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-(** * PHOAS → Named Representation of Gallina *)
-Require Import Crypto.Compilers.Named.Context.
-Require Import Crypto.Compilers.Named.Syntax.
-Require Import Crypto.Compilers.Named.NameUtil.
-Require Import Crypto.Compilers.Named.NameUtilProperties.
-Require Import Crypto.Compilers.Named.ContextDefinitions.
-Require Import Crypto.Compilers.Named.ContextProperties.
-Require Import Crypto.Compilers.Named.ContextProperties.NameUtil.
-Require Import Crypto.Compilers.Syntax.
-Require Import Crypto.Compilers.Wf.
-Require Import Crypto.Compilers.Named.Compile.
-Require Import Crypto.Util.PointedProp.
-Require Import Crypto.Util.Option.
-Require Import Crypto.Util.Decidable.
-Require Import Crypto.Util.Prod.
-Require Import Crypto.Util.ListUtil.
-Require Import Crypto.Util.Tactics.BreakMatch.
-Require Import Crypto.Util.Tactics.DestructHead.
-Require Import Crypto.Util.Tactics.SpecializeBy.
-
-Local Open Scope ctype_scope.
-Local Open Scope nexpr_scope.
-Local Open Scope expr_scope.
-Section language.
- Context {base_type_code}
- {op : flat_type base_type_code -> flat_type base_type_code -> Type}
- {Name : Type}
- {interp_base_type : base_type_code -> Type}
- {interp_op : forall src dst, op src dst -> interp_flat_type interp_base_type src -> interp_flat_type interp_base_type dst}
- {base_type_dec : DecidableRel (@eq base_type_code)}
- {Name_dec : DecidableRel (@eq Name)}
- {Context : @Context base_type_code Name interp_base_type}
- {ContextOk : ContextOk Context}.
-
- Local Notation flat_type := (flat_type base_type_code).
- Local Notation type := (type base_type_code).
- Local Notation exprf := (@exprf base_type_code op (fun _ => Name)).
- Local Notation expr := (@expr base_type_code op (fun _ => Name)).
- Local Notation Expr := (@Expr base_type_code op).
- Local Notation wff := (@wff base_type_code op (fun _ => Name) interp_base_type).
- Local Notation wf := (@wf base_type_code op (fun _ => Name) interp_base_type).
- Local Notation nexprf := (@Named.exprf base_type_code op Name).
- Local Notation nexpr := (@Named.expr base_type_code op Name).
- Local Notation ocompilef := (@ocompilef base_type_code op Name).
- Local Notation ocompile := (@ocompile base_type_code op Name).
- Local Notation compilef := (@compilef base_type_code op Name).
- Local Notation compile := (@compile base_type_code op Name).
-
- Lemma interpf_ocompilef (ctx : Context) {t} (e : exprf t) e' (ls : list (option Name))
- G
- (Hwf : wff G e e')
- (HG : forall t n x, List.In (existT _ t (n, x)%core) G -> lookupb t ctx n = Some x)
- v
- (H : ocompilef e ls = Some v)
- (Hls : oname_list_unique ls)
- (HGls : forall t n x, List.In (existT _ t (n, x)%core) G -> List.In (Some n) ls -> False)
- : Named.interpf (interp_op:=interp_op) (ctx:=ctx) v
- = Some (interpf interp_op e').
- Proof using ContextOk Name_dec base_type_dec.
