machine.re
Normal file
344
samples/Reason/Machine.re
Normal file
@@ -0,0 +1,344 @@
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open Format;
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let module Endo = {
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type t 'a = 'a => 'a;
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};
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let module Syntax = {
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let module Var = {
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type t = int;
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};
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let module Term = {
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type t =
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| App t t
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| Lam t
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| Var Var.t
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;
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};
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let module Sub = {
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type t 'a =
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| Cmp (t 'a) (t 'a)
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| Dot 'a (t 'a)
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| Id
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| Shift
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;
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let map f sgm => {
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let rec go = fun
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| Cmp sgm0 sgm1 => Cmp (go sgm0) (go sgm1)
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| Dot a sgm => Dot (f a) (go sgm)
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| Id => Id
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| Shift => Shift
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;
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go sgm;
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};
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let rec apply sgm e =>
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switch (sgm, e) {
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| (sgm, Term.App e0 e1) => Term.App (apply sgm e0) (apply sgm e1)
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| (sgm, Term.Lam e) => Term.Lam (apply (Dot (Term.Var 0) (Cmp sgm Shift)) e)
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| (Dot e _, Term.Var 0) => e
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| (Dot _ sgm, Term.Var i) => apply sgm (Term.Var (i - 1))
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| (Id, Term.Var i) => Term.Var i
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| (Shift, Term.Var i) => Term.Var (i + 1)
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| (Cmp rho sgm, e) => apply sgm (apply rho e)
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};
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};
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};
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let module Zip = {
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open Syntax;
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type t 'a =
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| App0 (t 'a) 'a
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| App1 'a (t 'a)
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| Halt
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| Lam (t 'a)
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;
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let map f sgm => {
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let rec go = fun
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| App0 zip e1 => App0 (go zip) (f e1)
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| App1 e0 zip => App1 (f e0) (go zip)
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| Halt => Halt
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| Lam zip => Lam (go zip)
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;
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go sgm;
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};
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let rec apply zip acc => switch zip {
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| App0 zip e1 => apply zip (Term.App acc e1)
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| App1 e0 zip => apply zip (Term.App e0 acc)
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| Halt => acc
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| Lam zip => apply zip (Term.Lam acc)
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};
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};
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let module Clo = {
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open Syntax;
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type t =
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| Clo Term.t (Sub.t t);
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let rec from (Clo term sgm) => Sub.apply (Sub.map from sgm) term;
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};
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let module Pretty = {
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let module Delim = {
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type t = string;
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let pp prev next fmt token => if (prev < next) { fprintf fmt "%s" token };
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};
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let module Prec = {
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type t = int;
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open Syntax.Term;
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let calc = fun
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| App _ _ => 1
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| Lam _ => 2
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| Var _ => 0
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;
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};
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let module Name = {
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type t = string;
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let suffix = {
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let script = fun
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| 0 => "₀"
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| 1 => "₁"
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| 2 => "₂"
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| 3 => "₃"
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| 4 => "₄"
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| 5 => "₅"
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| 6 => "₆"
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| 7 => "₇"
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| 8 => "₈"
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| 9 => "₉"
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| _ => failwith "bad subscript";
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let rec go acc => fun
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| 0 => acc
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| n => go (script (n mod 10) ^ acc) (n / 10);
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go ""
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};
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let gen = {
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let offset = 97;
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let width = 26;
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fun () i => {
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let code = i mod width + offset;
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let char = Char.chr code;
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let prime = i / width;
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let suffix = suffix prime;
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let name = Char.escaped char ^ suffix;
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Some name;
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}
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};
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};
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let module Env = {
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type t = {
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used: list Name.t,
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rest: Stream.t Name.t,
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};
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let mk () => {
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let used = [];
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let rest = Stream.from @@ Name.gen ();
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{ used, rest };
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};
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};
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type printer 'a = Env.t => Prec.t => formatter => 'a => unit;
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let module Term = {
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open Syntax.Term;
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let rec pp ({ Env.used: used, rest } as env) prev fmt e => {
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let next = Prec.calc e;
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switch e {
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| App e0 e1 =>
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fprintf fmt "@[%a%a@ %a%a@]"
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(Delim.pp prev next) "("
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(pp env 1) e0
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(pp env 0) e1
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(Delim.pp prev next) ")"
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| Lam e =>
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let name = Stream.next rest;
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let env = { ...env, Env.used: [name, ...used] };
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fprintf fmt "%aλ%a.%a%a"
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(Delim.pp prev next) "("
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(pp_print_string) name
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(pp env next) e
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(Delim.pp prev next) ")"
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| Var index =>
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fprintf fmt "%s" @@ try (List.nth used index) {
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| _ => "#" ^ string_of_int index
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}
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}
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};
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};
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let module Sub = {
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open Syntax.Sub;
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let rec pp pp_elem env prev fmt => fun
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| Cmp sgm1 sgm0 =>
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fprintf fmt "@[%a;@ %a@]"
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(pp pp_elem env prev) sgm1
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(pp pp_elem env prev) sgm0
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| Dot e sgm =>
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fprintf fmt "@[%a@ ·@ %a@]"
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(pp_elem env prev) e
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(pp pp_elem env prev) sgm
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| Id =>
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fprintf fmt "ι"
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| Shift =>
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fprintf fmt "↑"
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;
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};
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let module Clo = {
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let rec pp env prev fmt (Clo.Clo e sgm) => {
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let next = Prec.calc e;
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fprintf fmt "@[%a%a%a[%a]@]"
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(Delim.pp prev next) "("
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(Term.pp env next) e
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(Delim.pp prev next) ")"
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(Sub.pp pp env next) sgm
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};
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};
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let module Zip = {
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open Zip;
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let rec pp pp_elem env prev fmt => fun
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| App0 zip elem =>
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fprintf fmt "inl@[<v -1>⟨@,%a@,%a⟩@]"
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(pp pp_elem env prev) zip
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(pp_elem env prev) elem
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| App1 elem zip =>
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fprintf fmt "inr@[<v -1>⟨@,%a@,%a⟩@]"
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(pp_elem env prev) elem
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(pp pp_elem env prev) zip
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| Halt =>
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fprintf fmt "halt"
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| Lam zip =>
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fprintf fmt "lam@[<v -1>⟨@,%a⟩@]"
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(pp pp_elem env prev) zip
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;
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};
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};
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let module Machine = {
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type t = {
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clo: Clo.t,
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ctx: Zip.t Clo.t,
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};
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let into e => {
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open Clo;
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open Syntax.Sub;
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let clo = Clo e Id;
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let ctx = Zip.Halt;
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{ clo, ctx }
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};
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let from { clo, ctx } => Zip.apply (Zip.map Clo.from ctx) (Clo.from clo);
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let pp fmt rule state => {
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fprintf fmt "@[<v>ctx ::@[<v -5>@,%a@]@,clo ::@[<v -5>@,%a@]@,rule ::@[<v -5>@,%a@]@,term ::@[<v -5>@,%a@]@]@."
