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BSD-2-Clause: https://github.com/jscert/jscert * JSCorrectness.v * JSInterpreterExtraction.v * JSNumber.v * JSPrettyInterm.v MIT/Expat: https://github.com/clarus/coq-atm * Computation.v * Main.v * Spec.v
63 lines
1.9 KiB
Coq
63 lines
1.9 KiB
Coq
(** Specifications. *)
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Require Import Coq.Lists.List.
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Require Import Coq.Strings.Ascii.
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Require Import FunctionNinjas.All.
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Require Import ListString.All.
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Require Import Computation.
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Import ListNotations.
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Local Open Scope char.
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(** A run is an execution of the program with explicit answers for the
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system calls. *)
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Module Run.
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(** We define a run by induction on the structure of a computation. *)
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Inductive t : C.t -> Type :=
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| Ret : t C.Ret
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| Call : forall (command : Command.t) (answer : Command.answer command)
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{handler : Command.answer command -> C.t}, t (handler answer) ->
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t (C.Call command handler).
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(** The trace of a run. *)
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Fixpoint trace {x : C.t} (run : t x)
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: list {command : Command.t & Command.answer command} :=
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match run with
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| Ret => []
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| Call command answer _ run => existT _ command answer :: trace run
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end.
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End Run.
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Module Temporal.
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Module All.
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Inductive t (P : Command.t -> Prop) : C.t -> Prop :=
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| Ret : t P C.Ret
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| Call : forall (c : Command.t) (h : Command.answer c -> C.t),
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P c -> (forall a, t P (h a)) ->
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t P (C.Call c h).
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End All.
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Module One.
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Inductive t (P : Command.t -> Prop) : C.t -> Prop :=
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| CallThis : forall (c : Command.t) (h : Command.answer c -> C.t),
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P c ->
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t P (C.Call c h)
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| CallOther : forall (c : Command.t) (h : Command.answer c -> C.t),
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(forall a, t P (h a)) ->
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t P (C.Call c h).
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End One.
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Module Then.
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Inductive t (P1 P2 : Command.t -> Prop) : C.t -> Prop :=
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| Ret : t P1 P2 C.Ret
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| Call : forall (c : Command.t) (h : Command.answer c -> C.t),
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(forall a, t P1 P2 (h a)) ->
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t P1 P2 (C.Call c h)
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| CallThen : forall (c : Command.t) (h : Command.answer c -> C.t),
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P1 c -> (forall a, One.t P2 (h a)) ->
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t P1 P2 (C.Call c h).
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End Then.
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End Temporal.
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Module CardBeforeMoney.
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End CardBeforeMoney.
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