From bb280e882dde47f033d9c52bc04a86825202db88 Mon Sep 17 00:00:00 2001 From: Adrien Guatto Date: Wed, 25 Oct 2023 18:42:49 +0200 Subject: [PATCH] Cours 6 et typo jalon 2 --- cours/cours-04/.ocamlinit | 8 ++ cours/cours-04/Id.ml | 46 ++++++++ cours/cours-04/Id.mli | 31 ++++++ cours/cours-04/Lang0.ml | 162 +++++++++++++++++++++++++++ cours/cours-04/Lang1.ml | 180 ++++++++++++++++++++++++++++++ cours/cours-04/Lang2.ml | 194 +++++++++++++++++++++++++++++++++ cours/cours-04/Rewrite.ml | 57 ++++++++++ cours/cours-04/Rewrite.mli | 14 +++ cours/cours-04/Seq.ml | 46 ++++++++ cours/cours-04/dune | 5 + cours/cours-04/dune-project | 1 + cours/cours-interpretation.pdf | Bin 0 -> 439228 bytes cours/journal.org | 13 +++ jalons/jalon-2.pdf | Bin 352835 -> 352819 bytes 14 files changed, 757 insertions(+) create mode 100644 cours/cours-04/.ocamlinit create mode 100644 cours/cours-04/Id.ml create mode 100644 cours/cours-04/Id.mli create mode 100644 cours/cours-04/Lang0.ml create mode 100644 cours/cours-04/Lang1.ml create mode 100644 cours/cours-04/Lang2.ml create mode 100644 cours/cours-04/Rewrite.ml create mode 100644 cours/cours-04/Rewrite.mli create mode 100644 cours/cours-04/Seq.ml create mode 100644 cours/cours-04/dune create mode 100644 cours/cours-04/dune-project create mode 100644 cours/cours-interpretation.pdf diff --git a/cours/cours-04/.ocamlinit b/cours/cours-04/.ocamlinit new file mode 100644 index 0000000..4cd5be5 --- /dev/null +++ b/cours/cours-04/.ocamlinit @@ -0,0 +1,8 @@ +open Cours04;; + +#install_printer Lang0.pp;; +#install_printer Lang1.pp;; +#install_printer Lang2.pp;; +#install_printer Lang2.pp_value;; + +module R = Rewrite.Make(Lang1);; diff --git a/cours/cours-04/Id.ml b/cours/cours-04/Id.ml new file mode 100644 index 0000000..0bf736f --- /dev/null +++ b/cours/cours-04/Id.ml @@ -0,0 +1,46 @@ +module S = struct + type t = string + + let compare (x : t) y = Stdlib.compare x y + + let pp = Fmt.string +end + +include S + +let fresh, reset = + let r = ref 0 in + (fun () -> incr r; Printf.sprintf "_x%d" !r), + (fun () -> r := 0) + +type 'a subst = (t * 'a) list + +let pp_subst pp_val = + let pp_kv ff (x, v) = Format.fprintf ff "%a\\%a" pp x pp_val v in + Fmt.(box (list ~sep:comma pp_kv)) + +let empty = [] + +let extend x v xs = (x, v) :: xs + +let assoc = List.assoc + +let singleton x v = [(x, v)] + +let trim xs = + List.fold_right + (fun (x, v) xs -> (x, v) :: List.remove_assoc x xs) + xs + [] + +let domain xs = trim xs |> List.map fst + +type 'a rel = 'a -> 'a -> bool + +let included r xs ys = + try List.for_all (fun (x, v) -> r v (List.assoc x ys)) (trim xs) + with Not_found -> false + +let equal_subst eq xs ys = included eq xs ys && included eq ys xs + +module Set = Set.Make(S) diff --git a/cours/cours-04/Id.mli b/cours/cours-04/Id.mli new file mode 100644 index 0000000..86463ff --- /dev/null +++ b/cours/cours-04/Id.mli @@ -0,0 +1,31 @@ +type t = string + +val compare : t -> t -> int + +val pp : t Fmt.t + +val fresh : unit -> t + +type 'a subst = (t * 'a) list + +val pp_subst : 'a Fmt.t -> 'a subst Fmt.t + +val empty : 'a subst + +val extend : t -> 'a -> 'a subst -> 'a subst + +val assoc : t -> 'a subst -> 'a + +val singleton : t -> 'a -> 'a subst + +val domain : 'a subst -> t list + +type 'a rel = 'a -> 'a -> bool + +val included : 'a rel -> 'a subst rel + +val equal_subst : 'a rel -> 'a subst rel + +val reset : unit -> unit + +module Set : Set.S with type elt = t diff --git a/cours/cours-04/Lang0.ml b/cours/cours-04/Lang0.ml new file mode 100644 index 0000000..5c0d515 --- /dev/null +++ b/cours/cours-04/Lang0.ml @@ -0,0 +1,162 @@ +type t = + | Var of Id.t + | Lit of int + | Add of t * t + | Let of t * bound1 + +and bound1 = { bound : Id.t; body : t; } + +let rec pp ff = function + | Var x -> + Id.pp ff x + | Lit n -> + Format.fprintf ff "%d" n + | Add (e1, e2) -> + Format.fprintf ff "@[@[%a@]@ + @[%a@]@]" + pp e1 + pp e2 + | Let (e1, e2) -> + Format.fprintf ff "let(@[@[%a@],@ @[%a@]@])" + pp e1 + pp_bound1 e2 + +and pp_bound1 ff { bound; body; } = + Format.fprintf ff "@[%a.@,@[%a@]@]" + Id.pp bound + pp body + +let pp_substitution ff xs = + Fmt.list ~sep:Fmt.comma + (fun ff (x, e) -> + Format.fprintf ff "%a\\@[%a@]" Id.pp x pp e) + ff xs + +module Build = struct + let v x = Var x + let l i = Lit i + let ( + ) e1 e2 = Add (e1, e2) + let ( let* ) e1 mk_e2 = + let bound = Id.fresh () in + Let (e1, { bound; body = mk_e2 (Var bound); }) +end + +let rec subst s = function + | Var x -> + begin try Id.assoc x s with Not_found -> Var x end + | Lit k -> + Lit k + | Add (e1, e2) -> + Add (subst s e1, subst s e2) + | Let (e1, e2) -> + Let (subst s e1, subst_bound1 s e2) + +and subst_bound1 s { bound = x; body; } = + let x' = Id.fresh () in + { bound = x'; body = subst (Id.extend x (Var x') s) body; } + +let%expect_test "subst" = + Id.reset (); + let print_subst e x e' = + Format.printf "@[(@[%a@])[%a\\@[%a@]]@ = @[%a@]@]@." + pp e + Id.pp x + pp e' + pp (subst [(x, e')] e) + in + let open Build in + print_subst (l 1 + v "x") "x" (v "y"); + [%expect {| (1 + x)[x\y] = 1 + y |}]; + print_subst (Let (l 2, { bound = "y"; body = l 1 + v "x" + v "y"; })) + "x" (v "y"); + [%expect {| (let(2, y.1 + x + y))[x\y] = let(2, _x1.1 + y + _x1) |}]; + ();; + +let rec equal e e' = + match e, e' with + | Var x, Var x' -> + x = x' + | Lit i, Lit i' -> + i = i' + | Add (e1, e2), Add (e1', e2') -> + equal e1 e1' && equal e2 e2' + | Let (e1, e2), Let (e1', e2') -> + equal e1 e1' && equal_bound1 e2 e2' + | _ -> + false + +and equal_bound1 { bound = x; body = e; } { bound = x'; body = e'; } = + let y = Id.fresh () in + equal + (subst Id.(singleton x (Var y)) e) + (subst Id.