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Cleanup DawnEval.v

master
Danila Fedorin 2 months ago
parent
commit
abdc8e5056
  1. 148
      code/dawn/DawnEval.v

148
code/dawn/DawnEval.v

@ -1,6 +1,7 @@
Require Import Coq.Lists.List.
Require Import Dawn.
Require Import Coq.Program.Equality.
From Ltac2 Require Import Ltac2.
Inductive step_result :=
| err
@ -79,7 +80,7 @@ Lemma eval_chain_split : forall (e1 e2 : expr) (s s'' : list expr),
eval_chain s (e_comp e1 e2) s'' -> exists s', (eval_chain s e1 s') /\ (eval_chain s' e2 s'').
Proof.
intros e1 e2 s ss'' ch.
dependent induction ch.
ltac1:(dependent induction ch).
- simpl in P. destruct (eval_step s e1); inversion P.
- simpl in P. destruct (eval_step s e1) eqn:Hval; try (inversion P).
+ injection P as Hinj; subst. specialize (IHch e e2 H0) as [s'0 [ch1 ch2]].
@ -91,47 +92,6 @@ Proof.
* apply ch.
Qed.
Theorem eval_step_preservation : forall (e : expr) (vs : value_stack) (s' : list expr),
((exists e', eval_step (strip_value_list vs) e = middle e' s') ->
exists vs', (strip_value_list vs') = s') /\
((eval_step (strip_value_list vs) e = final s') ->
exists vs', (strip_value_list vs') = s').
Proof.
intros e vs. induction e; split.
- intros [e' Hst].
destruct i; try (destruct vs as [|v1 [|v2 vs]]; inversion Hst; fail).
* destruct vs as [|v1 [|v2 vs]]; inversion Hst;
destruct (projT1 v1); inversion H0.
destruct (projT1 v2); inversion H1.
* destruct vs as [|v1 vs]; inversion Hst.
destruct (projT1 v1); inversion H0.
eauto.
- intros Hst.
destruct i; try (destruct vs as [|v1 [|v2 vs]]; inversion Hst; fail).
* destruct vs as [|v1 [|v2 vs]]; inversion Hst. exists (v2 :: v1 :: vs). reflexivity.
* destruct vs as [|v1 vs]; inversion Hst. exists (v1 :: v1 :: vs). reflexivity.
* destruct vs as [|v1 vs]; inversion Hst. exists vs. reflexivity.
* destruct vs as [|v1 vs]; inversion Hst. exists (v_quote (projT1 v1) :: vs). reflexivity.
* destruct vs as [|v1 [|v2 vs]]; inversion Hst.
+ destruct (projT1 v1); inversion H0.
+ destruct (projT1 v1); destruct (projT1 v2); inversion H0.
exists (v_quote (e_comp e0 e) :: vs). reflexivity.
* destruct vs as [|v1 vs]; inversion Hst;
destruct (projT1 v1); inversion H0.
- intros [e' Hst]. inversion Hst.
- intros Hst. inversion Hst. exists (v_quote e :: vs). reflexivity.
- intros [e' Hst]. inversion Hst.
destruct (eval_step (strip_value_list vs) e1) eqn:Hst1.
* inversion H0.
* specialize (IHe1 s') as [IHe1 _]. apply IHe1. exists e.
injection H0 as Hinj; subst; auto.
* specialize (IHe1 s') as [_ IHe1]. apply IHe1.
injection H0 as Hinj; subst; auto.
- intros Hst.
inversion Hst. destruct (eval_step (strip_value_list vs) e1); inversion H0.
Qed.
Theorem val_step_sem : forall (e : expr) (vs vs' : value_stack),
Sem_expr vs e vs' -> eval_chain (strip_value_list vs) e (strip_value_list vs')
with eval_step_int : forall (i : intrinsic) (vs vs' : value_stack),
@ -158,67 +118,61 @@ Proof.
Qed.
Theorem eval_step_sem_back : forall (e : expr) (vs vs' : value_stack),
eval_chain (strip_value_list vs) e (strip_value_list vs') -> Sem_expr vs e vs'
with eval_step_int_back : forall (i : intrinsic) (vs vs' : value_stack),
eval_chain (strip_value_list vs) (e_int i) (strip_value_list vs') -> Sem_int vs i vs'.
eval_chain (strip_value_list vs) e (strip_value_list vs') -> Sem_expr vs e vs'.
Proof.
(* Thoughts: prove a "step value stack preservation" property. A step suggested by
eval_step will ensure the stack contains values if it contained values initially.
Done! eval_step_preservation.
From there, by induction, a chain preserves value stacks. *)
(* Thoughts: the issue is with the apparent nondeterminism of evalution. *)
Admitted.
