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make typed_store_model and example computable #114

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Jul 26, 2023
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make typed_store_model and example computable #114

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24 changes: 19 additions & 5 deletions monae_lib.v
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Original file line number Diff line number Diff line change
Expand Up @@ -211,26 +211,40 @@ Proof. by elim: n st => [|n IH] [|d st'] //= /IH ->. Qed.
End nth_error.
Arguments nth_error_size {T st n a}.

(* Equality *)
Section eqtype.
Variable T : Type.
Variable eq_dec : comparable T.
Definition compareb x y : bool := eq_dec x y.
Definition compareP' x y :=
match eq_dec x y as s return reflect (x = y) s with
| left a => ReflectT (x = y) a
| right b => ReflectF (x = y) b
end.
Definition eqP' (E : eqType) : Equality.axiom (@eq_op E) :=
match E with EqType sort (EqMixin op a) => a end.
End eqtype.

Section coerce.
Variables (X : eqType) (f : X -> Type).

Definition coerce (T1 T2 : X) (v : f T1) : option (f T2) :=
if @eqP _ T1 T2 is ReflectT H then Some (eq_rect _ _ v _ H) else None.
if @eqP' _ T1 T2 is ReflectT H then Some (eq_rect _ _ v _ H) else None.

Lemma coerce_sym (T T' : X) (s : f T) (s' : f T') : coerce T' s -> coerce T s'.
Proof.
by rewrite /coerce; case: eqP => //= h; case: eqP => //; rewrite h; auto.
by rewrite /coerce; case: eqP' => //= h; case: eqP' => //; rewrite h; auto.
Qed.

Lemma coerce_Some (T : X) (s : f T) : coerce T s = Some s.
Proof.
by rewrite /coerce; case: eqP => /= [?|]; [rewrite -eq_rect_eq|auto].
by rewrite /coerce; case: eqP' => /= [?|]; [rewrite -eq_rect_eq|auto].
Qed.

Lemma coerce_eq (T T' : X) (s : f T) : coerce T' s -> T = T'.
Proof. by rewrite /coerce; case: eqP. Qed.
Proof. by rewrite /coerce; case: eqP'. Qed.

Lemma coerce_None (T T' : X) (s : f T) : T != T' -> coerce T' s = None.
Proof. by rewrite /coerce; case: eqP. Qed.
Proof. by rewrite /coerce; case: eqP'. Qed.

End coerce.
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