(singleton x' (Var y)) e') + +and equal_subst sub1 sub2 = Id.equal_subst equal sub1 sub2 + +let%expect_test "equal" = + Id.reset (); + let print_equal e1 e2 = + Format.printf "@[@[%a@]@ = @[%a@]: %b@]@." + pp e1 + pp e2 + (equal e1 e2) + in + let open Build in + print_equal (let* x = l 1 in x) (let* y = l 1 in y); + [%expect {| let(1, _x2._x2) = let(1, _x1._x1): true |}]; + print_equal (let* x = l 1 in x) (let* y = l 2 in y); + [%expect {| let(1, _x5._x5) = let(2, _x4._x4): false |}]; + print_equal + (let* x = l 1 in let* k = l 2 in x + k) + (let* y = l 1 in let* k = l 2 in y + k); + [%expect {| + let(1, _x8.let(2, _x9._x8 + _x9)) = let(1, _x6.let(2, _x7._x6 + _x7)): true |}]; + print_equal + (let* x = l 1 in let* k = l 2 in x + k) + (let* y = l 1 in let* k = l 2 in k + y); + [%expect {| + let(1, _x16.let(2, _x17._x16 + _x17)) + = let(1, _x14.let(2, _x15._x15 + _x14)): false |}];; + +let rec free_vars : t -> Id.Set.t = function + | Var x -> Id.Set.singleton x + | Lit _ -> Id.Set.empty + | Add (e1, e2) -> Id.Set.union (free_vars e1) (free_vars e2) + | Let (e1, e2) -> Id.Set.union (free_vars e1) (free_vars_bound1 e2) + +and free_vars_bound1 { bound; body; } = + Id.Set.remove bound (free_vars body) + +let%expect_test "free_vars" = + Id.reset (); + let print_free_vars e = + Format.printf "@[free_vars (@[%a@])@ = {@[%a@]}@]@." + pp e + Fmt.(list ~sep:comma Id.pp) (free_vars e |> Id.Set.to_seq |> List.of_seq) + in + let open Build in + print_free_vars (l 1 + l 2); + [%expect {| free_vars (1 + 2) = {} |}]; + print_free_vars (let* x = l 12 in l 1 + x + v "y"); + [%expect {| free_vars (let(12, _x1.1 + _x1 + y)) = {y} |}]; + print_free_vars (let* x = l 12 in let* y = v "z" in l 1 + x + y); + [%expect {| free_vars (let(12, _x2.let(z, _x3.1 + _x2 + _x3))) = {z} |}]; + () + +let close_with { bound; body; } e = subst Id.(singleton bound e) body + +let rec eval : t -> int = + function + | Var _ -> failwith "open term" + | Lit k -> k + | Add (e1, e2) -> eval e1 + eval e2 + | Let (e, b) -> eval (close_with b e) + +(* Tests fixtures *) + +let e1, e2, e3, e4 = + Id.reset (); + let open Build in + (l 1 + l 1), + (let* x = l 1 + l 1 in x), + (let* x = l 1 + l 1 in l 40 + x), + (let* x = l 1 + l 1 in let* y = x + l 1 in let* x = l 3 in x + y) diff --git a/cours/cours-04/Lang1.ml b/cours/cours-04/Lang1.ml new file mode 100644 index 0000000..6e4cfb9 --- /dev/null +++ b/cours/cours-04/Lang1.ml @@ -0,0 +1,180 @@ +type t = + | Var of Id.t + | Lit of int + | Add of t * t + | Let of t * bound1 + | Hole of t Id.subst + +and bound1 = B of Id.t * t + +let rec pp ff = function + | Var x -> + Id.pp ff x + | Lit n -> + Format.fprintf ff "%d" n + | Add (e1, e2) -> + Format.fprintf ff "add(@[@[%a@],@ @[%a@]@])" + pp e1 + pp e2 + | Let (e1, e2) -> + Format.fprintf ff "let(@[@[%a@],@ @[%a@]@])" + pp e1 + pp_bound1 e2 + | Hole s -> + Format.fprintf ff "[]{@[%a@]}" + pp_substitution s + +and pp_bound1 ff (B (x, e)) = + Format.fprintf ff "@[%a.