feat: final commit

exm/main.zls

@@ -9,7 +9,7 @@
     - Model discrete systems and their continuous environment
     - Research language, design space for hybrid system modelers
     - Compilation to OCaml, execution with an off-the-shelf ODE solver
-    - Developed by the Inria PARKAS team *)
+    - Developed by M. Pouzet and T. Bourke in the Inria PARKAS team *)
 
 
 
@@ -20,6 +20,24 @@
 
 
 
+
+(** Plan:
+
+    - Zélus, the synchronous part
+    - Physical simulation, ODEs, and ODE solvers
+    - Zélus, the hybrid part
+    - Mixing discrete and continuous time, zero-crossing detection
+    - Informal operational semantics
+    - Low-level representation and runtime *)
+
+
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+
 (** Synchronous language kernel _à la_ Lustre:
     - programs are Mealy machines (outputs on each transition)
     - variables represent streams of values in time *)
@@ -27,9 +45,9 @@
 let node incr x = y where
   y = x + 1
 
-(*   x │ 8  3  2  7  5  3  …
-    ───┼─────────────────────
-     y │ 9  4  3  8  6  4  …   *)
+(*        x │ 8  3  2  7  5  3  …
+    ────────┼─────────────────────
+     incr x │ 9  4  3  8  6  4  …   *)
 
 
 
@@ -45,6 +63,7 @@ let node accumulate x = z where
     ──────────────┼─────────────────────
             pre x │    1  2  5  2  5  …
            0 -> x │ 0  2  5  2  5  3  …
+       0 -> pre x │ 0  1  2  5  2  5  …
      accumulate x │ 1  3  8 10 15 18  …   *)
 
 let node fib () = n where
@@ -52,7 +71,6 @@ let node fib () = n where
 
 (** - causality loops are forbidden ([rec x = x]) *)
 
-
 (** - we can reset streams at will *)
 
 let node stay x = y where            (* output the first value forever        *)
@@ -77,11 +95,10 @@ let node loop x = y where
 
 
 
-(** Math/physics reminder!
+(** Calculus reminder:
 
     - Ordinary differential equations (ODEs), initial value problems
-    - Zero-crossing event basics
-    - Background on solvers *)
+    - A little background on solvers *)
 
 
 
@@ -94,6 +111,7 @@ let node loop x = y where
 
 let dt = 0.01                         (* Integration step                     *)
 let g  = 9.81                         (* Gravitational constant               *)
+
 let node f_integr (x0, x') = x where  (* Forward Euler integrator             *)
   rec x = x0 -> pre (x +. x' *. dt)
 
@@ -112,12 +130,11 @@ let node bouncing_ball (p0, v0) = p where
 
 
 
-
 (** Cumbersome, and error-prone! *)
 
 let node sincos () = (sin, cos) where
-  rec sin = f_integr(0.0, cos)
-  and cos = f_integr(1.0, -. sin)
+  rec sin = f_integr (0.0, cos)        (** [(dsin/dt) t =  cos t, sin 0 = 0]  *)
+  and cos = f_integr (1.0, -. sin)     (** [(dcos/dt) t = -sin t, cos 0 = 1]  *)
 
 
 
@@ -136,10 +153,11 @@ let hybrid integr (x0, x') = x where
 let hybrid time () = t where
   der t = 1.0 init 0.0
 
-let hybrid position (p0, v0, a) = p where
-  rec der p = v init p0
-  and der v = a init v0
+let hybrid falling_ball (p0, v0) = p where
+  rec der p = v    init p0
+  and der v = -. g init v0
 
+(** How do we mix discrete time and continuous time together? *)
 
 
 
@@ -160,12 +178,3 @@ let hybrid time_bounces (p0, v0) = (p, b) where
     b = t -. last b
   done
 
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-(** - w FIXME e can mix discrete and continuous behaviours *)