feat: final commit
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55
exm/main.zls
55
exm/main.zls
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@ -9,7 +9,7 @@
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- Model discrete systems and their continuous environment
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- Research language, design space for hybrid system modelers
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- Compilation to OCaml, execution with an off-the-shelf ODE solver
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- Developed by the Inria PARKAS team *)
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- Developed by M. Pouzet and T. Bourke in the Inria PARKAS team *)
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@ -20,6 +20,24 @@
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(** Plan:
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- Zélus, the synchronous part
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- Physical simulation, ODEs, and ODE solvers
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- Zélus, the hybrid part
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- Mixing discrete and continuous time, zero-crossing detection
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- Informal operational semantics
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- Low-level representation and runtime *)
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(** Synchronous language kernel _à la_ Lustre:
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- programs are Mealy machines (outputs on each transition)
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- variables represent streams of values in time *)
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@ -27,9 +45,9 @@
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let node incr x = y where
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y = x + 1
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(* x │ 8 3 2 7 5 3 …
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───┼─────────────────────
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y │ 9 4 3 8 6 4 … *)
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(* x │ 8 3 2 7 5 3 …
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────────┼─────────────────────
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incr x │ 9 4 3 8 6 4 … *)
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@ -45,6 +63,7 @@ let node accumulate x = z where
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──────────────┼─────────────────────
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pre x │ 1 2 5 2 5 …
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0 -> x │ 0 2 5 2 5 3 …
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0 -> pre x │ 0 1 2 5 2 5 …
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accumulate x │ 1 3 8 10 15 18 … *)
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let node fib () = n where
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@ -52,7 +71,6 @@ let node fib () = n where
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(** - causality loops are forbidden ([rec x = x]) *)
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(** - we can reset streams at will *)
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let node stay x = y where (* output the first value forever *)
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@ -77,11 +95,10 @@ let node loop x = y where
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(** Math/physics reminder!
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(** Calculus reminder:
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- Ordinary differential equations (ODEs), initial value problems
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- Zero-crossing event basics
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- Background on solvers *)
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- A little background on solvers *)
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@ -94,6 +111,7 @@ let node loop x = y where
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let dt = 0.01 (* Integration step *)
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let g = 9.81 (* Gravitational constant *)
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let node f_integr (x0, x') = x where (* Forward Euler integrator *)
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rec x = x0 -> pre (x +. x' *. dt)
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@ -112,12 +130,11 @@ let node bouncing_ball (p0, v0) = p where
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(** Cumbersome, and error-prone! *)
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let node sincos () = (sin, cos) where
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rec sin = f_integr(0.0, cos)
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and cos = f_integr(1.0, -. sin)
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rec sin = f_integr (0.0, cos) (** [(dsin/dt) t = cos t, sin 0 = 0] *)
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and cos = f_integr (1.0, -. sin) (** [(dcos/dt) t = -sin t, cos 0 = 1] *)
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@ -136,10 +153,11 @@ let hybrid integr (x0, x') = x where
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let hybrid time () = t where
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der t = 1.0 init 0.0
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let hybrid position (p0, v0, a) = p where
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rec der p = v init p0
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and der v = a init v0
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let hybrid falling_ball (p0, v0) = p where
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rec der p = v init p0
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and der v = -. g init v0
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(** How do we mix discrete time and continuous time together? *)
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@ -160,12 +178,3 @@ let hybrid time_bounces (p0, v0) = (p, b) where
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b = t -. last b
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done
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(** - w FIXME e can mix discrete and continuous behaviours *)
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12
justfile
12
justfile
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@ -2,10 +2,22 @@ exm1:
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timeout 1s dune exec exm_ball | \
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feedgnuplot --stream --domain --lines
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balld:
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timeout 1s dune exec exm_ball | \
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feedgnuplot --stream --domain --lines
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exm2:
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timeout 10s dune exec exm_sincos | \
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feedgnuplot --stream --domain --lines
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sincos:
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timeout 10s dune exec exm_sincos | \
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feedgnuplot --stream --domain --lines
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exm3:
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dune exec ballc.exe | \
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feedgnuplot --stream --domain --lines
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ballc:
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dune exec ballc.exe | \
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feedgnuplot --stream --domain --lines
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@ -1,19 +1,20 @@
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[@@@warning "-27-50-69"]
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let todo = assert false
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(* Little OCaml reminder: *)
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type _s = A | B of int | C of float * string (* sum types *)
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type _t = { a : int; b : int; } (* product types *)
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type _t = { a : int; b : int; }
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let _f () =
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let x = { a = 0; b = 1 } in
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let y = { x with a = 2 } in (* same as "x", except field "a" *)
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assert (y = { a = 2; b = 1 })
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(* Everything is immutable, except explicitly declared record fields! *)
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type _q = { c : int (* immutable *); mutable d : int; }
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(* Everything is immutable (at least in this presentation)! *)
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(* Types can be parameterized by other types: *)
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type 'a _llist = Nil | Cons of { v : 'a; mutable next : 'a _llist }
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@ -29,7 +30,7 @@ type ('i, 'o, 'r) dnode =
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(** Run a discrete node on a list of inputs *)
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let drun (DNode n : ('i, 'o, 'r) dnode) (i : 'i list) : 'o list =
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snd (List.fold_left_map n.step n.state i)
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todo
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@ -153,7 +154,7 @@ let compose_solvers : ('y, 'yder) csolver ->
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let step (cstate, zstate) h =
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let cstate, y = csolver.step cstate h in
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let zstate, (h, z) = zsolver.step zstate y in
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(cstate, zstate), ({ y with h }, z) in
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(cstate, zstate), (todo (*?*), z) in
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let reset (cstate, zstate) (ivp, zcp) =
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(csolver.reset cstate ivp, zsolver.reset zstate zcp) in
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DNode { state; step; reset }
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@ -206,12 +207,12 @@ let dstep (State ({ model = HNode m; solver = DNode s; _ } as state)) =
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else if state.time >= i.h then
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State { state with input = None; model; time = 0. }
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else
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let y0 = m.cget ms and h = i.h -. state.time and ofs = (+.) state.time in
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let y0 = todo (*?*) and h = i.h -. state.time and ofs = (+.) state.time in
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let ivp = { h; y0; fder = fun t y -> m.fder ms (ofs t) (i.f (ofs t)) y } in
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let zcp = { h; y0; fzer = fun t y -> m.fzer ms (ofs t) (i.f (ofs t)) y } in
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let solver = DNode { s with state = s.reset s.state (ivp, zcp) } in
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let input = Some { h; f = fun t -> i.f (ofs t) } in
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State { model; solver; mode = C; time = 0.; input } in
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State { model; solver; mode = todo (*?*); time = 0.; input } in
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state, Some { h = 0.; f = fun _ -> o }
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@ -264,3 +265,6 @@ let hrun (model : ('i, 'o, 'r, 'y, 'yder, 'zin, 'zout) hnode)
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if o = None then (sim, List.rev_map Option.get os)
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else step (o :: os) sim None in
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List.fold_left_map (step []) sim i |> snd |> List.flatten
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