├── .gitignore ├── .merlin ├── LICENSE ├── README.md ├── ast.ml ├── ast.mli ├── context.ml ├── context.mli ├── equality.ml ├── kinding.ml ├── lexer.mll ├── parser.mly ├── util.ml └── util.mli /.gitignore: -------------------------------------------------------------------------------- 1 | *.annot 2 | *.cmo 3 | *.cma 4 | *.cmi 5 | *.a 6 | *.o 7 | *.cmx 8 | *.cmxs 9 | *.cmxa 10 | *~ 11 | parser.ml 12 | lexer.ml 13 | a.out 14 | 15 | # ocamlbuild working directory 16 | _build/ 17 | 18 | # ocamlbuild targets 19 | *.byte 20 | *.native 21 | 22 | # oasis generated files 23 | setup.data 24 | setup.log 25 | -------------------------------------------------------------------------------- /.merlin: -------------------------------------------------------------------------------- 1 | S . 2 | B _build/ -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | {one line to give the program's name and a brief idea of what it does.} 635 | Copyright (C) {year} {name of author} 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Linear ML 2 | 3 | This is a small implementation of a linear type theory in the style of 4 | the Benton-Wadler adjoint calculus 5 | ([*Linear logic, monads, and the lambda calculus*](http://homepages.inf.ed.ac.uk/wadler/topics/linear-logic.html#linearmonad)), 6 | which shows how to extend ordinary functional programming with support 7 | for the connectives of linear logic. 8 | 9 | In addition, the linear type theory has support for logical 10 | connectives drawn from temporal logic. This gives a logical 11 | interpretation for a reactive, event-based programming style, and so 12 | the language should be compilable into Javascript in a way that 13 | integrates cleanly with the event loop and DOM. 14 | 15 | The language is intended to support polymorphism using an algorithm 16 | extending the one in my 2013 paper with Joshua 17 | Dunfield, 18 | [*Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism*](http://www.cs.cmu.edu/%7Ejoshuad/papers/bidir/). 19 | 20 | 21 | -------------------------------------------------------------------------------- /ast.ml: -------------------------------------------------------------------------------- 1 | type 'a monoid = {unit : 'a ; join : 'a -> 'a -> 'a} 2 | 3 | type var = string 4 | type conid = string (* Leading uppercase *) 5 | type field = string 6 | 7 | module V = Set.Make(struct type t = var let compare = compare end) 8 | let variables = {unit = V.empty ; join = V.union} 9 | 10 | type pat = PVar | PTuple of pat list | PCon of conid * pat | PF of pat | PAlways of pat | PEvent of pat 11 | 12 | type loc = Lexing.position * Lexing.position 13 | 14 | type 'a exp = 15 | | Var of var 16 | | Abs of var * 'a 17 | | Lam of pat * 'a 18 | | App of 'a * 'a 19 | | Record of (field * 'a) list 20 | | Proj of 'a * field 21 | | Tuple of 'a list 22 | | Con of conid 23 | | Case of 'a * (pat * 'a) list 24 | | Annot of 'a * 'a 25 | | Num of int 26 | | Select of ('a * 'a) list 27 | | Yield of 'a 28 | | Forall of 'a * 'a 29 | | Exists of 'a * 'a 30 | | Lolli of 'a * 'a 31 | | Arrow of 'a * 'a 32 | | Karrow of 'a * 'a 33 | | Tensor of 'a list 34 | | With of (field * 'a) list 35 | | Sum of (conid * 'a) list 36 | | Mu of 'a * 'a 37 | | F of 'a 38 | | G of 'a 39 | | Always of 'a 40 | | Event of 'a 41 | | Type 42 | | Linear 43 | 44 | let map f (e : 'a exp) = 45 | match e with 46 | | Var x -> Var x 47 | | Abs (x,e) -> Abs(x, f e) 48 | | Lam (p,e) -> Lam(p, f e) 49 | | App (e, e') -> App(f e, f e') 50 | | Record nes -> Record (List.map (fun (n, e) -> (n, f e)) nes) 51 | | Proj (e, n) -> Proj (f e, n) 52 | | Tuple es -> Tuple (List.map f es) 53 | | Con c -> Con c 54 | | Case (e,pes) -> Case(f e, List.map (fun (p, e) -> (p, f e)) pes) 55 | | Annot (e,e') -> Annot(f e, f e') 56 | | Num n -> Num n 57 | | Select ets -> Select (List.map (fun (e, t) -> (f e, f t)) ets) 58 | | Yield e -> Yield (f e) 59 | | Forall(e,e') -> Forall (f e, f e') 60 | | Exists(e,e') -> Exists (f e, f e') 61 | | Lolli (e,e') -> Lolli(f e, f e') 62 | | Arrow (e,e') -> Arrow(f e, f e') 63 | | Karrow (e,e') -> Karrow(f e, f e') 64 | | Tensor es -> Tensor (List.map f es) 65 | | With nes -> With (List.map (fun (n, e) -> (n, f e)) nes) 66 | | Sum ces -> With (List.map (fun (c, e) -> (c, f e)) ces) 67 | | Mu (e, e') -> Mu (f e, f e') 68 | | F e -> F (f e) 69 | | G e -> G (f e) 70 | | Always e -> Always (f e) 71 | | Event e -> Event (f e) 72 | | Type -> Type 73 | | Linear -> Linear 74 | 75 | module Seq(M : Util.IDIOM) = struct 76 | open M 77 | module L = Util.Seq(M) 78 | 79 | let seq (e : 'a M.t exp) = 80 | match e with 81 | | Var x -> return (Var x) 82 | | Abs (x, c) -> c |> map (fun v -> Abs(x, v)) 83 | | Lam (p, c) -> c |> map (fun v -> Lam(p, v)) 84 | | App (c1, c2) -> L.pair (c1, c2) 85 | |> map (fun (v1, v2) -> App(v1, v2)) 86 | | Record ncs -> let (ns, cs) = List.split ncs in 87 | L.list cs 88 | |> map (fun vs -> Record (List.combine ns vs)) 89 | | Proj (c, n) -> c |> map (fun v -> Proj(v, n)) 90 | | Tuple cs -> L.list cs |> map (fun vs -> Tuple vs) 91 | | Con c -> return (Con c) 92 | | Case (e, pcs) -> let (ps, cs) = List.split pcs in 93 | e ** L.list cs 94 | |> map (fun (v, vs) -> Case(v, List.combine ps vs)) 95 | | Annot (c1, c2) -> c1 ** c2 96 | |> map (fun (v1, v2) -> Annot(v1, v2)) 97 | | Num n -> return (Num n) 98 | | Select ets -> L.list (List.map L.pair ets) 99 | |> map (fun ets' -> Select ets') 100 | | Yield c -> c |> map (fun v -> Yield v) 101 | | Forall(c1,c2) -> L.pair (c1, c2) |> map (fun (v1, v2) -> Forall(v1, v2)) 102 | | Exists(c1,c2) -> L.pair (c1, c2) |> map (fun (v1, v2) -> Exists(v1, v2)) 103 | | Lolli (c1,c2) -> L.pair (c1, c2) 104 | |> map (fun (v1, v2) -> Lolli(v1, v2)) 105 | | Arrow (c1,c2) -> L.pair (c1, c2) 106 | |> map (fun (v1, v2) -> Arrow(v1, v2)) 107 | | Karrow (c1,c2) -> L.pair (c1, c2) 108 | |> map (fun (v1, v2) -> Karrow(v1, v2)) 109 | | Tensor es -> L.list es 110 | |> map (fun vs -> Tensor vs) 111 | | With ncs -> let (ns, cs) = List.split ncs in 112 | L.list cs 113 | |> map (fun vs -> With (List.combine ns vs)) 114 | | Sum ncs -> let (ns, cs) = List.split ncs in 115 | L.list cs 116 | |> map (fun vs -> Sum (List.combine ns vs)) 117 | | Mu(c1,c2) -> L.pair (c1, c2) 118 | |> map (fun (v1, v2) -> Mu(v1, v2)) 119 | | F c -> c |> map (fun v -> F v) 120 | | G c -> c |> map (fun v -> G v) 121 | | Always c -> c |> map (fun v -> Always v) 122 | | Event c -> c |> map (fun v -> Event v) 123 | | Type -> return Type 124 | | Linear -> return Linear 125 | end 126 | 127 | let join (type a) (m : a monoid) (e : a exp) = 128 | let module S = Seq(Util.MkIdiom(struct 129 | type 'a t = a 130 | let map f x = x 131 | let unit () = m.unit 132 | let ( ** ) x y = m.join x y 133 | end)) 134 | in 135 | S.seq e 136 | 137 | type t = In of loc * V.t * t exp 138 | 139 | let loc (In(loc, _, _)) = loc 140 | let fvs (In(_, vs, _)) = vs 141 | let out (In(_, _, body)) = body 142 | 143 | let into loc body = 144 | let vs = 145 | match map fvs body with 146 | | Var x -> V.singleton x 147 | | Abs(x, vs) -> V.remove x vs 148 | | evs -> join variables evs 149 | in 150 | In(loc, vs, body) 151 | 152 | let rec rename x y e = 153 | into (loc e) 154 | (match out e with 155 | | Var z when x = z -> Var y 156 | | Abs(z, e') when x = z -> Abs(z, e') 157 | | body -> map (rename x y) body) 158 | 159 | 160 | module type CONSTR = sig 161 | type con 162 | 163 | val var : var -> con 164 | val abs : var * con -> con 165 | val lam : pat * con -> con 166 | val app : con * con -> con 167 | val record : (field * con) list -> con 168 | val proj : con * field -> con 169 | val tuple : con list -> con 170 | val con : conid -> con 171 | val case : con * (pat * con) list -> con 172 | val annot : con * con -> con 173 | val num : int -> con 174 | val yield : con -> con 175 | val select : (con * con) list -> con 176 | val forall : con -> con -> con 177 | val exists : con -> con -> con 178 | val lolli : con * con -> con 179 | val tensor : con list -> con 180 | val witht : (field * con) list -> con 181 | val sum : (conid * con) list -> con 182 | val mu : con * con -> con 183 | val f : con -> con 184 | val g : con -> con 185 | val always : con -> con 186 | val event : con -> con 187 | val type' : con 188 | val linear : con 189 | 190 | val (@) : con -> loc -> con 191 | 192 | val get : con -> loc -> t 193 | end 194 | 195 | module Constr : CONSTR = struct 196 | type con = loc -> t 197 | 198 | let var : var -> con = 199 | fun x loc -> into loc (Var x) 200 | 201 | 202 | 203 | let abs : var * con -> con = 204 | fun (x, c) loc -> 205 | into loc (Abs(x, c loc)) 206 | 207 | let lam : pat * con -> con = 208 | fun (p, c) loc -> 209 | into loc (Lam(p, c loc)) 210 | 211 | let app : con * con -> con = 212 | fun (f, e) loc -> into loc (App(f loc, e loc)) 213 | 214 | let record : (field * con) list -> con = 215 | fun fcs loc -> let fts = List.map (fun (f, c) -> (f, c loc)) fcs in 216 | into loc (Record fts) 217 | 218 | let proj : con * field -> con = 219 | fun (c, f) loc -> into loc (Proj(c loc, f)) 220 | 221 | let tuple : con list -> con = 222 | fun cs loc -> into loc (Tuple (List.map ((|>) loc) cs)) 223 | 224 | let con : conid -> con = 225 | fun con loc -> into loc (Con con) 226 | 227 | let case : con * (pat * con) list -> con = 228 | fun (c, pcs) loc -> 229 | into loc (Case(c loc, List.map (fun (p, c) -> (p, c loc)) pcs)) 230 | 231 | let annot : con * con -> con = 232 | fun (f, e) loc -> into loc (Annot(f loc, e loc)) 233 | 234 | let num : int -> con = 235 | fun x loc -> into loc (Num x) 236 | 237 | let select : (con * con) list -> con = 238 | fun ets loc -> into loc (Select (List.map (fun (e, t) -> (e loc, t loc)) ets)) 239 | 240 | 241 | let yield : con -> con = 242 | fun e loc -> into loc (Yield (e loc)) 243 | 244 | let forall : con -> con -> con = 245 | fun e1 e2 loc -> into loc (Forall(e1 loc, e2 loc)) 246 | 247 | let exists : con -> con -> con = 248 | fun e1 e2 loc -> into loc (Exists(e1 loc, e2 loc)) 249 | 250 | let lolli : con * con -> con = 251 | fun (f, e) loc -> into loc (Lolli(f loc, e loc)) 252 | 253 | let tensor : con list -> con = 254 | fun cs loc -> into loc (Tensor (List.map ((|>) loc) cs)) 255 | 256 | let witht : (field * con) list -> con = 257 | fun fcs loc -> let fts = List.map (fun (f, c) -> (f, c loc)) fcs in 258 | into loc (With fts) 259 | 260 | let sum : (conid * con) list -> con = 261 | fun ncs loc -> let nts = List.map (fun (n, c) -> (n, c loc)) ncs in 262 | into loc (Sum nts) 263 | 264 | let mu : con * con -> con = 265 | fun (e, e') loc -> into loc (Mu(e loc, e' loc)) 266 | 267 | 268 | let f : con -> con = 269 | fun e loc -> into loc (F(e loc)) 270 | 271 | let g : con -> con = 272 | fun e loc -> into loc (G(e loc)) 273 | 274 | let always : con -> con = 275 | fun e loc -> into loc (Always(e loc)) 276 | 277 | let event : con -> con = 278 | fun e loc -> into loc (Event(e loc)) 279 | 280 | let type' = fun loc -> into loc Type 281 | 282 | let linear = fun loc -> into loc Linear 283 | 284 | 285 | let (@) : con -> loc -> con = 286 | fun c loc _ -> c loc 287 | 288 | let get : con -> loc -> t = 289 | fun c l -> c l 290 | 291 | end 292 | 293 | 294 | -------------------------------------------------------------------------------- /ast.mli: -------------------------------------------------------------------------------- 1 | type var = string 2 | type conid = string 3 | type field = string 4 | type loc = Lexing.position * Lexing.position 5 | 6 | module V : (Set.S with type elt = var) 7 | 8 | type pat = 9 | PVar 10 | | PTuple of pat list 11 | | PCon of conid * pat 12 | | PF of pat 13 | | PAlways of pat 14 | | PEvent of pat 15 | 16 | type 'a exp = 17 | | Var of var 18 | | Abs of var * 'a 19 | | Lam of pat * 'a 20 | | App of 'a * 'a 21 | | Record of (field * 'a) list 22 | | Proj of 'a * field 23 | | Tuple of 'a list 24 | | Con of conid 25 | | Case of 'a * (pat * 'a) list 26 | | Annot of 'a * 'a 27 | | Num of int 28 | | Select of ('a * 'a) list 29 | | Yield of 'a 30 | | Forall of 'a * 'a 31 | | Exists of 'a * 'a 32 | | Lolli of 'a * 'a 33 | | Arrow of 'a * 'a 34 | | Karrow of 'a * 'a 35 | | Tensor of 'a list 36 | | With of (field * 'a) list 37 | | Sum of (conid * 'a) list 38 | | Mu of 'a * 'a 39 | | F of 'a 40 | | G of 'a 41 | | Always of 'a 42 | | Event of 'a 43 | | Type 44 | | Linear 45 | 46 | val map : ('a -> 'b) -> 'a exp -> 'b exp 47 | 48 | module Seq(M : Util.IDIOM) : sig 49 | val seq : 'a M.t exp -> 'a exp M.t 50 | end 51 | 52 | 53 | type t = In of loc * V.t * t exp 54 | 55 | val loc : t -> loc 56 | val fvs : t -> V.t 57 | val out : t -> t exp 58 | 59 | val into : loc -> t exp -> t 60 | 61 | val rename : var -> var -> t -> t 62 | 63 | module Constr : sig 64 | type con 65 | val var : var -> con 66 | val abs : var * con -> con 67 | val lam : pat * con -> con 68 | val app : con * con -> con 69 | val record : (field * con) list -> con 70 | val proj : con * field -> con 71 | val tuple : con list -> con 72 | val con : conid -> con 73 | val case : con * (pat * con) list -> con 74 | val annot : con * con -> con 75 | val num : int -> con 76 | val yield : con -> con 77 | val select : (con * con) list -> con 78 | val forall : con -> con 79 | val exists : con -> con 80 | val lolli : con * con -> con 81 | val tensor : con list -> con 82 | val witht : (field * con) list -> con 83 | val sum : (conid * con) list -> con 84 | val mu : con * con -> con 85 | val f : con -> con 86 | val g : con -> con 87 | val always : con -> con 88 | val event : con -> con 89 | val type' : con 90 | val linear : con 91 | val ( @ ) : con -> loc -> con 92 | val get : con -> loc -> t 93 | end 94 | 95 | -------------------------------------------------------------------------------- /context.ml: -------------------------------------------------------------------------------- 1 | open Ast 2 | open Util 3 | 4 | type time = Later | Now | Always 5 | type count = One | Zero | Aff 6 | type usage = Int | Lin of count * time 7 | type sort = Univ | Exist 8 | 9 | type tp = Ast.t 10 | type kind = Ast.t 11 | 12 | type hide = Linear | Transient 13 | 14 | (* TODO: add markers to model !A *) 15 | type hyp = 16 | | Tm of tp * usage 17 | | Tp of sort * kind * tp option 18 | | Mark 19 | | Hide of hide 20 | (* | Def of int * tp (* Arity plus definition (with arity binders) *) *) 21 | 22 | type ctx = (var * (hyp * loc)) list 23 | 24 | type error = 25 | | Unbound of var 26 | | Reuse of var 27 | | Usage of var 28 | | Hidden of hide * var 29 | | Unused of var * loc 30 | | NotEvar of var 31 | | IllSorted of var * string 32 | | NotEqual of tp * tp * string 33 | | Synth_mismatch of tp * string 34 | | Check_mismatch of tp * string 35 | | IllFormedKind 36 | 37 | type state = {ctx : ctx; gensym : int} 38 | 39 | type 'a t = Cmd of (loc -> state -> ('a * state, error * loc) result) 40 | 41 | let return x = Cmd(fun loc s -> Ok(x, s)) 42 | let (>>=) (Cmd c) f = 43 | Cmd(fun loc s -> 44 | match c loc s with 45 | | Error err -> Error err 46 | | Ok(v, s) -> let Cmd c = f v in c loc s) 47 | let map f (Cmd c) = 48 | Cmd(fun loc s -> 49 | match c loc s with 50 | | Error err -> Error err 51 | | Ok(v, s) -> Ok(f v, s)) 52 | 53 | module M = struct type 'a s = 'a t 54 | type 'a t = 'a s 55 | let map = map 56 | let return = return 57 | let (>>=) = (>>=) 58 | end 59 | 60 | let seq_ast e = 61 | let module S = Ast.Seq(Util.Monoidal(M)) in 62 | S.seq e 63 | 64 | let error err = Cmd(fun loc s -> Error (err, loc)) 65 | 66 | let ( @@ ) loc (Cmd c) = Cmd(fun _ s -> c loc s) 67 | let get_loc = Cmd(fun loc s -> Ok(loc, s)) 68 | 69 | let get_ctx = Cmd(fun loc s -> Ok(s.ctx, s)) 70 | let set_ctx ctx = Cmd(fun loc s -> Ok((), {s with ctx = ctx})) 71 | 72 | 73 | let gensym name = Cmd(fun loc state -> 74 | Ok(Printf.sprintf "%s_%d" name state.gensym, 75 | {state with gensym = state.gensym + 1})) 76 | 77 | 78 | 79 | let acquire usage hidden = 80 | let open Result in 81 | match usage with 82 | | Int -> return(Int, Int) 83 | | Lin(Zero, _) -> Error (fun x -> Reuse x) 84 | | Lin(u, t) when List.mem Linear hidden -> Error(fun x -> Hidden(Linear, x)) 85 | | Lin(u, Later) when List.mem Transient hidden -> Error(fun x -> Hidden(Transient, x)) 86 | | Lin(u, Now) when List.mem Transient hidden -> Error(fun x -> Hidden(Transient, x)) 87 | | Lin(u, t) -> return (Lin(u, t), Lin(Zero, t)) 88 | 89 | let rec lookup hidden x ctx = 90 | let open Result in 91 | match ctx with 92 | | [] -> Error (fun x -> Unbound x) 93 | | (y, (Tm(tp, u), loc)) :: ctx when y = x -> acquire u hidden >>= fun (u, u') -> 94 | return (Tm(tp, u), (y, (Tm(tp, u'), loc)) :: ctx) 95 | | (y, (h, loc)) :: ctx when y = x -> return (h, (y, (h, loc)) :: ctx) 96 | | (y, (Hide h, loc)) :: ctx -> lookup (h :: hidden) x ctx >>= fun (r, ctx) -> 97 | return (r, (y, (Hide h, loc)) :: ctx) 98 | | (y, h) :: ctx -> lookup hidden x ctx >>= fun (v, ctx) -> 99 | return (v, (y, h) :: ctx) 100 | 101 | 102 | 103 | 104 | let lookup x = get_ctx >>= fun ctx -> 105 | match lookup [] x ctx with 106 | | Error e -> error (e x) 107 | | Ok (v, ctx) -> set_ctx ctx >>= fun () -> 108 | return v 