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(Pretty.Zip.pp Pretty.Clo.pp (Pretty.Env.mk ()) 2) state.ctx
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(Pretty.Clo.pp (Pretty.Env.mk ()) 2) state.clo
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(pp_print_string) rule
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(Pretty.Term.pp (Pretty.Env.mk ()) 2) (from state)
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};
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let halted state => {
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open Clo;
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open Syntax.Sub;
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open Syntax.Term;
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switch state {
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| { clo: Clo (Var _) Id, _ } => true
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| _ => false
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} [@warning "-4"];
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};
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let step state => {
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open Clo;
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open Syntax.Sub;
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open Syntax.Term;
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let rule = ref "";
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let state = switch state {
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/* left */
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| { clo: Clo (App e0 e1) sgm, ctx } =>
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let clo = Clo e0 sgm;
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let ctx = Zip.App0 ctx (Clo e1 sgm);
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rule := "LEFT";
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{ clo, ctx };
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/* beta */
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| { clo: Clo (Lam e) sgm, ctx: Zip.App0 ctx c0 } =>
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let clo = Clo e (Cmp (Dot c0 sgm) Id);
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rule := "BETA";
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{ clo, ctx };
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/* lambda */
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| { clo: Clo (Lam e) sgm, ctx } =>
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let clo = Clo e (Cmp (Dot (Clo (Var 0) Id) (Cmp sgm Shift)) Id);
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let ctx = Zip.Lam ctx;
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rule := "LAMBDA";
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{ clo, ctx };
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/* associate */
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| { clo: Clo (Var n) (Cmp (Cmp pi rho) sgm), ctx } =>
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let clo = Clo (Var n) (Cmp pi (Cmp rho sgm));
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rule := "ASSOCIATE";
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{ clo, ctx };
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/* head */
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| { clo: Clo (Var 0) (Cmp (Dot (Clo e pi) _) sgm), ctx } =>
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let clo = Clo e (Cmp pi sgm);
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rule := "HEAD";
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{ clo, ctx };
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/* tail */
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| { clo: Clo (Var n) (Cmp (Dot (Clo _ _) rho) sgm), ctx } =>
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let clo = Clo (Var (n - 1)) (Cmp rho sgm);
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rule := "TAIL";
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{ clo, ctx };
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/* shift */
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| { clo: Clo (Var n) (Cmp Shift sgm), ctx } =>
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let clo = Clo (Var (n + 1)) sgm;
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rule := "SHIFT";
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{ clo, ctx };
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/* id */
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| { clo: Clo (Var n) (Cmp Id sgm), ctx } =>
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let clo = Clo (Var n) sgm;
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rule := "ID";
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{ clo, ctx };
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| _ =>
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pp std_formatter !rule state;
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failwith "bad state";
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} [@warning "-4"];
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pp std_formatter !rule state;
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state;
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};
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let norm e => {
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let count = ref 0;
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let state = ref (into e);
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while (not (halted !state)) {
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fprintf std_formatter "@\n--- step[%d] ---@\n" !count;
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incr count;
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state := step !state;
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};
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from !state;
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};
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};
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let module Test = {
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open Syntax.Term;
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let l e => Lam e;
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let ( *@ ) e0 e1 => App e0 e1;
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let ff = l (l (Var 1));
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let tt = l (l (Var 0));
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let zero = l (l (Var 1));
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let succ = l (l (l (Var 0 *@ Var 2)));
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let one = succ *@ zero;
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let two = succ *@ one;
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let three = succ *@ two;
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let const = l (l (Var 1));
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let fix = l (l (Var 1 *@ (Var 0 *@ Var 0)) *@ l (Var 1 *@ (Var 0 *@ Var 0)));
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let add = fix *@ l (l (l (Var 1 *@ Var 0 *@ l (succ *@ Var 3 *@ Var 0 *@ Var 1))));
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let init = l (l (Var 0) *@ l (l (Var 1)));
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};
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let module Run = {
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let go () => Machine.norm Test.init;
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};
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