- revert dependent ctx; revert dependent ls; induction Hwf;
- repeat first [ progress intros
- | progress subst
- | progress inversion_option
- | apply (f_equal (@Some _))
- | apply (f_equal (@interp_op _ _ _))
- | solve [ eauto ]
- | progress simpl in *
- | progress unfold option_map, LetIn.Let_In in *
- | progress break_innermost_match_step
- | progress break_match_hyps
- | progress destruct_head' or
- | progress inversion_prod
- | progress specialize_by_assumption
- | progress specialize_by auto using oname_list_unique_nil
- | match goal with
- | [ H : forall x, oname_list_unique ?ls -> _ |- _ ]
- => specialize (fun pf x => H x pf)
- | [ H : context[snd (split_onames _ _)] |- _ ]
- => rewrite snd_split_onames_skipn in H
- | [ H : oname_list_unique (List.skipn _ _) -> _ |- _ ]
- => specialize (fun pf => H (@oname_list_unique_skipn _ _ _ pf))
- | [ IH : forall v ls, ocompilef ?e ls = Some v -> _, H : ocompilef ?e ?ls' = Some ?v' |- _ ]
- => specialize (IH _ _ H)
- | [ IH : forall x1 x2 v ls, ocompilef (?e x1) ls = Some v -> _, H : ocompilef (?e ?x1') ?ls' = Some ?v' |- _ ]
- => specialize (fun x2 => IH _ x2 _ _ H)
- | [ H : context[List.In _ (_ ++ _)] |- _ ]
- => rewrite List.in_app_iff in H
- | [ H : forall ctx, _ -> Named.interpf ?e = Some _, H' : context[Named.interpf ?e] |- _ ]
- => rewrite H in H' by assumption
- | [ H : forall x2 ctx, _ -> Named.interpf ?e = Some _ |- Named.interpf ?e = Some _ ]
- => apply H; clear H
- | [ H : forall x2, _ -> forall ctx, _ -> Named.interpf ?e = Some _ |- Named.interpf ?e = Some _ ]
- => apply H; clear H
- end ];
- repeat match goal with
- | _ => erewrite lookupb_extend by assumption
- | [ |- context[find_Name_and_val ?tdec ?ndec ?a ?b ?c ?d ?default] ]
- => lazymatch default with None => fail | _ => idtac end;
- rewrite (find_Name_and_val_split tdec ndec (default:=default))
- | [ H : _ |- _ ] => erewrite H by eassumption
- | _ => progress unfold dec in *
- | _ => progress break_innermost_match_step
- | _ => progress subst
- | _ => progress destruct_head' and
- | _ => congruence
- | [ H : List.In _ (flatten_binding_list _ _) |- _ ]
- => erewrite <- (flatten_binding_list_find_Name_and_val_unique _ _) in H;
- [ | | apply path_prod_uncurried; split; [ eassumption | simpl; reflexivity ] ];
- [ | solve [ eauto using oname_list_unique_firstn, oname_list_unique_skipn ] ]
- | [ H : _ |- _ ]
- => first [ erewrite find_Name_and_val_wrong_type in H by eassumption
- | rewrite find_Name_and_val_different in H by assumption
- | rewrite snd_split_onames_skipn in H ]
- | _ => solve [ eauto using In_skipn, In_firstn
- | eapply split_onames_find_Name_Some_unique; [ | apply path_prod; simpl | ]; eauto ]
- | [ H : find_Name_and_val _ _ ?t ?n ?N ?V None = Some _, H' : List.In (Some ?n) (List.skipn _ ?ls) |- False ]
- => eapply find_Name_and_val_find_Name_Some, split_onames_find_Name_Some_unique in H;
- [ | | apply path_prod_uncurried; split; [ eassumption | simpl; reflexivity ] ];
- [ | solve [ eauto using oname_list_unique_firstn, oname_list_unique_skipn ] ]
- | [ H : List.In (existT _ ?t (?n, _)%core) ?G,
- H' : List.In (Some ?n) (List.skipn _ ?ls),
- IH : forall t' n' x', List.In (existT _ t' (n', x')%core) ?G -> List.In (Some n') ?ls -> False
- |- False ]
- => apply (IH _ _ _ H); clear IH H
- | [ H : List.In (existT _ ?t (?n, _)%core) ?G,
- H' : find_Name _ ?n ?N = Some ?t',
- IH : forall t' n' x', List.In (existT _ t' (n', x')%core) ?G -> List.In (Some n') ?ls -> False
- |- _ ]
- => exfalso; apply (IH _ _ _ H); clear IH H
- end.
