From be19ef348e8614a4aff4d610dddc9adbe90e1124 Mon Sep 17 00:00:00 2001 From: Jason Gross Date: Sun, 19 Mar 2017 18:07:41 -0400 Subject: Add MapCastWf --- _CoqProject | 1 + src/Reflection/Named/MapCastWf.v | 235 +++++++++++++++++++++++++++++++++++++++ 2 files changed, 236 insertions(+) create mode 100644 src/Reflection/Named/MapCastWf.v diff --git a/_CoqProject b/_CoqProject index 0a73eba6f..27d5984f5 100644 --- a/_CoqProject +++ b/_CoqProject @@ -168,6 +168,7 @@ src/Reflection/Named/InterpretToPHOASInterp.v src/Reflection/Named/InterpretToPHOASWf.v src/Reflection/Named/MapCast.v src/Reflection/Named/MapCastInterp.v +src/Reflection/Named/MapCastWf.v src/Reflection/Named/NameUtil.v src/Reflection/Named/NameUtilProperties.v src/Reflection/Named/PositiveContext.v diff --git a/src/Reflection/Named/MapCastWf.v b/src/Reflection/Named/MapCastWf.v new file mode 100644 index 000000000..d5015a87c --- /dev/null +++ b/src/Reflection/Named/MapCastWf.v @@ -0,0 +1,235 @@ +Require Import Coq.Bool.Sumbool. +Require Import Coq.Logic.Eqdep_dec. +Require Import Crypto.Reflection.SmartMap. +Require Import Crypto.Reflection.Relations. +Require Import Crypto.Reflection.Syntax. +Require Import Crypto.Reflection.Named.Syntax. +Require Import Crypto.Reflection.Named.ContextDefinitions. +Require Import Crypto.Reflection.Named.ContextProperties. +Require Import Crypto.Reflection.Named.ContextProperties.SmartMap. +Require Import Crypto.Reflection.Named.Wf. +Require Import Crypto.Reflection.Named.MapCast. +Require Import Crypto.Util.PointedProp. +Require Import Crypto.Util.ZUtil. +Require Import Crypto.Util.Bool. +Require Import Crypto.Util.Option. +Require Import Crypto.Util.Sigma. +Require Import Crypto.Util.Decidable. +Require Import Crypto.Util.Tactics.BreakMatch. +Require Import Crypto.Util.Tactics.SpecializeBy. +Require Import Crypto.Util.Tactics.DestructHead. + +Local Open Scope nexpr_scope. +Section language. + Context {base_type_code : Type} + {op : flat_type base_type_code -> flat_type base_type_code -> Type} + {Name : Type} + {interp_base_type_bounds : base_type_code -> Type} + (interp_op_bounds : forall src dst, op src dst -> interp_flat_type interp_base_type_bounds src -> interp_flat_type interp_base_type_bounds dst) + (pick_typeb : forall t, interp_base_type_bounds t -> base_type_code). + Local Notation pick_type t v := (SmartFlatTypeMap pick_typeb (t:=t) v). + Context (cast_op : forall t tR (opc : op t tR) args_bs, + op (pick_type _ args_bs) (pick_type _ (interp_op_bounds t tR opc args_bs))) + {BoundsContext : Context Name interp_base_type_bounds} + (BoundsContextOk : ContextOk BoundsContext) + {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) + (cast_backb: forall t b, interp_base_type (pick_typeb t b) -> interp_base_type t). + Let cast_back : forall t b, interp_flat_type interp_base_type (@pick_type t b) -> interp_flat_type interp_base_type t + := fun t b => SmartFlatTypeMapUnInterp cast_backb. + Context {Context : Context Name interp_base_type} + (ContextOk : ContextOk Context) + (base_type_dec : DecidableRel (@eq base_type_code)) + (Name_dec : DecidableRel (@eq Name)). + + Local Notation mapf_cast := (@mapf_cast _ op Name _ interp_op_bounds pick_typeb cast_op BoundsContext). + Local Notation map_cast := (@map_cast _ op Name _ interp_op_bounds pick_typeb cast_op BoundsContext). + + Local Ltac handle_options_step := + match goal with + | _ => progress inversion_option + | [ H : ?x = Some _ |- context[?x] ] => rewrite H + | [ H : ?x = None |- context[?x] ] => rewrite H + | [ H : ?x = Some _, H' : context[?x] |- _ ] => rewrite H in H' + | [ H : ?x = None, H' : context[?x] |- _ ] => rewrite H in H' + | [ H : Some _ <> None \/ _ |- _ ] => clear H + | [ H : Some ?x <> Some ?y |- _ ] => assert (x <> y) by congruence; clear H + | [ H : None <> Some _ |- _ ] => clear H + | [ H : Some _ <> None |- _ ] => clear H + | [ H : ?x <> ?x \/ _ |- _ ] => destruct H; [ exfalso; apply H; reflexivity | ] + | [ H : _ \/ None = Some _ |- _ ] => destruct H; [ | exfalso; clear -H; congruence ] + | [ H : _ \/ Some _ = None |- _ ] => destruct H; [ | exfalso; clear -H; congruence ] + | [ H : ?x = Some ?y, H' : ?x = Some ?y' |- _ ] + => assert (y = y') by congruence; (subst y' || subst y) + | _ => progress simpl @option_map + | _ => progress unfold option_map in * + end. + + Local Ltac handle_lookupb_step := + let do_eq_dec dec t t' := + first [ constr_eq t t'; fail 1 + | lazymatch goal with + | [ H : t = t' |- _ ] => fail 1 + | [ H : t <> t' |- _ ] => fail 1 + | [ H : t = t' -> False |- _ ] => fail 1 + | _ => destruct (dec t t') + end ] in + let do_type_dec := do_eq_dec base_type_dec in + match goal with + | _ => progress unfold dec in * + | _ => handle_options_step + (* preprocess *) + | [ H : context[lookupb (extend _ _ _) _] |- _ ] + => first [ rewrite (fun C => lookupb_extend C base_type_dec Name_dec) in H by assumption + | setoid_rewrite (fun C => lookupb_extend C base_type_dec Name_dec) in H; [ | assumption.. ] ] + | [ |- context[lookupb (extend _ _ _) _] ] + => first [ rewrite (fun C => lookupb_extend C base_type_dec Name_dec) by assumption + | setoid_rewrite (fun C => lookupb_extend C base_type_dec Name_dec); [ | assumption.. ] ] + | _ => progress subst + (* handle multiple hypotheses *) + | [ H : find_Name _ ?n ?N = Some ?t', H'' : context[find_Name_and_val _ _ ?t ?n ?N ?x ?default] |- _ ] + => do_type_dec t t' + (* clear the default value *) + | [ H : context[find_Name_and_val ?tdec ?ndec ?t ?n (T:=?T) ?N ?V ?default] |- _ ] + => lazymatch default with None => fail | _ => idtac end; + rewrite find_Name_and_val_split in H + (* generic handlers *) + | [ H : find_Name _ ?n ?N = Some ?t', H' : ?t <> ?t', H'' : context[find_Name_and_val _ _ ?t ?n ?N ?x ?default] |- _ ] + => erewrite find_Name_and_val_wrong_type in H'' by eassumption + | [ H : context[find_Name _ _ (SmartFlatTypeMapInterp2 _ _ _)] |- _ ] + => rewrite find_Name_SmartFlatTypeMapInterp2 with (base_type_code_dec:=base_type_dec) in H + | [ H : find_Name_and_val _ _ _ _ _ _ _ = None |- _ ] + => apply find_Name_and_val_None_iff in H + (* destructers *) + | [ |- context[find_Name_and_val ?tdec ?ndec ?t ?n ?N ?V ?default] ] + => destruct (find_Name_and_val tdec ndec t n N V default) eqn:? + | [ H : context[match find_Name_and_val ?tdec ?ndec ?t ?n ?N ?V ?default with _ => _ end] |- _ ] + => destruct (find_Name_and_val tdec ndec t n N V default) eqn:? + | [ H : context[match find_Name ?ndec ?n ?N with _ => _ end] |- _ ] + => destruct (find_Name ndec n N) eqn:? + | [ H : context[match base_type_dec ?x ?y with _ => _ end] |- _ ] + => destruct (base_type_dec x y) + | [ H : context[match Name_dec ?x ?y with _ => _ end] |- _ ] + => destruct (Name_dec x y) + end. + + Local Ltac handle_exists_in_goal := + lazymatch goal with + | [ |- exists v, Some ?k = Some v /\ @?B v ] + => exists k; split; [ reflexivity | ] + | [ |- exists v, Some ?k = Some v ] + => exists k; reflexivity + | [ |- (exists v, None = Some v /\ @?B v) ] + => exfalso + | [ |- ?A /\ (exists v, Some ?k = Some v /\ @?B v) ] + => cut (A /\ B k); [ clear; solve [ intuition eauto ] | cbv beta ] + | [ |- ?A /\ (exists v, None = Some v /\ @?B v) ] + => exfalso + end. + Local Ltac specializer_t_step := + match goal with + | [ H : ?T, H' : ?T |- _ ] => clear H + | [ H : forall x, Some _ = Some x -> _ |- _ ] => specialize (H _ eq_refl) + | [ H : ?x = Some _, IH : forall a b, ?x = Some _ -> _ |- _ ] + => specialize (IH _ _ H) + | [ H : ?x = Some _, IH : forall a, ?x = Some _ -> _ |- _ ] + => specialize (IH _ H) + | [ H : forall t n v, lookupb ?ctx n = _ -> _, H' : lookupb ?ctx ?n' = _ |- _ ] + => specialize (H _ _ _ H') + | _ => progress specialize_by auto + end. + + Local Ltac break_t_step := + first [ progress subst + | progress destruct_head'_ex + | progress destruct_head'_and + | progress inversion_option + | progress inversion_sigma + | progress autorewrite with push_prop_of_option in * + | progress break_match_hyps ]. + + Local Ltac do_specialize_IHe := + repeat match goal with + | [ IH : context[mapf_cast _ ?e], H' : mapf_cast ?ctx ?e = _ |- _ ] + => let check_tac _ := (rewrite H' in IH) in + first [ specialize (IH ctx); check_tac () + | specialize (fun a => IH a ctx); check_tac () + | specialize (fun a b => IH a b ctx); check_tac () ] + | [ H : forall x y z w, Some _ = Some _ -> _ |- _ ] + => first [ specialize (H _ _ _ _ eq_refl) + | specialize (fun x y => H x y _ _ eq_refl) ] + | [ H : forall x y z, Some _ = Some _ -> _ |- _ ] + => first [ specialize (H _ _ _ eq_refl) + | specialize (fun x => H x _ _ eq_refl) ] + | [ H : forall x y, Some _ = Some _ -> _ |- _ ] + => first [ specialize (H _ _ eq_refl) + | specialize (fun x => H x _ eq_refl) ] + | _ => progress specialize_by_assumption + | [ H : forall a b, prop_of_option (Named.wff a ?e) -> _, H' : prop_of_option (Named.wff _ ?e) |- _ ] + => specialize (fun b => H _ b H') + | [ H : forall a b, prop_of_option (Named.wff a ?e) -> _, H' : forall v, prop_of_option (Named.wff _ ?e) |- _ ] + => specialize (fun b v => H _ b (H' v)) + | [ H : forall b v, _ -> prop_of_option (Named.wff b ?e) |- prop_of_option (Named.wff ?ctx ?e) ] + => specialize (H ctx) + end. + + Local Ltac t_step := + first [ progress intros + | progress simpl in * + | break_t_step + | handle_lookupb_step + | handle_exists_in_goal + | apply conj + | solve [ auto | exfalso; auto ] + | specializer_t_step + | progress do_specialize_IHe + | match goal with + | [ IH : forall v, _ -> ?T, v' : interp_flat_type _ _ |- ?T ] + => apply (IH (cast_back _ _ v')); clear IH + end ]. + Local Ltac t := repeat t_step. + + + Lemma wff_mapf_cast + {t} (e:exprf base_type_code op Name t) + : forall + (oldValues:Context) + (newValues:Context) + (varBounds:BoundsContext) + {b} e' (He':mapf_cast varBounds e = Some (existT _ b e')) + (Hwf : prop_of_option (Named.wff oldValues e)) + (Hctx:forall {t} n v, + lookupb (t:=t) oldValues n = Some v + -> exists b, lookupb (t:=t) varBounds n = Some b + /\ exists v', lookupb (t:=pick_typeb t b) newValues n = Some v'), + prop_of_option (Named.wff newValues e'). + Proof. induction e; t. Qed. + + Lemma wf_map_cast + {t} (e:expr base_type_code op Name t) + (input_bounds : interp_flat_type interp_base_type_bounds (domain t)) + : forall + (oldValues:Context) + (newValues:Context) + (varBounds:BoundsContext) + {b} e' (He':map_cast varBounds e input_bounds = Some (existT _ b e')) + (Hwf : Named.wf oldValues e) + (Hctx:forall {t} n v, + lookupb (t:=t) oldValues n = Some v + -> exists b, lookupb (t:=t) varBounds n = Some b + /\ exists v', lookupb (t:=pick_typeb t b) newValues n = Some v'), + Named.wf newValues e'. + Proof. + unfold Named.wf, map_cast, option_map, interp; simpl; intros. + repeat first [ progress subst + | progress inversion_option + | progress inversion_sigma + | progress break_match_hyps + | progress destruct_head' sigT + | progress simpl in * ]. + match goal with v : _ |- _ => specialize (Hwf (cast_back _ _ v)) end. + eapply wff_mapf_cast; eauto; []. + t. + Qed. +End language. -- cgit v1.2.3