@,@[%a@]@]" + Id.pp x + pp e + +and pp_substitution ff xs = + Fmt.list ~sep:Fmt.comma + (fun ff (x, e) -> + Format.fprintf ff "%a\\@[%a@]" Id.pp x pp e) + ff xs + +module Builder = struct + let v x = Var x + let l i = Lit i + let ( + ) e1 e2 = Add (e1, e2) + let ( let* ) e1 mk_e2 = let x = Id.fresh () in Let (e1, B (x, mk_e2 (Var x))) + let h = Hole [] +end + +let rec subst s = function + | Var x -> + begin try Id.assoc x s with Not_found -> Var x end + | Lit k -> + Lit k + | Add (e1, e2) -> + Add (subst s e1, subst s e2) + | Let (e1, e2) -> + Let (subst s e1, subst_bound1 s e2) + | Hole s' -> + Hole (compose s' s) + +and subst_bound1 s (B (x, e)) = + let x' = Id.fresh () in + B (x', subst (Id.extend x (Var x') s) e) + +and compose s1 s2 = + match s1 with + | [] -> s2 + | (x, t) :: s1 -> (x, subst s2 t) :: compose s1 s2 + +let rec equal e e' = + match e, e' with + | Var x, Var x' -> + x = x' + | Lit i, Lit i' -> + i = i' + | Add (e1, e2), Add (e1', e2') -> + equal e1 e1' && equal e2 e2' + | Let (e1, e2), Let (e1', e2') -> + equal e1 e1' && equal_bound1 e2 e2' + | Hole sub1, Hole sub2 -> + equal_subst sub1 sub2 + | _ -> + false + +and equal_bound1 (B (x, e)) (B (x', e')) = + let y = Id.fresh () in + equal + (subst Id.(singleton x (Var y)) e) + (subst Id.(singleton x' (Var y)) e') + +and equal_subst sub1 sub2 = Id.equal_subst equal sub1 sub2 + +let%expect_test "e1" = + Id.reset (); + let print e1 e2 = + Format.printf "@[@[%a@]@ = @[%a@]: %b@]@." + pp e1 + pp e2 + (equal e1 e2) + in + let open Builder in + print (let* x = l 1 in x) (let* y = l 1 in y); + [%expect {| let(1, _x2._x2) = let(1, _x1._x1): true |}]; + print (let* x = l 1 in x) (let* y = l 2 in y); + [%expect {| let(1, _x5._x5) = let(2, _x4._x4): false |}]; + print + (let* x = l 1 in let* k = l 2 in x + k) + (let* y = l 1 in let* k = l 2 in y + k); + [%expect {| + let(1, _x8.let(2, _x9.add(_x8, _x9))) + = let(1, _x6.let(2, _x7.add(_x6, _x7))): true |}]; + print + (let* x = l 1 in let* k = l 2 in x + k) + (let* y = l 1 in let* k = l 2 in k + y); + [%expect {| + let(1, _x16.let(2, _x17.add(_x16, _x17))) + = let(1, _x14.let(2, _x15.add(_x15, _x14))): false |}];; + +let close_with (B (x, e)) e' = subst Id.(singleton x e') e + +let rec plug k e = + match k with + | (Var _ | Lit _) as k -> k + | Add (k1, k2) -> Add (plug k1 e, plug k2 e) + | Let (k1, k2) -> Let (plug k1 e, plug_bound1 k2 e) + | Hole s -> subst s e + +and plug_bound1 (B (x, k)) e = B (x, plug k e) + +let beta0 : t -> t option + = function + | Add (Lit k1, Lit k2) -> + Some (Lit (k1 + k2)) + | Let (e1, e2) -> + Some (close_with e2 e1) + | _ -> + None + +let wrap f (k, e) = (f k, e) + +let rec decompose t = + Seq.cons (Hole [], t) (decompose_subterms t) + +and decompose_subterms = function + | Var _ | Lit _ | Hole _ -> + Seq.empty + | Add (e1, e2) -> + Seq.interleave + (decompose e1 |> Seq.map (wrap (fun k -> Add (k, e2)))) + (decompose e2 |> Seq.map (wrap (fun k -> Add (e1, k)))) + | Let (e1, B (x, e2)) -> + Seq.interleave + (decompose e1 |> Seq.map (wrap (fun k -> Let (k, B (x, e2))))) + (decompose e2 |> Seq.map (wrap (fun k -> Let (e1, B (x, k))))) + +let rewrite e = + decompose e + |> Seq.filter_map (fun (k, e) -> beta0 e |> Option.map (fun e -> (k, e))) + |> Seq.map (fun (k, e) -> plug k e) + +(* Test fixtures *) + +let e1, e2, e3, e4 = + Id.reset (); + let open Builder in + (l 1 + l 1), + (let* x = l 1 + l 1 in x), + (let* x = l 1 + l 1 in l 40 + x), + (let* x = l 1 + l 1 in let* y = x + l 1 in let* x = l 3 in x + y) + +let%expect_test "rew0" = + Id.reset (); + let e = Builder.(let* x = l 1 + l 1 in l 28 + l 12 + x) in + Format.printf "%a@." pp e; + [%expect {| let(add(1, 1), _x1.add(add(28, 12), _x1)) |}]; + Format.printf "@[@[%a@]@ -> @[%a@]@]@." + pp e + Fmt.(list ~sep:comma pp) (rewrite e |> List.of_seq); + [%expect {| + let(add(1, 1), _x1.add(add(28, 12), _x1)) + -> add(add(28, 12), add(1, 1)), + let(2, _x1.add(add(28, 12), _x1)), + let(add(1, 1), _x1.add(40, _x1)) |}] diff --git a/cours/cours-04/Lang2.ml b/cours/cours-04/Lang2.ml new file mode 100644 index 0000000..031360a --- /dev/null +++ b/cours/cours-04/Lang2.ml @@ -0,0 +1,194 @@ +(** {2 Abstract Syntax Trees} *) + +type t = Var of Id.t (* occurrence "x", "y", etc. *) + | Int of int (* constante litérale "42", etc. *) + | Add of t * t (* somme "e1 + e2" *) + | Bool of bool (* booléen litéral "true", "false" *) + | If of t * t * t (* conditionnelle *) + | Let of t * bound1 (* déf. locale "let e1 be x in e2" *) + | Fun of bound1 (* fonction anonyme "fun x -> e" *) + | App of t * t (* application "e1 e2" *) + | Ref of t (* allocation "ref e" *) + | Read of t (* déréférencement "!e" *) + | Asgn of t * t (* assignation "e1 := e2" *) + | Unit (* 0-uplet *) + | Seq of t * t (* séquence "e1; e2" *) + +and bound1 = { bound : Id.t; body : t; } + +(** {2 Evaluation} *) + +type env = (Id.t * value) list + +and value = + | VInt of int + | VBool of bool + | VFun of bound1 * env + | VRef of value ref + | VUnit + +let rec eval env = function + | Var x -> List.assoc x env + | Int n -> VInt n + | Add (e1, e2) -> add_values (eval env e1) (eval env e2) + | Bool b -> VBool b + | If (e1, e2, e3) -> if_value (eval env e1) env e2 e3 + | Let (e, b) -> eval_bound1 env b (eval env e) + | Fun b -> VFun (b, env) + | App (e1, e2) -> app_values (eval env e1) (eval env e2) + | Ref e -> VRef (ref (eval env e)) + | Read e -> read_value (eval env e) + | Asgn (e1, e2) -> asgn_values (eval env e1) (eval env e2) + | Unit -> VUnit + | Seq (e1, e2) -> seq_value (eval env e1) env e2 + +and eval_bound1 env { bound; body; } v = + eval ((bound, v) :: env) body + +and add_values v1 v2 = + match v1, v2 with + | VInt n1, VInt n2 -> VInt (n1 + n2) + | _ -> failwith "ill-typed" + +and if_value v1 env e2 e3 = + match