include "common/IO.ma".
include "common/SmallstepExec.ma".
include "arithmetics/nat.ma".

(* Functions to allow programs to be executed up to some number of steps, given
   a predetermined set of input values.  Note that we throw away the state if
   we stop at a continuation - it can be too large to work with. *)

definition get_input : ∀o:io_out. eventval → res (io_in o) ≝
λo,ev.
match io_in_typ o return λt. res (eventval_type t) with
[ ASTint sz _ ⇒ match ev with [ EVint sz' i ⇒ intsize_eq_elim ? sz' sz ? i (λi.OK ? i) (Error ? (msg IllTypedEvent)) | _ ⇒ Error ? (msg IllTypedEvent) ]
| ASTfloat _ ⇒ match ev with [ EVfloat f ⇒ OK ? f | _ ⇒ Error ? (msg IllTypedEvent) ]
| ASTptr ⇒ Error ? (msg IllTypedEvent)
].

inductive snapshot (state:Type[0]) : Type[0] ≝
| running : trace → state → snapshot state
| finished : trace → int → state → snapshot state
| input_exhausted : trace → snapshot state.

axiom StoppedMidIO : String.

let rec up_to_nth_step (n:nat) (state:Type[0]) (input:list eventval) (e:execution state io_out io_in) (t:trace) : res (snapshot state) ≝
match n with
[ O ⇒ match e with [ e_step tr s _ ⇒ OK ? (running ? (t⧺tr) s)
                   | e_stop tr r m ⇒ OK ? (finished ? (t⧺tr) r m)
                   | e_interact o k ⇒ Error ? (msg StoppedMidIO)
                   | e_wrong m ⇒ Error ? m ]
| S m ⇒ match e with [ e_step tr s e' ⇒ up_to_nth_step m state input e' (t⧺tr)
                     | e_stop tr r m ⇒ OK ? (finished ? (t⧺tr) r m)
                     | e_interact o k ⇒ 
                         match input with
                         [ nil ⇒ OK ? (input_exhausted ? t)
                         | cons h tl ⇒ do i ← get_input o h;
                                       up_to_nth_step m state tl (k i) t
                         ]
                     | e_wrong m ⇒ Error ? m
                     ]
].

definition exec_up_to : ∀fx:fullexec io_out io_in. ∀p:program ?? fx. nat → list eventval → res (snapshot (state ?? fx (make_global … p))) ≝
λfx,p,n,i. up_to_nth_step n ? i (exec_inf ?? fx p) E0.

(* A version of exec_up_to that reports the state prior to failure. *)

inductive snapshot' (state:Type[0]) : Type[0] ≝
| running' : trace → state → snapshot' state
| finished' : nat → trace → int → state → snapshot' state
| input_exhausted' : trace → snapshot' state
| failed' : errmsg → nat → state → snapshot' state
| init_state_fail' : errmsg → snapshot' state.

let rec up_to_nth_step' (n:nat) (total:nat) (state:Type[0]) (input:list eventval) (e:execution state io_out io_in) (prev:state) (t:trace) : snapshot' state ≝
match n with
[ O ⇒ match e with [ e_step tr s _ ⇒ running' ? (t⧺tr) s
                   | e_stop tr r m ⇒ finished' ? total (t⧺tr) r m
                   | e_interact o k ⇒ failed' ? (msg StoppedMidIO) total prev
                   | e_wrong m ⇒ failed' ? m total prev ]
| S m ⇒ match e with [ e_step tr s e' ⇒ up_to_nth_step' m total state input e' s (t⧺tr)
                     | e_stop tr r m ⇒ finished' ? (minus total n) (t⧺tr) r m
                     | e_interact o k ⇒ 
                         match input with
                         [ nil ⇒ input_exhausted' ? t
                         | cons h tl ⇒ match get_input o h with
                                       [ OK i ⇒ up_to_nth_step' m total state tl (k i) prev t
                                       | Error m ⇒ failed' ? m (minus total n) prev
                                       ]
                         ]
                     | e_wrong m ⇒ failed' ? m (minus total n) prev
                     ]
].

definition exec_up_to' : ∀fx:fullexec io_out io_in. ∀p:program ?? fx. nat → list eventval → snapshot' (state ?? fx (make_global … p)) ≝
λfx,p,n,i. 
match make_initial_state ?? fx p with
[ OK s ⇒ up_to_nth_step' n n (state ?? fx (make_global … p)) i (exec_inf ?? fx p) s E0
| Error m ⇒ init_state_fail' ? m
].

(* Provide an easy way to get a term in proof mode for reduction.
   For example,
   
   example exec: result ? (exec_up_to myprog 20 [EVint (repr 12)]).
   normalize  (* you can examine the result here *)
   % qed.
   
 *)

inductive result (A:Type[0]) : A → Type[0] ≝
| witness : ∀a:A. result A a.

inductive finishes_with : int → ∀S.res (snapshot S) → Prop ≝
fw_ok : ∀r,S,t,s. finishes_with r S (OK ? (finished S t r s)).

include "common/GenMem.ma".

(* Hide the representation of memory to make displaying the results easier. *)

notation < "'MEM'" with precedence 1 for @{ 'mem }.
interpretation "hide memory" 'mem = (mk_mem ???).