109 | 110 | let with_hyp (x, h) cmd = 111 | let rec pop = function 112 | | [] -> assert false 113 | | (y, (h, loc)) :: ctx when x = y -> ((y, h, loc), ctx) 114 | | (y, (h, loc)) :: ctx -> pop ctx 115 | in 116 | let check = function 117 | | Tm(_, Lin(One, _)) -> false 118 | | _ -> true 119 | in 120 | get_loc >>= fun loc -> 121 | get_ctx >>= fun ctx -> 122 | set_ctx ((x, (h, loc)) :: ctx) >>= fun () -> 123 | cmd >>= fun v -> 124 | get_ctx >>= fun ctx -> 125 | let ((y, h, loc), ctx) = pop ctx in 126 | if check h then 127 | set_ctx ctx >>= fun () -> 128 | return v 129 | else 130 | error (Unused(y, loc)) 131 | 132 | let rec split_context x = function 133 | | [] -> assert false 134 | | (y, h) :: ctx when x = y -> ([y, h], ctx) 135 | | (y, h) :: ctx -> let (front, back) = split_context x ctx in 136 | ((y, h) :: front, back) 137 | 138 | let before x cmd = 139 | get_ctx >>= fun ctx -> 140 | let (front, back) = split_context x ctx in 141 | set_ctx back >>= fun () -> 142 | cmd >>= fun v -> 143 | get_ctx >>= fun back' -> 144 | set_ctx (front @ back') >>= fun () -> 145 | return v 146 | 147 | let into e = 148 | get_loc >>= fun loc -> 149 | return (Ast.into loc e) 150 | 151 | let out e = 152 | match Ast.out e with 153 | | Abs(x, e) -> gensym x >>= fun y -> 154 | return (Abs(y, Ast.rename x y e)) 155 | | e' -> return e' 156 | 157 | let rec subst e x ebody = 158 | out ebody >>= function 159 | | Var z when x = z -> return e 160 | | t -> seq_ast (Ast.map (subst e x) t) >>= fun t' -> 161 | return (Ast.into (loc ebody) t') 162 | 163 | let rec merge f err (oldctx : ctx) (newctx : ctx) = 164 | match oldctx, newctx with 165 | | [], newctx -> 166 | return newctx 167 | | (x1, (h1, l1)) :: oldctx, (x2, (h2, l2)) :: newctx when x1 = x2 -> 168 | (match f h1 h2 with 169 | | Some h -> merge f err oldctx newctx >>= fun ctx -> 170 | return ((x2, (h, l2)) :: ctx) 171 | | None -> error (err x1)) 172 | | oldctx, (x, h) :: newctx when not (List.mem_assoc x oldctx) -> 173 | merge f err oldctx newctx >>= fun ctx -> 174 | return ((x, h) :: ctx) 175 | | _, _ -> assert false 176 | 177 | 178 | let reset_usage (oldctx : ctx) (newctx : ctx) = 179 | let reset (oldh : hyp) (newh : hyp) = 180 | match oldh, newh with 181 | | Tm(_, u), Tm(tp, _) -> Some (Tm(tp, u)) 182 | | _, _ -> Some newh 183 | in 184 | merge reset (fun x -> Usage x) oldctx newctx 185 | 186 | 187 | let join_usage_lin u u' = 188 | match u, u' with 189 | | Aff, One -> Some One 190 | | One, Aff -> Some One 191 | | Aff, Zero -> Some Zero 192 | | Zero, Aff -> Some Zero 193 | | _ -> if u = u' then Some u else None 194 | 195 | let join_usage u u' = 196 | let open Util.Option in 197 | match u, u' with 198 | | Int, Int -> return Int 199 | | Lin(u, t), Lin(u', t') -> join_usage_lin u u' >>= fun u'' -> 200 | if t = t' then return (Lin(u'', t)) else assert false 201 | | _ -> none 202 | 203 | let join_hyp oldh newh = 204 | let open Util.Option in 205 | match oldh, newh with 206 | | Tm(_, u), Tm(tp, u') -> join_usage u u' |> map (fun u'' -> Tm(tp, u'')) 207 | | _ -> return newh 208 | 209 | let rec compatible oldctx newctx = 210 | merge join_hyp (fun x -> Usage x) oldctx newctx 211 | 212 | let parallel c1 c2 = 213 | get_ctx >>= fun old -> 214 | c1 >>= fun v1 -> 215 | get_ctx >>= fun ctx1 -> 216 | reset_usage old ctx1 >>= fun old' -> 217 | set_ctx old' >>= fun () -> 218 | c2 >>= fun v2 -> 219 | get_ctx >>= fun ctx2 -> 220 | compatible ctx1 ctx2 >>= fun ctx -> 221 | set_ctx ctx >>= fun () -> 222 | return (v1, v2) 223 | 224 | module Par = Util.Seq(Util.MkIdiom(struct 225 | type 'a s = 'a t 226 | type 'a t = 'a s 227 | let map = map 228 | let unit () = return () 229 | let ( ** ) = parallel 230 | end)) 231 | 232 | module Seq = Util.Seq(Util.Monoidal(M)) 233 | 234 | 235 | 236 | 237 | let evar kind = 238 | gensym "?a" >>= fun a -> 239 | get_loc >>= fun loc -> 240 | get_ctx >>= fun ctx -> 241 | set_ctx ((a, (Tp(Exist, kind, None), loc)) :: ctx) >>= fun () -> 242 | return a 243 | 244 | let inst x tm = 245 | let rec loop = function 246 | | [] -> error (Unbound x) 247 | | (y, (Tp(Exist, k, None), loc)) :: ctx when x = y -> return ((x, (Tp(Exist, k, Some tm), loc)) :: ctx) 248 | | (y, h) :: ctx when x = y -> error (NotEvar x) 249 | | (y, h) :: ctx -> loop ctx >>= fun ctx -> 250 | return ((y, h) :: ctx) 251 | in 252 | get_ctx >>= fun ctx -> 253 | loop ctx >>= fun ctx -> 254 | set_ctx ctx 255 | 256 | let run ctx loc (Cmd cmd) = 257 | let state = { ctx = ctx; gensym = 0 } in 258 | Result.map fst Fn.id (cmd loc state) 259 | -------------------------------------------------------------------------------- /context.mli: -------------------------------------------------------------------------------- 1 | type time = Later | Now | Always 2 | type count = One | Zero | Aff 3 | type usage = Int | Lin of count * time 4 | type sort = Univ | Exist 5 | type tp = Ast.t 6 | type kind = Ast.t 7 | type hide = Linear | Transient 8 | type hyp = 9 | Tm of tp * usage 10 | | Tp of sort * kind * tp option 11 | | Mark 12 | | Hide of hide 13 | type ctx = (Ast.var * (hyp * Ast.loc)) list 14 | type error = 15 | Unbound of Ast.var 16 | | Reuse of Ast.var 17 | | Usage of Ast.var 18 | | Hidden of hide * Ast.var 19 | | Unused of Ast.var * Ast.loc 20 | | NotEvar of Ast.var 21 | | IllSorted of Ast.var * string 22 | | NotEqual of tp * tp * string 23 | | Synth_mismatch of tp * string 24 | | Check_mismatch of tp * string 25 | | IllFormedKind 26 | 27 | 28 | type 'a t 29 | 30 | val return : 'a -> 'a t 31 | val ( >>= ) : 'a t -> ('a -> 'b t) -> 'b t 32 | val map : ('a -> 'b) -> 'a t -> 'b t 33 | 34 | val seq_ast : 'a t Ast.exp -> 'a Ast.exp t 35 | val error : error -> 'a t 36 | 37 | val get_loc : Ast.loc t 