include "Clight/Csyntax.ma".
include "utilities/extranat.ma".

definition sz_eq_dec : ∀s1,s2:intsize. (s1 = s2) + (s1 ≠ s2).
#s1 cases s1; #s2 cases s2; /2/; %2 ; % #H destruct; qed.
definition sg_eq_dec : ∀s1,s2:signedness. (s1 = s2) + (s1 ≠ s2).
#s1 cases s1; #s2 cases s2; /2/; %2 ; % #H destruct; qed.

let rec type_eq_dec (t1,t2:type) : Sum (t1 = t2) (t1 ≠ t2) ≝
match t1 return λt'. Sum (t' = t2) (t' ≠ t2) with
[ Tvoid ⇒ match t2 return λt'. Sum (Tvoid = t') (Tvoid ≠ t') with [ Tvoid ⇒ inl ?? (refl ??) | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tint sz sg ⇒ match t2 return λt'. Sum (Tint ?? = t') (Tint ?? ≠ t')  with [ Tint sz' sg' ⇒
    match sz_eq_dec sz sz' with [ inl e1 ⇒
    match sg_eq_dec sg sg' with [ inl e2 ⇒ inl ???
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tpointer t ⇒ match t2 return λt'. Sum (Tpointer ? = t') (Tpointer ? ≠ t')  with [ Tpointer t' ⇒
      match type_eq_dec t t' with [ inl e2 ⇒ inl ??? 
      | inr e2 ⇒ inr ?? (nmk ? (λH.match e2 with [ nmk e' ⇒ e' ? ])) ] 
    | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tarray t n ⇒ match t2 return λt'. Sum (Tarray ?? = t') (Tarray ?? ≠ t')  with [ Tarray t' n' ⇒
      match type_eq_dec t t' with [ inl e2 ⇒
        match eq_nat_dec n n' with [ inl e3 ⇒ inl ???
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | _ ⇒ inr ?? (nmk ? (λH.?)) ]
(*
| Tpointer s t ⇒ match t2 return λt'. Sum (Tpointer ?? = t') (Tpointer ?? ≠ t')  with [ Tpointer s' t' ⇒
    match eq_region_dec s s' with [ inl e1 ⇒
      match type_eq_dec t t' with [ inl e2 ⇒ inl ??? 
      | inr e2 ⇒ inr ?? (nmk ? (λH.match e2 with [ nmk e' ⇒ e' ? ])) ] 
    | inr e1 ⇒ inr ?? (nmk ? (λH.match e1 with [ nmk e' ⇒ e' ? ])) ] | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tarray s t n ⇒ match t2 return λt'. Sum (Tarray ??? = t') (Tarray ??? ≠ t')  with [ Tarray s' t' n' ⇒
    match eq_region_dec s s' with [ inl e1 ⇒
      match type_eq_dec t t' with [ inl e2 ⇒
        match eq_nat_dec n n' with [ inl e3 ⇒ inl ???
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | _ ⇒ inr ?? (nmk ? (λH.?)) ]
*)
| Tfunction tl t ⇒ match t2 return λt'. Sum (Tfunction ?? = t') (Tfunction ?? ≠ t')  with [ Tfunction tl' t' ⇒
    match typelist_eq_dec tl tl' with [ inl e1 ⇒ 
    match type_eq_dec t t' with [ inl e2 ⇒ inl ???
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
  | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tstruct i fl ⇒
    match t2 return λt'. Sum (Tstruct ?? = t') (Tstruct ?? ≠ t')  with [ Tstruct i' fl' ⇒
    match ident_eq i i' with [ inl e1 ⇒
    match fieldlist_eq_dec fl fl' with [ inl e2 ⇒ inl ???
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tunion i fl ⇒
