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Require Import Crypto.Compilers.Syntax.
Require Import Crypto.Compilers.Wf.
Require Import Crypto.Compilers.SmartMap.
Require Import Crypto.Compilers.WfProofs.
Require Import Crypto.Util.LetIn.
Require Import Crypto.Util.Sigma Crypto.Util.Prod.
Require Import Crypto.Util.Tactics.RewriteHyp.
Local Open Scope ctype_scope.
Section language.
Context (base_type_code : Type).
Local Notation flat_type := (flat_type base_type_code).
Local Notation type := (type base_type_code).
Context (interp_base_type : base_type_code -> Type).
Context (op : flat_type (* input tuple *) -> flat_type (* output type *) -> Type).
Local Notation interp_type := (interp_type interp_base_type).
Local Notation interp_flat_type := (interp_flat_type interp_base_type).
Context (interp_op : forall src dst, op src dst -> interp_flat_type src -> interp_flat_type dst).
Lemma interpf_LetIn tx ex tC eC
: Syntax.interpf interp_op (LetIn (tx:=tx) ex (tC:=tC) eC)
= dlet x := Syntax.interpf interp_op ex in
Syntax.interpf interp_op (eC x).
Proof using Type. reflexivity. Qed.
Lemma interpf_SmartVarf t v
: Syntax.interpf interp_op (SmartVarf (t:=t) v) = v.
Proof using Type.
unfold SmartVarf; induction t;
repeat match goal with
| _ => reflexivity
| _ => progress simpl in *
| _ => progress rewrite_hyp *
| _ => rewrite <- surjective_pairing
end.
Qed.
Lemma interpf_SmartVarVarf {t t'} v x x'
(Hin : List.In
(existT (fun t : base_type_code => (exprf base_type_code op (Tbase t) * interp_base_type t)%type)
t (x, x'))
(flatten_binding_list (t := t') (SmartVarVarf v) v))
: interpf interp_op x = x'.
Proof using Type.
clear -Hin.
induction t'; simpl in *; try tauto.
{ intuition (inversion_sigma; inversion_prod; subst; eauto). }
{ apply List.in_app_iff in Hin.
intuition (inversion_sigma; inversion_prod; subst; eauto). }
Qed.
Lemma interpf_SmartVarVarf_eq {t t'} v v' x x'
(Heq : v = v')
(Hin : List.In
(existT (fun t : base_type_code => (exprf base_type_code op (Tbase t) * interp_base_type t)%type)
t (x, x'))
(flatten_binding_list (t := t') (SmartVarVarf v') v))
: interpf interp_op x = x'.
Proof using Type.
subst; eapply interpf_SmartVarVarf; eassumption.
Qed.
End language.
Hint Rewrite @interpf_LetIn @interpf_SmartVarf : reflective_interp.
Hint Rewrite @interpf_SmartVarVarf using assumption : reflective_interp.
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