38 | val (@@) : Ast.loc -> 'a t -> 'a t 39 | 40 | val gensym : string -> string t 41 | 42 | val lookup : Ast.var -> hyp t 43 | val with_hyp : Ast.var * hyp -> 'a t -> 'a t 44 | 45 | val before : Ast.var -> 'a t -> 'a t 46 | val into : Ast.t Ast.exp -> Ast.t t 47 | val out : Ast.t -> Ast.t Ast.exp t 48 | val subst : Ast.t -> Ast.var -> Ast.t -> Ast.t t 49 | 50 | module Par : (Util.SEQ with type 'a t = 'a t) 51 | module Seq : (Util.SEQ with type 'a t = 'a t) 52 | 53 | val evar : kind -> Ast.var t 54 | val inst : Ast.var -> tp -> unit t 55 | 56 | val run : ctx -> Ast.loc -> 'a t -> ('a, error * Ast.loc) result 57 | -------------------------------------------------------------------------------- /equality.ml: -------------------------------------------------------------------------------- 1 | (* Implementation of type equality *) 2 | 3 | open Util 4 | open Ast 5 | open Context 6 | 7 | 8 | 9 | let rec expand a vars kind tp = 10 | let open Constr in 11 | let exp e = before a (evar kind >>= fun b -> 12 | expand b vars kind e >>= fun () -> 13 | return (var b @ loc e)) 14 | in 15 | out tp >>= function 16 | | Var x -> expand_var a vars kind x 17 | | App (e, e') -> 18 | | Forall(e,e') -> 19 | | Exists(e,e') -> 20 | | Lolli (e,e') -> exp e >>= fun b -> 21 | exp e' >>= fun c -> 22 | inst a (get (lolli (b, c)) (loc tp)) 23 | | Tensor es -> Seq.list (List.map exp es) >>= fun bs -> 24 | inst a (get (tensor bs) (loc tp)) 25 | | With nes -> let (ns, es) = List.split nes in 26 | Seq.list (List.map exp es) >>= fun bs -> 27 | inst a (get (witht (List.combine ns bs)) (loc tp)) 28 | | Sum ces -> let (cs, es) = List.split ces in 29 | Seq.list (List.map exp es) >>= fun bs -> 30 | inst a (get (sum (List.combine cs bs)) (loc tp)) 31 | | Mu e -> Mu (f e) 32 | | F e -> F (f e) 33 | | G e -> G (f e) 34 | | Always e -> exp e >>= fun b -> 35 | inst a (get (always b) (loc tp)) 36 | | Event e -> exp e >>= fun b -> 37 | inst a (get (event b) (loc tp)) 38 | | Record _ 39 | | Proj (_, _) 40 | | Tuple _ 41 | | Con _ 42 | | Case (_,_) 43 | | Annot (_,_) 44 | | Num _ 45 | | Select _ 46 | | Yield _ 47 | | Abs (_,_) 48 | | Lam (_,_) 49 | | Type 50 | | Linear -> assert false 51 | 52 | and expand_var a vars kind x = 53 | lookup x >>= function 54 | | Tm (_,_) -> error 55 | | Tp (_,_,_) -> (??) 56 | | Mark -> (??) 57 | | Hide _ -> (??) 58 | 59 | -------------------------------------------------------------------------------- /kinding.ml: -------------------------------------------------------------------------------- 1 | (* Kind checking, bidirectionally *) 2 | 3 | open Util 4 | open Ast 5 | open Context 6 | 7 | 8 | 9 | let rec base_kind kind = 10 | (loc kind) 11 | @@ (out kind >>= function 12 | | Type -> return () 13 | | Linear -> return () 14 | | Arrow(k1, k2) -> base_kind k1 >>= fun () -> 15 | base_kind k2 16 | | Karrow(_, _) -> error IllFormedKind 17 | | _ -> assert false) 18 | 19 | let rec kind_wf kind = 20 | (loc kind) 21 | @@ (out kind >>= function 22 | | Type -> return () 23 | | Linear -> return () 24 | | Arrow(k1, k2) -> base_kind k1 >>= fun () -> 25 | base_kind k2 26 | | Karrow(k1, k2) -> kind_wf k1 >>= fun () -> 27 | kind_wf k2 28 | | _ -> assert false) 29 | 30 | 31 | let rec kind_eq kind kind' = 32 | match (Ast.out kind, Ast.out kind') with 33 | | Linear, Linear -> return () 34 | | Type, Type -> return () 35 | | Arrow(k1, k2), Arrow(k1', k2') -> kind_eq k1 k1' >>= fun () -> 36 | kind_eq k2 k2' 37 | | _, _ -> error (NotEqual(kind, kind', "kind mismatch")) 38 | 39 | 40 | let rec check_kind tp kind = 41 | Seq.pair (out tp, out kind) >>= fun (t, k) -> 42 | match t, k with 43 | | Lam (PVar, tbody), Arrow(k1, k2) -> 44 | (out tbody >>= function 45 | | Abs(x, tbody) -> with_hyp (x, Tp(Univ, k1, None)) (check_kind tbody k2) 46 | | _ -> assert false) 47 | | Lam (PVar, tbody), _ -> error (Check_mismatch(kind, "function occurs here")) 48 | | Lam (p, _), _ -> assert false 49 | | Forall(kind', tbody), _ 50 | | Exists(kind', tbody), _ -> check_kind tbody (Ast.into (loc tp) (Arrow(kind', kind))) 51 | | Lolli (tp1, tp2), Linear -> check_kind tp1 kind >>= fun () -> 52 | check_kind tp2 kind 53 | | Lolli (tp1, tp2), _ -> error (Check_mismatch(kind, "linear type occurs here")) 54 | | Arrow (tp1, tp2), Type -> check_kind tp1 kind >>= fun () -> 55 | check_kind tp2 kind 56 | | Arrow (tp1, tp2), _ -> error (Check_mismatch(kind, "intuitionistic function type occurs here")) 57 | | Tensor tps, Linear -> Seq.list (List.map (fun tp -> check_kind tp kind) tps) >>= fun _ -> 58 | return () 59 | | Tensor _, _ -> error (Check_mismatch(kind, "linear tensor product type occurs here")) 60 | | With nts, Linear -> Seq.list (List.map (fun (_, tp) -> check_kind tp kind) nts) >>= fun _ -> 61 | return () 62 | | With _, _ -> error (Check_mismatch(kind, "linear cartesian product type occurs here")) 63 | | Sum cts, Linear -> Seq.list (List.map (fun (_, tp) -> check_kind tp kind) cts) >>= fun _ -> 64 | return () 65 | | Sum cts, Type -> Seq.list (List.map (fun (_, tp) -> check_kind tp kind) cts) >>= fun _ -> 66 | return () 67 | | Sum _, _ -> error (Check_mismatch(kind, "sum type constructor occurs here")) 68 | | Mu(kind', tbody), _ -> 69 | kind_eq kind kind' >>= fun () -> 70 | (out tbody >>= function 71 | | Abs(x, tbody) -> with_hyp (x, Tp(Univ, kind', None)) (check_kind tbody kind') 72 | | _ -> assert false) 73 | | F tp', Linear -> check_kind tp' (Ast.into (loc tp) Type) 74 | | F _, _ -> error (Check_mismatch(kind, "linear F type constructor occurs here")) 75 | | G tp', Type -> check_kind tp' (Ast.into (loc tp) Linear) 76 | | G _, _ -> error (Check_mismatch(kind, "linear G type constructor occurs here")) 77 | | Always tp', Linear -> check_kind