Added interval domains + fixed nix

Makefile

@@ -21,7 +21,7 @@ cleantest:
 # Use `make test TEST_OPT="--flags"` to run tests with extra flags.
 TEST_OPT::=""
 test: cleantest all
-	@scripts/test.sh . ${TEST_OPT}
+	@bash scripts/test.sh . ${TEST_OPT}
 
 doc: all
 	@dune build @doc-private

domains/interval.ml

@@ -0,0 +1,122 @@
+open Naked
+open Abstract_syntax_tree
+
+module Interval : NAKED_VALUE_DOMAIN = struct
+  type t = { lower : Z.t; upper : Z.t }
+
+  let const a = { lower = a; upper = a }
+  let rand a b = { lower = Z.min a b; upper = Z.max a b }
+  let infty = Z.of_int64_unsigned Int64.max_int
+  let min_infty = Z.neg infty
+
+  let rand3 a b c =
+    let mi = List.fold_left Z.min a [ a; b; c ] in
+    let ma = List.fold_left Z.max a [ a; b; c ] in
+    rand mi ma
+
+  let rand4 a b c d =
+    let mi = List.fold_left Z.min a [ a; b; c; d ] in
+    let ma = List.fold_left Z.max a [ a; b; c; d ] in
+    rand mi ma
+
+  let minus z = rand (Z.neg z.upper) (Z.neg z.lower)
+  
+  let join z1 z2 = rand4 z1.lower z2.lower z1.upper z2.upper
+  let meet z1 z2 =
+    if Z.leq z1.upper z2.lower || Z.leq z2.upper z1.lower then raise Absurd
+    else rand (Z.max z1.lower z2.lower) (Z.min z1.upper z2.upper)
+  let widen z1 z2 =
+    rand
+      (if Z.leq z1.lower z2.lower then z1.lower else min_infty)
+      (if Z.geq z1.upper z2.upper then z1.upper else infty)
+  let narrow = meet
+  let subset z1 z2 = Z.geq z1.lower z2.lower && Z.leq z1.upper z2.upper
+
+
+  let binary z1 z2 = function
+    | AST_PLUS -> rand (Z.add z1.lower z2.lower) (Z.add z1.upper z2.upper)
+    | AST_MINUS -> rand (Z.sub z1.lower z2.upper) (Z.sub z1.upper z2.lower)
+    | AST_MULTIPLY ->
+        rand4 (Z.mul z1.lower z2.lower) (Z.mul z1.upper z2.lower)
+          (Z.mul z1.lower z2.upper) (Z.mul z1.upper z2.upper)
+    | AST_DIVIDE ->
+        if Z.sign z2.lower <> Z.sign z2.upper || Z.sign z2.lower = 0 then
+          raise Absurd
+        else
+          rand4 (Z.div z1.lower z2.lower) (Z.div z1.upper z2.lower)
+            (Z.div z1.lower z2.upper) (Z.div z1.upper z2.upper)
+    | AST_MODULO ->
+        if Z.sign z2.lower <> Z.sign z2.upper || Z.sign z2.lower = 0 then raise Absurd
+        else
+          rand4 (Z.rem z1.lower z2.lower) (Z.rem z1.upper z2.lower)
+            (Z.rem z1.lower z2.upper) (Z.rem z1.upper z2.upper)
+
+  let is_only_zero z = Z.equal z.lower Z.zero && Z.equal z.upper Z.zero
+  let multiples_of z = if is_only_zero z then const Z.zero else raise NeedTop
+  let divisors_of z = if is_only_zero z then const Z.zero else raise NeedTop
+  let remainders z = if is_only_zero z then const Z.zero else raise NeedTop
+  let convex_sym z = if is_only_zero z then const Z.zero else raise NeedTop
+
+  let compatible z = function
+    | AST_EQUAL -> z
+    | AST_NOT_EQUAL -> raise NeedTop
+    | AST_LESS ->
+        if Z.equal z.lower min_infty then raise Absurd
+        else rand min_infty z.lower
+    | AST_LESS_EQUAL -> rand min_infty z.lower
+    | AST_GREATER ->
+        if Z.equal z.upper infty then raise Absurd else rand z.upper infty
+    | AST_GREATER_EQUAL -> rand z.upper infty
+
+  let rec compare z1 z2 = function
+    | AST_EQUAL ->
+        let z = join z1 z2 in
+        (z, z)
+    | AST_NOT_EQUAL ->
+        if
+          Z.equal z1.lower z1.upper && Z.equal z1.upper z2.lower
+          && Z.equal z2.lower z2.upper
+        then raise Absurd
+        else (z1, z2)
+    | AST_LESS ->
+        if Z.leq z2.upper z1.lower then raise Absurd
+        else
+          let r1 =
+            rand z1.lower
+              (if Z.geq z1.upper z2.upper then Z.pred z2.upper else z1.upper)
+          in
+          let r2 =
+            rand
+              (if Z.geq z1.lower z2.lower then Z.succ z2.lower else z1.lower)
+              z2.upper
+          in
+          (r1, r2)
+    | AST_LESS_EQUAL ->
+        if Z.lt z2.upper z1.lower then raise Absurd
+        else
+          let r1 = rand z1.lower (Z.min z1.upper z2.upper) in
+          let r2 = rand (Z.max z1.lower z2.lower) z2.upper in
+          (r1, r2)
+    | AST_GREATER -> compare z2 z1 AST_LESS
+    | AST_GREATER_EQUAL -> compare z2 z1 AST_GREATER_EQUAL
+
+  let bwd_binary z1 z2 op r =
+    match op with
+    | AST_PLUS ->
+        (meet z1 (binary r z2 AST_MINUS), meet z2 (binary r z1 AST_MINUS))
+    | AST_MINUS ->
+        (meet z1 (binary r z2 AST_PLUS), meet z2 (binary z1 r AST_MINUS))
+    | AST_MULTIPLY ->
+        (meet z1 (binary r z2 AST_DIVIDE), meet z2 (binary r z1 AST_DIVIDE))
+    | AST_DIVIDE ->
+        (meet z1 (binary r z2 AST_MULTIPLY), meet z2 (binary z1 r AST_DIVIDE))
+    | AST_MODULO -> (z1, z2)
+
+
+  let print fmt z =
+    Format.pp_print_string fmt "[";
+    Z.pp_print fmt z.lower;
+    Format.pp_print_string fmt "; ";
+    Z.pp_print fmt z.upper;
+    Format.pp_print_string fmt "]"
+end

flake.nix

@@ -14,6 +14,8 @@
           inherit system;
         };
         ocamlLibs = with pkgs.ocamlPackages; [
+          camlidl
+          apron
           findlib
           zarith
           menhir
@@ -26,6 +28,7 @@
       {
         devShell = pkgs.mkShell {
           buildInputs = with pkgs; [
+            mpfr
             gnumake
             dune_3
             ocaml