- Qed.
-
- Lemma interp_ocompile (ctx : Context) {t} (e : expr t) e' (ls : list (option Name))
- (Hwf : wf e e')
- f
- (Hls : oname_list_unique ls)
- (H : ocompile e ls = Some f)
- : forall v, Named.interp (interp_op:=interp_op) (ctx:=ctx) f v
- = Some (interp interp_op e' v).
- Proof using ContextOk Name_dec base_type_dec.
- revert H; destruct Hwf;
- repeat first [ progress simpl in *
- | progress unfold option_map, Named.interp in *
- | congruence
- | progress break_innermost_match
- | progress inversion_option
- | progress subst
- | progress intros ].
- eapply interpf_ocompilef;
- [ eauto | | eassumption
- | inversion_prod; subst; rewrite snd_split_onames_skipn; eauto using oname_list_unique_skipn
- |intros ???; erewrite <- (flatten_binding_list_find_Name_and_val_unique _ _) by eassumption;
- let H := fresh in
- intro H; apply find_Name_and_val_find_Name_Some in H;
- eapply split_onames_find_Name_Some_unique in H; [ | eassumption.. ];
- intuition ].
- { intros ???.
- repeat first [ solve [ auto ]
- | rewrite (lookupb_extend _ _ _)
- | progress subst
- | progress break_innermost_match
- | erewrite <- (flatten_binding_list_find_Name_and_val_unique _ _) by eassumption
- | congruence
- | match goal with
- | [ |- context[find_Name_and_val ?tdec ?ndec ?a ?b ?c ?d ?default] ]
- => lazymatch default with None => fail | _ => idtac end;
- rewrite (find_Name_and_val_split tdec ndec (default:=default))
- | [ H : _ |- _ ] => first [ erewrite find_Name_and_val_wrong_type in H by eassumption
- | erewrite find_Name_and_val_different in H by eassumption ]
- end
- | progress intros ]. }
- Qed.
-
- Lemma interpf_compilef (ctx : Context) {t} (e : exprf t) e' (ls : list Name)
- G
- (Hwf : wff G e e')
- (HG : forall t n x, List.In (existT _ t (n, x)%core) G -> lookupb t ctx n = Some x)
- v
- (H : compilef e ls = Some v)
- (Hls : name_list_unique ls)
- (HGls : forall t n x, List.In (existT _ t (n, x)%core) G -> List.In n ls -> False)
- : Named.interpf (interp_op:=interp_op) (ctx:=ctx) v
- = Some (interpf interp_op e').
- Proof using ContextOk Name_dec base_type_dec.
- eapply interpf_ocompilef; try eassumption.
- setoid_rewrite List.in_map_iff; intros; destruct_head' ex; destruct_head' and; inversion_option; subst.
- eauto.
- Qed.
-
- Lemma interp_compile (ctx : Context) {t} (e : expr t) e' (ls : list Name)
- (Hwf : wf e e')
- f
- (Hls : name_list_unique ls)
- (H : compile e ls = Some f)
- : forall v, Named.interp (interp_op:=interp_op) (ctx:=ctx) f v
- = Some (interp interp_op e' v).
- Proof using ContextOk Name_dec base_type_dec. eapply interp_ocompile; eassumption. Qed.
-
- Lemma Interp_compile {t} (e : Expr t) (ls : list Name)
- (Hwf : Wf e)
- f
- (Hls : name_list_unique ls)
- (H : compile (e _) ls = Some f)
- : forall v, Named.Interp (Context:=Context) (interp_op:=interp_op) f v
- = Some (Interp interp_op e v).
- Proof using ContextOk Name_dec base_type_dec. eapply interp_compile; eauto. Qed.
-End language.
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-18 04:58:03 +0000