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(* -*- mode: coq; coq-prog-args: ("-emacs" "-top" "atomic" "-Q" "." "iris" "-R" "." "stdpp") -*- *)
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(* coqc version 8.8.0 (May 2018) compiled on May 2 2018 16:49:46 with OCaml 4.02.3
coqtop version 8.8.0 (May 2018) *)
(* This was triggering a "Not_found" at the time of printing/showing the goal *)
Require Coq.Unicode.Utf8.
Notation "t $ r" := (t r)
(at level 65, right associativity, only parsing).
Inductive tele : Type :=
| TeleO : tele
| TeleS {X} (binder : X -> tele) : tele.
Fixpoint tele_fun (TT : tele) (T : Type) : Type :=
match TT with
| TeleO => T
| TeleS b => forall x, tele_fun (b x) T
end.
Inductive tele_arg : tele -> Type :=
| TargO : tele_arg TeleO
| TargS {X} {binder} (x : X) : tele_arg (binder x) -> tele_arg (TeleS binder).
Axiom tele_app : forall {TT : tele} {T} (f : tele_fun TT T), tele_arg TT -> T.
Coercion tele_arg : tele >-> Sortclass.
Inductive val :=
| LitV
| PairV (v1 v2 : val)
| InjLV (v : val)
| InjRV (v : val).
Axiom coPset : Set.
Axiom atomic_update : forall {PROP : Type} {TA TB : tele}, coPset -> coPset -> (TA -> PROP) -> (TA -> TB -> PROP) -> (TA -> TB -> PROP) -> PROP.
Import Coq.Unicode.Utf8.
Notation "'AU' '<<' ∀ x1 .. xn , α '>>' @ Eo , Ei '<<' β , 'COMM' Φ '>>'" :=
(atomic_update (TA:=TeleS (λ x1, .. (TeleS (λ xn, TeleO)) .. ))
(TB:=TeleO)
Eo Ei
(tele_app (TT:=TeleS (λ x1, .. (TeleS (λ xn, TeleO)) .. )) $
λ x1, .. (λ xn, α) ..)
(tele_app (TT:=TeleS (λ x1, .. (TeleS (λ xn, TeleO)) .. )) $
λ x1, .. (λ xn, tele_app (TT:=TeleO) β) .. )
(tele_app (TT:=TeleS (λ x1, .. (TeleS (λ xn, TeleO)) .. )) $
λ x1, .. (λ xn, tele_app (TT:=TeleO) Φ) .. )
)
(at level 20, Eo, Ei, α, β, Φ at level 200, x1 binder, xn binder,
format "'[ ' 'AU' '<<' ∀ x1 .. xn , α '>>' '/' @ Eo , Ei '/' '[ ' '<<' β , '/' COMM Φ '>>' ']' ']'") : bi_scope.
Axiom ident : Set.
Inductive env (A : Type) : Type := Enil : env A | Esnoc : env A → ident → A → env A.
Record envs (PROP : Type) : Type
:= Envs { env_spatial : env PROP }.
Axiom positive : Set.
Axiom Qp : Set.
Axiom one : positive.
Goal forall (T : Type) (T0 : forall _ : T, Type) (P : Set)
(u : T) (γs : P) (Q : T0 u) (Φ o : forall _ : val, T0 u)
(stack_content0 : forall (_ : P) (_ : list val), T0 u)
(c c0 : coPset) (l : forall (A : Type) (_ : list A), list A)
(e0 : forall (_ : env (T0 u)) (_ : positive), envs (T0 u))
(i0 : ident) (o1 : forall (_ : Qp) (_ : val), T0 u)
(b0 : forall _ : env (T0 u), T0 u) (P0 : forall _ : T0 u, Type)
(u0 : forall (_ : T0 u) (_ : T0 u), T0 u),
P0
(@atomic_update (T0 u)
(@TeleS val (fun _ : val => @TeleS Qp (fun _ : Qp => TeleO))) TeleO c c0
(@tele_app (@TeleS val (fun _ : val => @TeleS Qp (fun _ : Qp => TeleO)))
(T0 u) (fun (v : val) (q : Qp) => o1 q v))
(@tele_app (@TeleS val (fun _ : val => @TeleS Qp (fun _ : Qp => TeleO)))
(forall _ : tele_arg TeleO, T0 u)
(fun (v : val) (q : Qp) => @tele_app TeleO (T0 u) (o1 q v)))
(@tele_app (@TeleS val (fun _ : val => @TeleS Qp (fun _ : Qp => TeleO)))
(forall _ : tele_arg TeleO, T0 u)
(fun (x : val) (_ : Qp) =>
@tele_app TeleO (T0 u)
(u0
(b0
match
e0
(@Esnoc (T0 u) (@Enil (T0 u)) i0
(@atomic_update (T0 u)
(@TeleS (list val) (fun _ : list val => TeleO)) TeleO
c c0
(@tele_app
(@TeleS (list val) (fun _ : list val => TeleO))
(T0 u) (fun l0 : list val => stack_content0 γs l0))
(@tele_app
(@TeleS (list val) (fun _ : list val => TeleO))
(forall _ : tele_arg TeleO, T0 u)
(fun l0 : list val =>
@tele_app TeleO (T0 u)
(stack_content0 γs (l val l0))))
(@tele_app
(@TeleS (list val) (fun _ : list val => TeleO))
(forall _ : tele_arg TeleO, T0 u)
(fun x1 : list val =>
@tele_app TeleO (T0 u)
(u0 Q
(Φ
match x1 return val with
| nil => InjLV LitV
| cons v _ => InjRV v
end)))))) one
return (env (T0 u))
with
| Envs _ env_spatial0 => env_spatial0
end) (o x)))))
.
Show.
Abort.
|