    match t2 return λt'. Sum (Tunion ?? = t') (Tunion ?? ≠ t')  with [ Tunion i' fl' ⇒
    match ident_eq i i' with [ inl e1 ⇒
    match fieldlist_eq_dec fl fl' with [ inl e2 ⇒ inl ???
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    |  _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tcomp_ptr i ⇒ match t2 return λt'. Sum (Tcomp_ptr ? = t') (Tcomp_ptr ? ≠ t')  with [ Tcomp_ptr i' ⇒ 
      match ident_eq i i' with [ inl e2 ⇒ inl ???
      | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | _ ⇒ inr ?? (nmk ? (λH.?)) ]
(*
| Tcomp_ptr r i ⇒ match t2 return λt'. Sum (Tcomp_ptr ? ? = t') (Tcomp_ptr ? ? ≠ t')  with [ Tcomp_ptr r' i' ⇒ 
    match eq_region_dec r r' with [ inl e1 ⇒
      match ident_eq i i' with [ inl e2 ⇒ inl ???
      | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | _ ⇒ inr ?? (nmk ? (λH.?)) ]
*)
]
and typelist_eq_dec (tl1,tl2:typelist) : Sum (tl1 = tl2) (tl1 ≠ tl2) ≝
match tl1 return λtl'. Sum (tl' = tl2) (tl' ≠ tl2) with
[ Tnil ⇒ match tl2 return λtl'. Sum (Tnil = tl') (Tnil ≠ tl') with [ Tnil ⇒ inl ?? (refl ??) | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Tcons t1 ts1 ⇒ match tl2 return λtl'. Sum (Tcons ?? = tl') (Tcons ?? ≠ tl') with [ Tnil ⇒ inr ?? (nmk ? (λH.?)) | Tcons t2 ts2 ⇒ 
    match type_eq_dec t1 t2 with [ inl e1 ⇒
    match typelist_eq_dec ts1 ts2 with [ inl e2 ⇒ inl ???
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
    | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ] ]
]
and fieldlist_eq_dec (fl1,fl2:fieldlist) : Sum (fl1 = fl2) (fl1 ≠ fl2) ≝
match fl1 return λfl'. Sum (fl' = fl2) (fl' ≠ fl2) with
[ Fnil ⇒ match fl2 return λfl'. Sum (Fnil = fl') (Fnil ≠ fl') with [ Fnil ⇒ inl ?? (refl ??) | _ ⇒ inr ?? (nmk ? (λH.?)) ]
| Fcons i1 t1 fs1 ⇒ match fl2 return λfl'. Sum (Fcons ??? = fl') (Fcons ??? ≠ fl') with [ Fnil ⇒ inr ?? (nmk ? (λH.?)) | Fcons i2 t2 fs2 ⇒ 
    match ident_eq i1 i2 with [ inl e1 ⇒
      match type_eq_dec t1 t2 with [ inl e2 ⇒
        match fieldlist_eq_dec fs1 fs2 with [ inl e3 ⇒ inl ???
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ]
        | inr e ⇒ inr ?? (nmk ? (λH.match e with [ nmk e' ⇒ e' ? ])) ] ]
]. try destruct; //
qed.

definition assert_type_eq : ∀t1,t2:type. res (t1 = t2) ≝
λt1,t2. match type_eq_dec t1 t2 with [ inl p ⇒ OK ? p | inr _ ⇒ Error ? (msg TypeMismatch)].

definition type_eq : type → type → bool ≝
λt1,t2. match type_eq_dec t1 t2 with [ inl _ ⇒ true | inr _ ⇒ false ].


definition if_type_eq : ∀t1,t2:type. ∀P:type → type → Type[0]. P t1 t1 → P t1 t2 → P t1 t2 ≝
λt1,t2,P. match type_eq_dec t1 t2 return λ_. P t1 t1 → P t1 t2 → P t1 t2 with [ inl E ⇒ λx,d. x⌈P t1 t1 ↦ P t1 t2⌉ | inr _ ⇒ λx,d. d ].
// qed.