From 75ce199bb0e0f644f91b905087ec81a5cf23096e Mon Sep 17 00:00:00 2001
From: Simon Cruanes <simon.cruanes.2007@m4x.org>
Date: Thu, 11 Feb 2021 17:17:43 -0500
Subject: [PATCH] wip: new simplex

---
 src/arith/lra/simplex2.ml | 123 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 123 insertions(+)
 create mode 100644 src/arith/lra/simplex2.ml

diff --git a/src/arith/lra/simplex2.ml b/src/arith/lra/simplex2.ml
new file mode 100644
index 00000000..0fbb56b8
--- /dev/null
+++ b/src/arith/lra/simplex2.ml
@@ -0,0 +1,123 @@
+
+(** {1 Fast Simplex for CDCL(T)}
+
+    We follow the paper "Integrating Simplex with DPLL(T )" from
+    de Moura and Dutertre.
+*)
+
+module type VAR = Linear_expr_intf.VAR
+
+(** {2 Basic operator} *)
+module Op = struct
+  type t =
+    | Leq
+    | Lt
+    | Geq
+    | Gt
+
+  let to_string = function
+    | Leq -> "<="
+    | Lt -> "<"
+    | Geq -> ">="
+    | Gt -> ">"
+  let pp out op = Fmt.string out (to_string op)
+end
+
+module type S = sig
+  module V : VAR
+
+  type num = Q.t (** Numbers *)
+
+  module Constraint : sig
+    type op = Op.t
+
+    (** A constraint is the comparison of a variable to a constant. *)
+    type t = private {
+      op: op;
+      lhs: V.t;
+      rhs: num;
+    }
+
+    val pp : t Fmt.printer
+  end
+
+  type t
+
+  val create : unit -> t
+  (** Create a new simplex. *)
+
+  val define : t -> V.t -> (num * V.t) list -> unit
+  (** Define a basic variable in terms of other variables.
+      This is useful to "name" a linear expression and get back a variable
+      that can be used in a {!Constraint.t} *)
+end
+
+module Make(Var: VAR)
+  : S with module V = Var
+= struct
+  module V = Var
+
+  type num = Q.t (** Numbers *)
+
+  module Constraint = struct
+    type op = Op.t
+
+    (** A constraint is the comparison of a variable to a constant. *)
+    type t = {
+      op: op;
+      lhs: V.t;
+      rhs: num;
+    }
+
+    let pp out (self:t) =
+      Fmt.fprintf out "(@[%a %s@ %a@])" V.pp self.lhs
+        (Op.to_string self.op) Q.pp_print self.rhs
+  end
+
+  (** An extended rational, used to introduce ε so we can use strict
+      comparisons in an algorithm designed to handle >= only.
+
+      In a way, an extended rational is a tuple `(base, factor)`
+      ordered lexicographically. *)
+  type erat = {
+    base: num; (** reference number *)
+    eps_factor: num; (** coefficient for epsilon, the infinitesimal *)
+  }
+
+  (** {2 Epsilon-rationals, used for strict bounds} *)
+  module Erat = struct
+    type t = erat
+
+    let zero : t = {base=Q.zero; eps_factor=Q.zero}
+
+    let[@inline] make base eps_factor : t = {base; eps_factor}
+    let[@inline] base t = t.base
+    let[@inline] eps_factor t = t.eps_factor
+    let[@inline] mul k e = make Q.(k * e.base) Q.(k * e.eps_factor)
+    let[@inline] sum e1 e2 = make Q.(e1.base + e2.base) Q.(e1.eps_factor + e2.eps_factor)
+    let[@inline] compare e1 e2 = match Q.compare e1.base e2.base with
+      | 0 -> Q.compare e1.eps_factor e2.eps_factor
+      | x -> x
+
+    let[@inline] lt a b = compare a b < 0
+    let[@inline] gt a b = compare a b > 0
+
+    let[@inline] min x y = if compare x y <= 0 then x else y
+    let[@inline] max x y = if compare x y >= 0 then x else y
+
+    let[@inline] evaluate (epsilon:Q.t) (e:t) : Q.t = Q.(e.base + epsilon * e.eps_factor)
+
+    let pp out e : unit =
+      if Q.equal Q.zero (eps_factor e)
+      then Q.pp_print out (base e)
+      else
+        Fmt.fprintf out "(@[<h>%a + @<1>ε * %a@])"
+          Q.pp_print (base e) Q.pp_print (eps_factor e)
+  end
+
+  type t = unit
+
+  let create () : t = ()
+
+  let define _ = assert false (* TODO *)
+end