Ltac2 Type exn ::= [ | Not_intrinsic ].
Ltac2 rec destruct_n (n : int) (vs : constr) : unit :=
if Int.le n 0 then () else
let v := Fresh.in_goal @v in
let vs' := Fresh.in_goal @vs in
destruct $vs as [|$v $vs']; Control.enter (fun () =>
try (destruct_n (Int.sub n 1) (Control.hyp vs'))
).
Ltac2 int_arity (int : constr) : int :=
match! int with
| swap => 2
| clone => 1
| drop => 1
| quote => 1
| compose => 2
| apply => 1
| _ => Control.throw Not_intrinsic
end.
Theorem eval_step_sem_not : forall (e : expr) (vs : value_stack),
~ (exists vs', Sem_expr vs e vs') -> ~(exists vs', eval_chain (strip_value_list vs) e (strip_value_list vs'))
with eval_step_int_not : forall (i : intrinsic) (vs : value_stack),
~ (exists vs', Sem_int vs i vs') -> ~(exists vs', eval_chain (strip_value_list vs) (e_int i) (strip_value_list vs')).
Ltac2 destruct_int_stack (int : constr) (va: constr) := destruct_n (int_arity int) va.
Ltac2 ensure_valid_value_stack () := Control.enter (fun () =>
match! goal with
| [h : eval_step (strip_value_list ?a) (e_int ?b) = ?c |- _] =>
let h := Control.hyp h in
destruct_int_stack b a;
try (inversion $h; fail)
| [|- _ ] => ()
end).
Ltac2 ensure_valid_stack () := Control.enter (fun () =>
match! goal with
| [h : eval_step ?a (e_int ?b) = ?c |- _] =>
let h := Control.hyp h in
destruct_int_stack b a;
try (inversion $h; fail)
| [|- _ ] => ()
end).
Theorem test : forall (s s': list expr), eval_step s (e_int swap) = final s' ->
exists v1 v2 s'', s = v1 :: v2 :: s'' /\ s' = v2 :: v1 :: s''.
Proof.
(*
- intros e vs Hnsem [vs' Hev].
destruct e.
+ specialize (eval_step_sem_not _ _ Hnsem). apply eval_step_sem_not.
eexists. apply Hev.
+ apply Hnsem. eexists. apply Sem_e_quote.
+ inversion Hev.
* simpl in P. destruct (eval_step (strip_value_list vs) e1); inversion P.
* specialize (eval_chain_split e1 e2 (strip_value_list vs) (strip_value_list vs') Hev) as [s' [ch1 ch2]].
assert (Hnboth : ~ (exists vsi, Sem_expr vs e1 vsi /\ Sem_expr vsi e2 vs')).
{ intros [vsi [H1 H2]]. apply Hnsem. exists vs'. eapply Sem_e_comp. apply H1. apply H2. }
assert (Hncomp : ~ (exists vsi, Sem_expr vs e1 vsi) \/ exists vsi, Sem_expr vs e1 vsi /\ ~(Sem_expr vsi e2 vs')).
{
- intros i vs Hnint [vs' Hev]. destruct i.
+ destruct vs as [|v [|v' vs]]; inversion Hev; simpl in P; inversion P.
apply Hnint. eexists. apply Sem_swap.
+ destruct vs as [|v vs]; inversion Hev; simpl in P; inversion P.
apply Hnint. eexists. apply Sem_clone.
+ destruct vs as [|v vs]; inversion Hev; simpl in P; inversion P.
apply Hnint. eexists. apply Sem_drop.
+ destruct vs as [|v vs]; inversion Hev; simpl in P; inversion P.
apply Hnint. eexists. apply Sem_quote.
+ destruct vs as [|v [|v' vs]];
try (destruct v; destruct x);
try (destruct v'; destruct x0);
simpl in Hev; inversion Hev; simpl in P; inversion P; subst.
destruct i; destruct i0.
apply Hnint. eexists. apply Sem_compose.
+ destruct vs as [|v vs].
* simpl in Hev; inversion Hev; simpl in P; inversion P.
* (* Monkey at keyboard mode engaged here. *)
destruct v eqn:Hv. destruct i eqn:Hi.
simpl in Hev; inversion Hev; simpl in P; inversion P.
injection P as Heq. subst.
assert (Hna : ~(exists vs', Sem_expr vs ei vs')).
{ intros [vs'0 Hsem]. apply Hnint. eexists. apply Sem_apply. apply Hsem. }
specialize (eval_step_sem_not _ _ Hna). apply eval_step_sem_not. eexists.
apply rest.
*)
Admitted.
intros s s' Heq.
ensure_valid_stack ().
simpl in Heq. injection Heq as Hinj. subst. eauto.
Qed.
Require Extraction.
Require Import ExtrHaskellBasic.
Extraction Language Haskell.
Extraction "UccGen.hs" eval_step true false or.
Extraction "UccGen.hs" expr eval_step true false or.

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