v1 with + | VBool true -> eval env e2 + | VBool false -> eval env e3 + | _ -> failwith "ill-typed" + +and app_values v1 v2 = + match v1 with + | VFun (b, env) -> eval_bound1 env b v2 + | _ -> failwith "ill-typed" + +and read_value v = + match v with VRef r -> !r | _ -> failwith "ill-typed" + +and asgn_values v1 v2 = + match v1 with VRef r -> r := v2; VUnit | _ -> failwith "ill-typed" + +and seq_value v1 env e2 = + match v1 with VUnit -> eval env e2 | _ -> failwith "ill-typed" + +(** {2 Pretty-printing} *) + +let rec pp ff = + let pp_maybe_paren ?(space = true) prefix pp ff e = + match e with + | Var _ | Int _ | Bool _ | Unit -> + Format.fprintf ff "@[%s%a@[%a@]@]" + prefix + Fmt.(if space then sp else nop) () + pp e + | _ -> + Format.fprintf ff "@[%s(@[%a@])@]" + prefix + pp e + in + function + | Var x -> + Id.pp ff x + | Int n -> + Format.fprintf ff "%d" n + | Add (e1, e2) -> + Format.fprintf ff "(@[@[%a@] +@ @[%a@]@])" + pp e1 + pp e2 + | Bool b -> + Format.fprintf ff "%b" b + | If (e1, e2, e3) -> + Format.fprintf ff "if(@[@[%a@],@ @[%a@],@ @[%a@]@])" + pp e1 + pp e2 + pp e3 + | Let (e1, e2) -> + Format.fprintf ff "let(@[@[%a@],@ @[%a@]@])" + pp e1 + pp_bound1 e2 + | Fun b -> + Format.fprintf ff "fun(@[%a@])" + pp_bound1 b + | App (e1, e2) -> + Format.fprintf ff "(@[@[%a@]@ @[%a@]@])" + pp e1 + pp e2 + | Ref e -> + pp_maybe_paren "ref" pp ff e + | Read e -> + pp_maybe_paren ~space:false "!" pp ff e + | Asgn (e1, e2) -> + Format.fprintf ff "(@[@[%a@]@ := @[%a@]@])" + pp e1 + pp e2 + | Unit -> + Format.fprintf ff "()" + | Seq (e1, e2) -> + Format.fprintf ff "(@[@[%a@];@ @[%a@]@])" + pp e1 + pp e2 + +and pp_bound1 ff { bound; body; } = + Format.fprintf ff "@[%a.@,@[%a@]@]" + Id.pp bound + pp body + +let rec pp_value ff = function + | VInt n -> + Format.fprintf ff "%d" n + | VBool b -> + Format.fprintf ff "%b" b + | VRef _ -> + Format.fprintf ff "ref(..)" + | VUnit -> + Format.fprintf ff "()" + | VFun (b, env) -> + Format.fprintf ff "@[fun(@[%a@])@,[@[%a@]]@]" + pp_bound1 b + pp_env env + +and pp_env ff env = + let pp_binding ff (x, v) = + Format.fprintf ff "@[%a@ = @[%a@]@]" + Id.pp x + pp_value v + in + Fmt.(list ~sep:comma pp_binding) ff env + +(** {2 AST Building Helpers} *) + +module Build = struct + let fresh_bound1 mk = + let x = Id.fresh () in { bound = x; body = mk (Var x); } + + let v x = Var x + let i n = Int n + let ( + ) e1 e2 = Add (e1, e2) + let b b = Bool b + let if_ e1 e2 e3 = If (e1, e2, e3) + let ( let* ) e1 mk_e2 = Let (e1, fresh_bound1 mk_e2) + let fun_ mk_body = Fun (fresh_bound1 mk_body) + let app f args = List.fold_left (fun f arg -> App (f, arg)) f args + let ref_ e = Ref e + let ( ! ) e = Read e + let ( := ) e1 e2 = Asgn (e1, e2) + let s = function + | [] -> Unit + | e :: es -> List.fold_left (fun e1 e2 -> Seq (e1, e2)) e es +end + +(** {2 Tests} *) + +let print_eval e = + let v = eval [] e in + Format.printf "@[@[%a@]@ => @[%a@]@]@." + pp e + pp_value v + +let%expect_test "test" = + Id.reset (); + let open Build in + print_eval (i 1 + i 2); + [%expect {| (1 + 2) => 3 |}]; + print_eval (let* x = ref_ (i 1) in + s [x := i 2; !x] + !x); + [%expect {| let(ref 1, _x1.