tp' kind 78 | | Always tp', _ -> error (Check_mismatch(kind, "linear always type constructor occurs here")) 79 | | Event tp', Linear -> check_kind tp' kind 80 | | Event tp', _ -> error (Check_mismatch(kind, "linear event type constructor occurs here")) 81 | | Var _, _ 82 | | Annot (_,_), _ (* Do we want this? *) 83 | | App (_,_), _ -> synth_kind tp >>= fun kind' -> 84 | kind_eq kind kind' 85 | | Type, _ 86 | | Linear, _ 87 | | Karrow(_, _), _ 88 | | Record _, _ 89 | | Proj (_,_), _ 90 | | Tuple _, _ 91 | | Con _, _ 92 | | Case (_,_), _ 93 | | Num _, _ 94 | | Select _, _ 95 | | Yield _, _ 96 | | Abs (_,_), _ -> assert false 97 | 98 | and synth_kind tp = 99 | out tp >>= function 100 | | Var x -> 101 | (lookup x >>= function 102 | | Context.Tm (_,_) -> error (IllSorted(x, "term variable occurring in type")) 103 | | Context.Tp (_,kind,_) -> return kind 104 | | Context.Mark -> assert false 105 | | Context.Hide _ -> assert false) 106 | | App (tp1, tp2) -> 107 | (synth_kind tp1 >>= fun k1 -> 108 | out k1 >>= function 109 | | Arrow(k2, kind) -> check_kind tp2 k2 >>= fun () -> 110 | return kind 111 | | _ -> error (Synth_mismatch(k1, "function kind"))) 112 | (* Do we want this? *) 113 | | Annot(tp, kind) -> check_kind tp kind >>= fun () -> 114 | return kind 115 | | _ -> assert false 116 | 117 | 118 | -------------------------------------------------------------------------------- /lexer.mll: -------------------------------------------------------------------------------- 1 | { 2 | open Parser 3 | 4 | let stringfold f init s = 5 | let n = String.length s in 6 | let r = ref init in 7 | for i = 0 to n-1 do r := f s.[i] (!r) done; 8 | !r 9 | 10 | let count_newlines s = 11 | stringfold (fun c n -> if c = '\n' then n+1 else n) 0 s 12 | 13 | let repeat n thunk = for i = 0 to n-1 do thunk() done 14 | } 15 | let comment = "//" [^'\n']* "\n" 16 | let digit = ['0'-'9'] 17 | let int = '-'? digit+ 18 | let lident = ['a' - 'z']['a'-'z' 'A'-'Z' '0'-'9' '_' '\'' '?']* 19 | let uident = ['A' - 'Z']['a'-'z' 'A'-'Z' '0'-'9' '_' '\'' '?']* 20 | let whitespace = ['\t' ' ']+ 21 | let new_line = '\n' | '\r' | '\r' '\n' 22 | let string_literal = ([^'\\' '\"' '\n'] | "\\n" | "\\t" | "\\\\" |"\\\"" )* 23 | 24 | rule token = parse 25 | | "type" {TYPE} 26 | | "forall" {FORALL} 27 | | "∀" {FORALL} 28 | | "of" {OF} 29 | | "." {DOT} 30 | | "(" {LPAREN} 31 | | ")" {RPAREN} 32 | | "{" {LBRACE} 33 | | "}" {RBRACE} 34 | | "[" {LBRACK} 35 | | "}" {RBRACK} 36 | | "," {COMMA} 37 | | ";" {SEMI} 38 | | "!" {BANG} 39 | | "fun" {FUN} 40 | | "λ" {FUN} 41 | | "->" {TO} 42 | | "→" {TO} 43 | | "+" {PLUS} 44 | | "-" {MINUS} 45 | | "<" {LT} 46 | | "<=" {LEQ} 47 | | "≤" {LEQ} 48 | | ">=" {GEQ} 49 | | "≥" {GEQ} 50 | | ">" {GT} 51 | | "**" {TENSOR} 52 | | "⊗" {TENSOR} 53 | | "&" {AND} 54 | | "×" {AND} 55 | | "&&" {ANDAND} 56 | | "||" {OR} 57 | | "let" {LET} 58 | | ":" {COLON} 59 | | "=" {EQUAL} 60 | | "in" {IN} 61 | | "fix" {FIX} 62 | | "μ" {FIX} 63 | | "if" {IF} 64 | | "then" {THEN} 65 | | "else" {ELSE} 66 | | "val" {VAL} 67 | | "rec" {REC} 68 | | "match" {MATCH} 69 | | "with" {WITH} 70 | | "|" {BAR} 71 | | "_" {UNDERSCORE} 72 | | int as n {NUM(int_of_string n)} 73 | | '\"' (string_literal as s) '\"' {repeat (count_newlines s) (fun () -> Lexing.new_line lexbuf); STRING s} 74 | | "run" {RUN} 75 | | "bool" {BOOLTYPE} 76 | | "int" {INTTYPE} 77 | | "-o" {LOLLI} 78 | | "⊸" {LOLLI} 79 | | "unit" {UNITTYPE} 80 | | "⊤" {UNITTYPE} 81 | | "I" {I} 82 | | "end" {END} 83 | | lident as s {IDENT s} 84 | | uident as s {CONID s} 85 | | comment {Lexing.new_line lexbuf; token lexbuf} 86 | | whitespace {token lexbuf} 87 | | new_line {Lexing.new_line lexbuf; token lexbuf} 88 | | eof {EOF} 89 | 90 | -------------------------------------------------------------------------------- /parser.mly: -------------------------------------------------------------------------------- 1 | %{ 2 | open Ast 3 | 4 | let make e = into (Parsing.symbol_start_pos(), Parsing.symbol_end_pos()) e 5 | 6 | let forall x tp = make (Forall (make (Abs(x, tp)))) 7 | 8 | let rec abs xs e = 9 | match xs with 10 | | [] -> e 11 | | x :: xs -> make (Abs(x, abs xs e)) 12 | 13 | let rec func (p, xs) e = 14 | make (Lam(p, abs xs e)) 15 | 16 | let rec make_tuple es = 17 | match es with 18 | | [e] -> e 19 | | es -> make (Tuple es) 20 | 21 | let rec make_ptuple ps = 22 | match ps with 23 | | [p] -> p 24 | | ps -> PTuple ps 25 | 26 | let rec make_fun (ps, xs) e = 27 | match ps with 28 | | [] -> abs xs e 29 | | p :: ps -> make (Lam(p, make_fun (ps, xs) e)) 30 | 31 | let rec make_tensor es = 32 | match es with 33 | | [e] -> e 34 | | es -> make (Tensor es) 35 | 36 | %} 37 | 38 | %token TYPE 39 | %token FORALL 40 | %token OF 41 | %token DOT 42 | %token LPAREN 43 | %token RPAREN 44 | %token LBRACE 45 | %token RBRACE 46 | %token LBRACK 47 | %token RBRACK 48 | %token COMMA 49 | %token SEMI 50 | %token BANG 51 | %token FUN 52 | %token TO 53 | %token PLUS 54 | %token MINUS 55 | %token LT 56 | %token LEQ 57 | %token GEQ 58 | %token GT 59 | %token TENSOR 60 | %token AND 61 | %token ANDAND 62 | %token OR 63 | %token LET 64 | %token COLON 65 | %token EQUAL 66 | %token IN 67 | %token FIX 68 | %token IF 69 | %token THEN 70 | %token ELSE 71 | %token VAL 72 | %token REC 73 | %token MATCH 74 | %token WITH 75 | %token BAR 76 | %token UNDERSCORE 77 | %token NUM 78 | %token RUN 79 | %token BOOLTYPE 80 | %token INTTYPE 81 | %token LOLLI 82 | %token UNITTYPE 83 | %token I 84 | %token END 85 | %token IDENT 86 | %token CONID 87 | %token STRING 88 | %token EOF 89 | 90 | 91 | %start tp_start exp_start 92 | %type tp_start 93 | %type exp_start 94 | 95 | %% 96 | 97 | tp_atom : 98 | | IDENT { make (Var $1) } 99 | | LBRACE record_fields RBRACE { make (With $2) } 100 | | LBRACK sum_fields RBRACK { make (Sum $2) } 101 | | LPAREN tp RPAREN { make (out $2) } 102 | | LPAREN tensor_fields RPAREN { make_tensor $2 } 103 | | FIX IDENT DOT LBRACK sum_fields RBRACK { make (Mu(abs [$2] (make (Sum $5)))) } 104 | | UNITTYPE { make_tensor [] } 105 | ; 106 | 107 | tp_app : 108 | | tp_atom { $1 } 109 | | BANG tp_atom { make (Bang $2) } 110 | | tp_app tp_atom { make (App($1, $2)) } 111 | ; 112 | 113 | tp : 114 | | tp_app { $1 } 115 | | tp_app LOLLI tp { make (Lolli($1, $3)) } 116 | | FORALL IDENT DOT tp { forall $2 $4 } 117 | ; 118 | 119 | 120 | record_fields : 121 | | { [] } 122 | | IDENT COLON tp { [$1, $3] } 123 | | IDENT COLON tp SEMI record_fields { ($1, $3) :: $5 } 124 | ; 125 | 126 | sum_fields : 127 | | { [] } 128 | | CONID COLON tp { [$1, $3] } 129 | | CONID COLON tp BAR record_fields { ($1, $3) :: $5 } 130 | ; 131 | 132 | tensor_fields : 133 | | TENSOR tp { [$2] } 134 | | TENSOR tp tensor_fields { $2 :: $3} 135 | ; 136 | 137 | exp_atom : 138 | | IDENT { make (Var $1) } 139 | | CONID { make (Con $1) } 140 | | LPAREN comma_exps RPAREN { make_tuple $2 } 141 | | LBRACE exp_fields RBRACE { make (Record $2) } 142 | | NUM { make (Num $1) } 143 | ; 144 | 145 | exp_fields : 146 | | { [] } 147 | | IDENT COLON exp { [$1, $3] } 148 | | IDENT COLON exp SEMI exp_fields { ($1, $3) :: $5 } 149 | ; 150 | 151 | comma_exps : 152 | | { [] } 153 | | exp { [$1] } 154 | | exp COMMA comma_exps { $1 :: $3} 155 | ; 156 | 157 | exp_app : 158 | | exp_atom { $1 } 159 | | exp_app exp_atom { make (App($1, $2)) } 160 | | exp_app DOT IDENT { make (Proj($1, $3)) } 161 | | BANG exp_atom { make (Bang $2) } 162 | ; 163 | 164 | exp : 165 | | exp_app { $1 } 166 | | exp_app COLON tp { make (Annot($1, $3)) } 167 | | MATCH exp WITH branches END { make (Case($2, $4)) } 168 | | FUN pat_list TO exp { make_fun $2 $4 } 169 | | LET pat EQUAL exp IN exp { let (p, xs) = $2 in 170 | let e = $4 in 171 | let e' = $6 in 172 | make (Case(e, [p, abs xs e'])) } 173 | | LET pat COLON tp EQUAL exp IN exp { let (p, xs) = $2 in 174 | let tp = $4 in 175 | let e = $6 in 176 | let e' = $8 in 177 | make (Case(make (Annot(e, tp)), [p, abs xs e'])) } 178 | | LET IDENT pat_list EQUAL exp IN exp { let f = $2 in 179 | let (ps, xs) = $3 in 180 | let e = $5 in 181 | let e' = $7 in 182 | let fn = make_fun (ps, xs) e in 183 | make (Case(fn, [PVar, abs [f] e'])) 184 | } 185 | 186 | | LET REC IDENT pat_list EQUAL exp IN exp { let f = $3 in 187 | let (ps, xs) = $4 in 188 | let e = $6 in 189 | let e' = $8 in 190 | let fn = make (Mu (abs [f] (make_fun (ps, xs) e))) in 191 | make (Case(fn, [PVar, abs [f] e'])) 192 | } 193 | 194 | | VAL IDENT COLON tp 195 | LET IDENT pat_list EQUAL exp IN exp { let f = $2 in 196 | let tp = $4 in 197 | let f' = $6 in 198 | let (ps, xs) = $7 in 199 | let e = $9 in 200 | let e' = $11 in 201 | if f = f' then 202 | let fn = make_fun (ps, xs) e in 203 | make (Case(make(Annot(fn, tp)), [PVar, abs [f] e'])) 204 | else begin 205 | Parsing.parse_error (Format.sprintf "'%s' does not match '%s'" f f'); 206 | raise Parsing.Parse_error 207 | end 208 | } 209 | 210 | | VAL IDENT COLON tp 211 | LET REC IDENT pat_list EQUAL exp IN exp { let f = $2 in 212 | let tp = $4 in 213 | let f' = $7 in 214 | let (ps, xs) = $8 in 215 | let e = $10 in 216 | let e' = $12 in 217 | if f = f' then 218 | let fn = make (Mu (abs [f] (make_fun (ps, xs) e))) in 219 | make (Case(make(Annot(fn, tp)), [PVar, abs [f] e'])) 220 | else begin 221 | Parsing.parse_error (Format.sprintf "'%s' does not match '%s'" f f'); 222 | raise Parsing.Parse_error 223 | end 224 | } 225 | 226 | ; 227 | 228 | branch : 229 | | pat TO exp { let (p, xs) = $1 in (p, abs xs $3) } 230 | ; 231 | 232 | branches : 233 | | { [] } 234 | | branch { [$1] } 235 | | branch BAR branches { $1 :: $3 } 236 | ; 237 | 238 | pat_atom : 239 | IDENT { (PVar, [$1]) } 240 | | LPAREN pat_commas RPAREN { let (ps, xs) = $2 in (make_ptuple ps, xs) } 241 | ; 242 | 243 | pat : 244 | pat_atom { $1 } 245 | | CONID pat_atom { let (p, xs) = $2 in (PCon($1, p), xs) } 246 | ; 247 | 248 | pat_list : 249 | | pat_atom pat_list { let (p, xs) = $1 in 250 | let (ps, ys) = $2 in 251 | (p :: ps, xs @ ys) } 252 | | pat_atom { let (p, xs) = $1 in ([p], xs) } 253 | ; 254 | 255 | pat_commas : 256 | | pat COMMA pat_commas { let (p, xs) = $1 in 257 | let (ps, ys) = $3 in 258 | (p :: ps, xs @ ys) } 259 | | pat { let (p, xs) = $1 in ([p], xs) } 260 | | { ([], []) } 261 | ; 262 | 263 | tp_start : 264 | tp EOF { $1 } 265 | ; 266 | 267 | exp_start : 268 | exp EOF { $1 } 269 | ; 270 | -------------------------------------------------------------------------------- /util.ml: -------------------------------------------------------------------------------- 1 | module type FUNCTOR = sig 2 | type 'a t 3 | val map : ('a -> 'b) -> 'a t -> 'b t 4 | end 5 | 6 | module type MONAD = sig 7 | include FUNCTOR 8 | val return : 'a -> 'a t 9 | val (>>=) : 'a t -> ('a -> 'b t) -> 'b t 10 | end 11 | 12 | module type MONOIDAL = sig 13 | include FUNCTOR 14 | val unit : unit -> unit t 15 | val ( ** ) : 'a t -> 'b t -> ('a * 'b) t 16 | end 17 | 18 | module type IDIOM = sig 19 | include MONOIDAL 20 | 21 | val return : 'a -> 'a t 22 | val app : ('a -> 'b) t -> 'a t -> 'b t 23 | end 24 | 25 | 26 | module type SEQ = sig 27 | type 'a t 28 | 29 | val pair : 'a t * 'b t -> ('a * 'b) t 30 | val option : 'a t option -> 'a option t 31 | val result : ('a t, 'b) result -> ('a,'b) result t 32 | val list : 'a t list -> 'a list t 33 | end 34 | 35 | module MkIdiom(M : MONOIDAL) : (IDIOM with type 'a t = 'a M.t) = struct 36 | include M 37 | 38 | let return x = map (fun () -> x) (unit()) 39 | let app f x = map (fun (f, x) -> f x) (f ** x) 40 | end 41 | 42 | 43 | 44 | module Monoidal(M : MONAD) : (IDIOM with type 'a t = 'a M.t) = struct 45 | include MkIdiom(struct 46 | type 'a t = 'a M.t 47 | 48 | let map = M.map 49 | 50 | let unit () = M.return () 51 | 52 | let ( ** ) m1 m2 = let open M in 53 | m1 >>= fun v1 -> 54 | m2 >>= fun v2 -> 55 | return (v1, v2) 56 | end) 57 | end 58 | 59 | module Seq(A : IDIOM) : SEQ with type 'a t = 'a A.t = struct 60 | type 'a t = 'a A.t 61 | 62 | open A 63 | 64 | let option = function 65 | | None -> return None 66 | | Some c -> app (return (fun v -> Some v)) c 67 | 68 | let result = function 69 | | Error v -> return (Error v) 70 | | Ok c -> app (return (fun v -> Ok v)) c 71 | 72 | let pair (c, c') = c ** c' 73 | 74 | let cons (x, xs) = x :: xs 75 | 76 | let rec list = function 77 | | [] -> return [] 78 | | m :: ms -> map cons (m ** (list ms)) 79 | end 80 | 81 | module Pair = struct 82 | type ('a, 'b) t = 'a * 'b 83 | let fst = fst 84 | let snd = snd 85 | let map f g (x, y) = (f x, g y) 86 | let pair f g x = (f x, g x) 87 | 88 | let swap (a, b) = (b, a) 89 | let assoc (a, (b, c)) = ((a, b), c) 90 | let assoc' ((a, b), c) = (a, (b, c)) 91 | 92 | let unit (a, ()) = a 93 | let unit' ((), a) = a 94 | 95 | end 96 | 97 | 98 | module Result = struct 99 | type ('a, 'b) t = ('a, 'b) result 100 | 101 | let ok v = Ok v 102 | let error v = Error v 103 | 104 | let result f g = function 105 | | Ok x -> f x 106 | | Error y -> g y 107 | 108 | let map f g = function 109 | | Ok v -> Ok (f v) 110 | | Error e -> Error (g e) 111 | 112 | let return = ok 113 | let (>>=) m f = 114 | match m with 115 | | Ok v -> f v 116 | | Error e -> Error e 117 | end 118 | 119 | module Option = struct 120 | type 'a t = 'a option 121 | 122 | let some v = Some v 123 | let none = None 124 | 125 | let option f y = function 126 | | Some x -> f x 127 | | None -> y 128 | 129 | let map f = function 130 | | Some v -> Some (f v) 131 | | None -> None 132 | 133 | let return = some 134 | let (>>=) m f = 135 | match m with 136 | | Some v -> f v 137 | | None -> None 138 | 139 | include (Monoidal(struct 140 | type 'a t = 'a option 141 | let map = map 142 | let return = return 143 | let (>>=) = (>>=) 144 | end): IDIOM with type 'a t := 'a option) 145 | end 146 | 147 | module Fn = struct 148 | let curry f a b = f (a, b) 149 | let uncurry f (a, b) = f a b 150 | let flip f x y = f y x 151 | let id x = x 152 | let compose f g x = f (g x) 153 | let (@) f g x = g (f x) 154 | let map f g h x = g (h (f x)) 155 | end 156 | 157 | 158 | 159 | 160 | -------------------------------------------------------------------------------- /util.mli: -------------------------------------------------------------------------------- 1 | module type FUNCTOR = sig 2 | type 'a t 3 | val map : ('a -> 'b) -> 'a t -> 'b t 4 | end 5 | 6 | module type MONAD = sig 7 | type 'a t 8 | val map : ('a -> 'b) -> 'a t -> 'b t 9 | val return : 'a -> 'a t 10 | val ( >>= ) : 'a t -> ('a -> 'b t) -> 'b t 11 | end 12 | 13 | module type MONOIDAL = sig 14 | type 'a t 15 | val map : ('a -> 'b) -> 'a t -> 'b t 16 | val unit : unit -> unit t 17 | val ( ** ) : 'a t -> 'b t -> ('a * 'b) t 18 | end 19 | 20 | module type IDIOM = sig 21 | type 'a t 22 | val map : ('a -> 'b) -> 'a t -> 'b t 23 | val unit : unit -> unit t 24 | val ( ** ) : 'a t -> 'b t -> ('a * 'b) t 25 | val return : 'a -> 'a t 26 | val app : ('a -> 'b) t -> 'a t -> 'b t 27 | end 28 | 29 | module type SEQ = sig 30 | type 'a t 31 | val pair : 'a t * 'b t -> ('a * 'b) t 32 | val option : 'a t option -> 'a option t 33 | val result : ('a t, 'b) result -> ('a, 'b) result t 34 | val list : 'a t list -> 'a list t 35 | end 36 | 37 | module MkIdiom : 38 | functor (M : MONOIDAL) -> (IDIOM with type 'a t = 'a M.t) 39 | 40 | module Monoidal : 41 | functor (M : MONAD) -> (IDIOM with type 'a t = 'a M.t) 42 | 43 | module Seq : 44 | functor (A : IDIOM) -> (SEQ with type 'a t = 'a A.t) 45 | 46 | module Pair : 47 | sig 48 | type ('a, 'b) t = 'a * 'b 49 | val fst : 'a * 'b -> 'a 50 | val snd : 'a * 'b -> 'b 51 | val map : ('a -> 'b) -> ('c -> 'd) -> 'a * 'c -> 'b * 'd 52 | val pair : ('a -> 'b) -> ('a -> 'c) -> 'a -> 'b * 'c 53 | val swap : 'a * 'b -> 'b * 'a 54 | val assoc : 'a * ('b * 'c) -> ('a * 'b) * 'c 55 | val assoc' : ('a * 'b) * 'c -> 'a * ('b * 'c) 56 | val unit : 'a * unit -> 'a 57 | val unit' : unit * 'a -> 'a 58 | end 59 | 60 | module Result : sig 61 | type ('a, 'b) t = ('a, 'b) result 62 | val ok : 'a -> ('a, 'b) t 63 | val error : 'a -> ('b, 'a) t 64 | val result : ('a -> 'b) -> ('c -> 'b) -> ('a, 'c) t -> 'b 65 | val map : ('a -> 'b) -> ('c -> 'd) -> ('a, 'c) t -> ('b, 'd) t 66 | val return : 'a -> ('a, 'b) t 67 | val ( >>= ) : ('a, 'b) t -> ('a -> ('c, 'b) t) -> ('c, 'b) t 68 | end 69 | 70 | module Option : sig 71 | type 'a t = 'a option 72 | val some : 'a -> 'a t 73 | val none : 'a t 74 | val option : ('a -> 'b) -> 'b -> 'a t -> 'b 75 | val return : 'a -> 'a t 76 | val ( >>= ) : 'a t -> ('a -> 'b t) -> 'b t 77 | val map : ('a -> 'b) -> 'a t -> 'b t 78 | val unit : unit -> unit t 79 | val ( ** ) : 'a t -> 'b t -> ('a * 'b) t 80 | val app : ('a -> 'b) t -> 'a t -> 'b t 81 | end 82 | 83 | module Fn : sig 84 | val curry : ('a * 'b -> 'c) -> 'a -> 'b -> 'c 85 | val uncurry : ('a -> 'b -> 'c) -> 'a * 'b -> 'c 86 | val flip : ('a -> 'b -> 'c) -> 'b -> 'a -> 'c 87 | val id : 'a -> 'a 88 | val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b 89 | val ( @ ) : ('a -> 'b) -> ('b -> 'c) -> 'a -> 'c 90 | val map : ('a -> 'b) -> ('c -> 'd) -> ('b -> 'c) -> 'a -> 'd 91 | end 92 | --------------------------------------------------------------------------------