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Diffstat (limited to 'src/versions/standard/Structures_standard.v')
-rw-r--r-- | src/versions/standard/Structures_standard.v | 35 |
1 files changed, 35 insertions, 0 deletions
diff --git a/src/versions/standard/Structures_standard.v b/src/versions/standard/Structures_standard.v new file mode 100644 index 0000000..04b396f --- /dev/null +++ b/src/versions/standard/Structures_standard.v @@ -0,0 +1,35 @@ +Require Import Int63. + +Require Import List. + + +Section Trace. + + Definition trace (step:Type) := ((list step) * step)%type. + + Definition trace_length {step:Type} (t:trace step) : int := + let (t,_) := t in + List.fold_left (fun i _ => (i+1)%int) t 0%int. + + Fixpoint trace_get_aux {step:Type} (t:list step) (def:step) (i:int) : step := + match t with + | nil => def + | s::ss => + if (i == 0)%int then + s + else + trace_get_aux ss def (i-1) + end. + Definition trace_get {step:Type} (t:trace step) : int -> step := + let (t,def) := t in trace_get_aux t def. + + Definition trace_fold {state step:Type} (transition: state -> step -> state) (s0:state) (t:trace step) := + let (t,_) := t in + List.fold_left transition t s0. + + Lemma trace_fold_ind (state step : Type) (P : state -> Prop) (transition : state -> step -> state) (t : trace step) + (IH: forall (s0 : state) (i : int), (i < trace_length t)%int = true -> P s0 -> P (transition s0 (trace_get t i))) : + forall s0 : state, P s0 -> P (trace_fold transition s0 t). + Admitted. + +End Trace. |