(((_x1 := 2); !_x1) + !_x1)) => 3 |}] diff --git a/cours/cours-04/Rewrite.ml b/cours/cours-04/Rewrite.ml new file mode 100644 index 0000000..11f3259 --- /dev/null +++ b/cours/cours-04/Rewrite.ml @@ -0,0 +1,57 @@ +module type LANG = sig + type t + val pp : t Fmt.t + val equal : t -> t -> bool + val rewrite : t -> t Seq.t +end + +module Make(L : LANG) = struct + type graph = (L.t * L.t) Seq.t + + let rec reductions t = + let open Seq in + let* t' = L.rewrite t in + cons (t, t') (reductions t') + + let is_normal t = + L.rewrite t |> Seq.uncons |> Option.is_none + + let normal_forms t = + let open Seq in + reductions t |> map snd |> filter is_normal |> Seq.dedup L.equal + + let to_graphviz g = + let b = Buffer.create 100 in + let ff = Format.formatter_of_buffer b in + + (* Disable line breaks. *) + let ff_funs = Format.pp_get_formatter_out_functions ff () in + Format.pp_set_formatter_out_functions + ff + { ff_funs with + out_newline = (fun _ -> ()); + out_indent = (fun _ -> ()); + out_spaces = (fun _ -> ()); + }; + + Format.fprintf ff "strict digraph {\n"; + Format.fprintf ff " overlap=scale;\n"; + Format.fprintf ff " splines=true;\n"; + Format.fprintf ff " rankdir=\"LR\";\n"; + Seq.iter (fun (t, t') -> + Format.fprintf ff "\"%a\" -> \"%a\";\n" + L.pp t + L.pp t') g; + Format.fprintf ff "}@."; + Buffer.contents b + + let display ?(verbose = false) ?(max = 20) g = + let gv_fn, oc = Filename.open_temp_file "red" ".dot" in + let pdf_fn = Filename.temp_file "graph" ".pdf" in + output_string oc @@ to_graphviz @@ Seq.take max g; + close_out oc; + if verbose then Printf.eprintf "Graph in %s, PDF in %s\n" gv_fn pdf_fn; + flush stderr; + ignore @@ Unix.system Printf.(sprintf "dot -Tpdf %s > %s" gv_fn pdf_fn); + ignore @@ Unix.system Printf.(sprintf "xdg-open %s" pdf_fn) +end diff --git a/cours/cours-04/Rewrite.mli b/cours/cours-04/Rewrite.mli new file mode 100644 index 0000000..3af2ed8 --- /dev/null +++ b/cours/cours-04/Rewrite.mli @@ -0,0 +1,14 @@ +module type LANG = sig + type t + val pp : t Fmt.t + val equal : t -> t -> bool + val rewrite : t -> t Seq.t +end + +module Make(L : LANG) : sig + type graph = (L.t * L.t) Seq.t + val reductions : L.t -> graph + val is_normal : L.t -> bool + val normal_forms : L.t -> L.t Seq.t + val display : ?verbose:bool -> ?max:int -> graph -> unit +end diff --git a/cours/cours-04/Seq.ml b/cours/cours-04/Seq.ml new file mode 100644 index 0000000..8ea4166 --- /dev/null +++ b/cours/cours-04/Seq.ml @@ -0,0 +1,46 @@ +include Stdlib.Seq + +let hd xs = uncons xs |> Option.map fst +let tl xs = uncons xs |> Option.map snd + +let rec const x () = cons x (const x) () + +let rec nth : type a. int -> a t -> a option = + fun n xs -> + if n = 0 then hd xs else tl xs |> Option.map (nth (n - 1)) |> Option.join + +let join : type a. a t t -> a t = + let rec aux todo n k xss = + let continue () = aux [] (n + 1) n (append List.(to_seq @@ rev todo) xss) in + if k < 0 then continue () + else + begin match uncons xss, todo with + | None, [] -> + empty + | None, _ :: _ -> + continue () + | Some (xs, xss), _ -> + begin match uncons xs with + | None -> aux todo n (k - 1) xss + | Some (x, xs) -> fun () -> cons x (aux (xs :: todo) n (k - 1) xss) () + end + end + in + fun xss () -> aux [] 1 0 xss () + +let ( let* ) xs f = map f xs |> concat + +let rec combine f xs ys = + match uncons xs, uncons ys with + | Some (x, xs), Some (y, ys) -> fun () -> cons (f x y) (combine f xs ys) () + | None, _ | _, None -> empty + +let rec dedup eq xs = + match uncons xs with + | None -> xs + | Some (x, xs) -> cons x (filter (fun x' -> not (eq x x')) (dedup eq xs)) + +let rec nat : int t = fun () -> cons 0 (map ((+) 1) nat) () + +let nats : (int * int) t t = + combine (fun x ys -> map (fun y -> (x, y)) ys) nat (const nat) diff --git a/cours/cours-04/dune b/cours/cours-04/dune new file mode 100644 index 0000000..26cb81f --- /dev/null +++ b/cours/cours-04/dune @@ -0,0 +1,5 @@ +(library + (name cours04) + (libraries fmt unix) + (inline_tests) + (preprocess (pps ppx_expect))) diff --git a/cours/cours-04/dune-project b/cours/cours-04/dune-project new file mode 100644 index 0000000..929c696 --- /dev/null +++ b/cours/cours-04/dune-project @@ -0,0 +1 @@ +(lang dune 2.0) diff --git a/cours/cours-interpretation.pdf b/cours/cours-interpretation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aba3e62c87280af6fe610802b131443c3ae0a867 GIT binary patch literal 439228 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<2023-10-18> + On revient sur la gestion de la liaison, et de l'évaluation, voir les + [[file:cours-semantique.pdf][transparents]]. +* Cours 06 <2023-10-25> + On termine les transparents précédents sur l'écriture d'évaluateurs. + + Attention : le fichier contenant les diapos a été renommé, c'est désormais + [[file:cours-interpretation.pdf][transparents]]. + + On décrit le jalon 2. diff --git a/jalons/jalon-2.pdf b/jalons/jalon-2.pdf index c3cd41720ab8610c8d483eeec47844e4691eb0c3..a78fe0b30546d71ab9ea66e3a48080db642892fc 100644 GIT binary patch delta 5201 zcmV-X6t3&T#1*r|6|i9!12i}}mmuo|D1Yr;S&tjX5q{ra!91CS!*<_?3@1oz$#CKX zNGv!Hk^xiPk;H&Yu1T(9*zkW(^<128*32}?Ay-QDu;8)Hn(jKjI{KocHzPXw`i7RT ze|~=R*)yd^j1i|4A3c9PVvbnJM@Cb^{WrIx7h_JuWXc#<?Z(a(;UQ!`f3;*BkqdfBlc~eZ$%q1(!?2IeH%@v8cD*KD4J1hti(7qnl@S;4zNkn5oH`gG!W%fc*Wrs zI0$_ZtZ4bu!=jW&RtRyqm@p7P{{AK9pi7$4@$IaV;_{P1M(-Az^=j26F@Gj4NJ<{^ zBj}bR!mz4MwksbpD>`uJ73prh*klNOEePXH@*E+r2varr--py|HH8runu@4~W<-hu 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