X-Git-Url: http://git.megacz.com/?a=blobdiff_plain;f=src%2FHaskProofFlattener.v;fp=src%2FHaskProofFlattener.v;h=0000000000000000000000000000000000000000;hb=94ad996f571e3c9fd622bc56d9b57118a7e5333a;hp=2797716e4fdd1d27263b074af4db1fe57135ab65;hpb=d6342fb07462cc126df948459ce98ea9caadb95c;p=coq-hetmet.git diff --git a/src/HaskProofFlattener.v b/src/HaskProofFlattener.v deleted file mode 100644 index 2797716..0000000 --- a/src/HaskProofFlattener.v +++ /dev/null @@ -1,396 +0,0 @@ -(*********************************************************************************************************************************) -(* HaskProofFlattener: *) -(* *) -(* The Flattening Functor. *) -(* *) -(*********************************************************************************************************************************) - -Generalizable All Variables. -Require Import Preamble. -Require Import General. -Require Import NaturalDeduction. -Require Import Coq.Strings.String. -Require Import Coq.Lists.List. - -Require Import HaskKinds. -Require Import HaskCoreTypes. -Require Import HaskLiteralsAndTyCons. -Require Import HaskStrongTypes. -Require Import HaskProof. -Require Import NaturalDeduction. -Require Import NaturalDeductionCategory. - -Require Import Algebras_ch4. -Require Import Categories_ch1_3. -Require Import Functors_ch1_4. -Require Import Isomorphisms_ch1_5. -Require Import ProductCategories_ch1_6_1. -Require Import OppositeCategories_ch1_6_2. -Require Import Enrichment_ch2_8. -Require Import Subcategories_ch7_1. -Require Import NaturalTransformations_ch7_4. -Require Import NaturalIsomorphisms_ch7_5. -Require Import BinoidalCategories. -Require Import PreMonoidalCategories. -Require Import MonoidalCategories_ch7_8. -Require Import Coherence_ch7_8. - -Require Import HaskStrongTypes. -Require Import HaskStrong. -Require Import HaskProof. -Require Import HaskStrongToProof. -Require Import HaskProofToStrong. -Require Import ProgrammingLanguage. -Require Import HaskProofStratified. - -Open Scope nd_scope. - -(* - * The flattening transformation. Currently only TWO-level languages are - * supported, and the level-1 sublanguage is rather limited. - * - * This file abuses terminology pretty badly. For purposes of this file, - * "PCF" means "the level-1 sublanguage" and "FC" (aka System FC) means - * the whole language (level-0 language including bracketed level-1 terms) - *) -Section HaskProofFlattener. - - Context {Γ:TypeEnv}. - Context {Δ:CoercionEnv Γ}. - Context {ec:HaskTyVar Γ ★}. - - Lemma unlev_lemma : forall (x:Tree ??(HaskType Γ ★)) lev, x = mapOptionTree unlev (x @@@ lev). - intros. - rewrite <- mapOptionTree_compose. - simpl. - induction x. - destruct a; simpl; auto. - simpl. - rewrite IHx1 at 1. - rewrite IHx2 at 1. - reflexivity. - Qed. - - Context (ga_rep : Tree ??(HaskType Γ ★) -> HaskType Γ ★ ). - Context (ga_type : HaskType Γ ★ -> HaskType Γ ★ -> HaskType Γ ★). - - Lemma magic : forall a b c, - ([] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type a b @@ nil]) -> - ([ga_type b c @@ nil] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type a c @@ nil]). - admit. - Qed. - - Context (ga_lit : forall lit, [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep [] ) (ga_rep [literalType lit])@@ nil]). - Context (ga_id : forall σ, [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep σ ) (ga_rep σ )@@ nil]). - Context (ga_cancell : forall c , [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep ([],,c)) (ga_rep c )@@ nil]). - Context (ga_cancelr : forall c , [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep (c,,[])) (ga_rep c )@@ nil]). - Context (ga_uncancell : forall c , [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep c ) (ga_rep ([],,c) )@@ nil]). - Context (ga_uncancelr : forall c , [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep c ) (ga_rep (c,,[]) )@@ nil]). - Context (ga_assoc : forall a b c, [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep ((a,,b),,c)) (ga_rep (a,,(b,,c)) )@@ nil]). - Context (ga_unassoc : forall a b c, [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep ( a,,(b,,c))) (ga_rep ((a,,b),,c)) @@ nil]). - Context (ga_swap : forall a b, [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep (a,,b) ) (ga_rep (b,,a) )@@ nil]). - Context (ga_copy : forall a , [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep a ) (ga_rep (a,,a) )@@ nil]). - Context (ga_drop : forall a , [] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep a ) (ga_rep [] )@@ nil]). - Context (ga_first : forall a b c, [ga_type (ga_rep a) (ga_rep b) @@nil] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep (a,,c)) (ga_rep (b,,c)) @@nil]). - Context (ga_second : forall a b c, [ga_type (ga_rep a) (ga_rep b) @@nil] ~~{TypesL (SystemFCa Γ Δ)}~~> [ga_type (ga_rep (c,,a)) (ga_rep (c,,b)) @@nil]). - Context (ga_comp : forall a b c, - [ga_type (ga_rep a) (ga_rep b) @@nil],,[ga_type (ga_rep b) (ga_rep c) @@nil] - ~~{TypesL (SystemFCa Γ Δ)}~~> - [ga_type (ga_rep a) (ga_rep c) @@nil]). - - Definition guestJudgmentAsGArrowType (lt:PCFJudg Γ ec) : HaskType Γ ★ := - match lt with - (x,y) => (ga_type (ga_rep x) (ga_rep y)) - end. - - Definition obact (X:Tree ??(PCFJudg Γ ec)) : Tree ??(LeveledHaskType Γ ★) := - mapOptionTree guestJudgmentAsGArrowType X @@@ nil. - - Hint Constructors Rule_Flat. - Context {ndr:@ND_Relation _ Rule}. - - (* - * Here it is, what you've all been waiting for! When reading this, - * it might help to have the definition for "Inductive ND" (see - * NaturalDeduction.v) handy as a cross-reference. - *) - Hint Constructors Rule_Flat. - Definition FlatteningFunctor_fmor - : forall h c, - (h~~{JudgmentsL (PCF Γ Δ ec)}~~>c) -> - ((obact h)~~{TypesL (SystemFCa Γ Δ)}~~>(obact c)). - - set (@nil (HaskTyVar Γ ★)) as lev. - - unfold hom; unfold ob; unfold ehom; simpl; unfold pmon_I; unfold obact; intros. - - induction X; simpl. - - (* the proof from no hypotheses of no conclusions (nd_id0) becomes RVoid *) - apply nd_rule; apply (org_fc _ _ [] [(_,_)] (RVoid _ _)). apply Flat_RVoid. - - (* the proof from hypothesis X of conclusion X (nd_id1) becomes RVar *) - apply nd_rule; apply (org_fc _ _ [] [(_,_)] (RVar _ _ _ _)). apply Flat_RVar. - - (* the proof from hypothesis X of no conclusions (nd_weak) becomes RWeak;;RVoid *) - eapply nd_comp; - [ idtac - | eapply nd_rule - ; eapply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RWeak _))) - ; auto ]. - eapply nd_rule. - eapply (org_fc _ _ [] [(_,_)] (RVoid _ _)); auto. apply Flat_RVoid. - apply Flat_RArrange. - - (* the proof from hypothesis X of two identical conclusions X,,X (nd_copy) becomes RVar;;RJoin;;RCont *) - eapply nd_comp; [ idtac | eapply nd_rule; eapply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RCont _))) ]. - eapply nd_comp; [ apply nd_llecnac | idtac ]. - set (snd_initial(SequentND:=pl_snd(ProgrammingLanguage:=SystemFCa Γ Δ)) - (mapOptionTree (guestJudgmentAsGArrowType) h @@@ lev)) as q. - eapply nd_comp. - eapply nd_prod. - apply q. - apply q. - apply nd_rule. - eapply (org_fc _ _ ([(_,_)],,[(_,_)]) [(_,_)] (RJoin _ _ _ _ _ _ )). - destruct h; simpl. - destruct o. - simpl. - apply Flat_RJoin. - apply Flat_RJoin. - apply Flat_RJoin. - apply Flat_RArrange. - - (* nd_prod becomes nd_llecnac;;nd_prod;;RJoin *) - eapply nd_comp. - apply (nd_llecnac ;; nd_prod IHX1 IHX2). - apply nd_rule. - eapply (org_fc _ _ ([(_,_)],,[(_,_)]) [(_,_)] (RJoin _ _ _ _ _ _ )). - apply (Flat_RJoin Γ Δ (mapOptionTree guestJudgmentAsGArrowType h1 @@@ nil) - (mapOptionTree guestJudgmentAsGArrowType h2 @@@ nil) - (mapOptionTree guestJudgmentAsGArrowType c1 @@@ nil) - (mapOptionTree guestJudgmentAsGArrowType c2 @@@ nil)). - - (* nd_comp becomes pl_subst (aka nd_cut) *) - eapply nd_comp. - apply (nd_llecnac ;; nd_prod IHX1 IHX2). - clear IHX1 IHX2 X1 X2. - apply (@snd_cut _ _ _ _ (pl_snd(ProgrammingLanguage:=SystemFCa Γ Δ))). - - (* nd_cancell becomes RVar;;RuCanL *) - eapply nd_comp; - [ idtac | eapply nd_rule; apply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RuCanL _))) ]. - apply (snd_initial(SequentND:=pl_cnd(ProgrammingLanguage:=(SystemFCa Γ Δ)))). - apply Flat_RArrange. - - (* nd_cancelr becomes RVar;;RuCanR *) - eapply nd_comp; - [ idtac | eapply nd_rule; apply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RuCanR _))) ]. - apply (snd_initial(SequentND:=pl_cnd(ProgrammingLanguage:=(SystemFCa Γ Δ)))). - apply Flat_RArrange. - - (* nd_llecnac becomes RVar;;RCanL *) - eapply nd_comp; - [ idtac | eapply nd_rule; apply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RCanL _))) ]. - apply (snd_initial(SequentND:=pl_cnd(ProgrammingLanguage:=(SystemFCa Γ Δ)))). - apply Flat_RArrange. - - (* nd_rlecnac becomes RVar;;RCanR *) - eapply nd_comp; - [ idtac | eapply nd_rule; apply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RCanR _))) ]. - apply (snd_initial(SequentND:=pl_cnd(ProgrammingLanguage:=(SystemFCa Γ Δ)))). - apply Flat_RArrange. - - (* nd_assoc becomes RVar;;RAssoc *) - eapply nd_comp; - [ idtac | eapply nd_rule; apply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RAssoc _ _ _))) ]. - apply (snd_initial(SequentND:=pl_cnd(ProgrammingLanguage:=(SystemFCa Γ Δ)))). - apply Flat_RArrange. - - (* nd_cossa becomes RVar;;RCossa *) - eapply nd_comp; - [ idtac | eapply nd_rule; apply (org_fc _ _ [(_,_)] [(_,_)] (RArrange _ _ _ _ _ (RCossa _ _ _))) ]. - apply (snd_initial(SequentND:=pl_cnd(ProgrammingLanguage:=(SystemFCa Γ Δ)))). - apply Flat_RArrange. - - destruct r as [r rp]. - rename h into h'. - rename c into c'. - rename r into r'. - - refine (match rp as R in @Rule_PCF _ _ _ H C _ - return - ND (OrgR Γ Δ) [] - [sequent (mapOptionTree guestJudgmentAsGArrowType H @@@ nil) - (mapOptionTree guestJudgmentAsGArrowType C @@@ nil)] - with - | PCF_RArrange h c r q => let case_RURule := tt in _ - | PCF_RLit lit => let case_RLit := tt in _ - | PCF_RNote Σ τ n => let case_RNote := tt in _ - | PCF_RVar σ => let case_RVar := tt in _ - | PCF_RLam Σ tx te => let case_RLam := tt in _ - | PCF_RApp Σ tx te p => let case_RApp := tt in _ - | PCF_RLet Σ σ₁ σ₂ p => let case_RLet := tt in _ - | PCF_RJoin b c d e => let case_RJoin := tt in _ - | PCF_RVoid => let case_RVoid := tt in _ - (*| PCF_RCase T κlen κ θ l x => let case_RCase := tt in _*) - (*| PCF_RLetRec Σ₁ τ₁ τ₂ lev => let case_RLetRec := tt in _*) - end); simpl in *. - clear rp h' c' r'. - - rewrite (unlev_lemma h (ec::nil)). - rewrite (unlev_lemma c (ec::nil)). - destruct case_RURule. - refine (match q as Q in Arrange H C - return - H=(h @@@ (ec :: nil)) -> - C=(c @@@ (ec :: nil)) -> - ND (OrgR Γ Δ) [] - [sequent - [ga_type (ga_rep (mapOptionTree unlev H)) (ga_rep r) @@ nil ] - [ga_type (ga_rep (mapOptionTree unlev C)) (ga_rep r) @@ nil ] ] - with - | RLeft a b c r => let case_RLeft := tt in _ - | RRight a b c r => let case_RRight := tt in _ - | RCanL b => let case_RCanL := tt in _ - | RCanR b => let case_RCanR := tt in _ - | RuCanL b => let case_RuCanL := tt in _ - | RuCanR b => let case_RuCanR := tt in _ - | RAssoc b c d => let case_RAssoc := tt in _ - | RCossa b c d => let case_RCossa := tt in _ - | RExch b c => let case_RExch := tt in _ - | RWeak b => let case_RWeak := tt in _ - | RCont b => let case_RCont := tt in _ - | RComp a b c f g => let case_RComp := tt in _ - end (refl_equal _) (refl_equal _)); - intros; simpl in *; - subst; - try rewrite <- unlev_lemma in *. - - destruct case_RCanL. - apply magic. - apply ga_uncancell. - - destruct case_RCanR. - apply magic. - apply ga_uncancelr. - - destruct case_RuCanL. - apply magic. - apply ga_cancell. - - destruct case_RuCanR. - apply magic. - apply ga_cancelr. - - destruct case_RAssoc. - apply magic. - apply ga_assoc. - - destruct case_RCossa. - apply magic. - apply ga_unassoc. - - destruct case_RExch. - apply magic. - apply ga_swap. - - destruct case_RWeak. - apply magic. - apply ga_drop. - - destruct case_RCont. - apply magic. - apply ga_copy. - - destruct case_RLeft. - apply magic. - (*apply ga_second.*) - admit. - - destruct case_RRight. - apply magic. - (*apply ga_first.*) - admit. - - destruct case_RComp. - apply magic. - (*apply ga_comp.*) - admit. - - destruct case_RLit. - apply ga_lit. - - (* hey cool, I figured out how to pass CoreNote's through... *) - destruct case_RNote. - eapply nd_comp. - eapply nd_rule. - eapply (org_fc _ _ [] [(_,_)] (RVar _ _ _ _)) . auto. - apply Flat_RVar. - apply nd_rule. - apply (org_fc _ _ [(_,_)] [(_,_)] (RNote _ _ _ _ _ n)). auto. - apply Flat_RNote. - - destruct case_RVar. - apply ga_id. - - (* - * class GArrow g (**) u => GArrowApply g (**) u (~>) where - * ga_applyl :: g (x**(x~>y) ) y - * ga_applyr :: g ( (x~>y)**x) y - * - * class GArrow g (**) u => GArrowCurry g (**) u (~>) where - * ga_curryl :: g (x**y) z -> g x (y~>z) - * ga_curryr :: g (x**y) z -> g y (x~>z) - *) - destruct case_RLam. - (* GArrowCurry.ga_curry *) - admit. - - destruct case_RApp. - (* GArrowApply.ga_apply *) - admit. - - destruct case_RLet. - admit. - - destruct case_RVoid. - apply ga_id. - - destruct case_RJoin. - (* this assumes we want effects to occur in syntactically-left-to-right order *) - admit. - Defined. - -(* - Instance FlatteningFunctor {Γ}{Δ}{ec} : Functor (JudgmentsL (PCF Γ Δ ec)) (TypesL (SystemFCa Γ Δ)) (obact) := - { fmor := FlatteningFunctor_fmor }. - Admitted. - - Definition ReificationFunctor Γ Δ : Functor (JudgmentsL _ _ (PCF n Γ Δ)) SystemFCa' (mapOptionTree brakifyJudg). - refine {| fmor := ReificationFunctor_fmor Γ Δ |}; unfold hom; unfold ob; simpl ; intros. - Admitted. - - Definition PCF_SMME (n:nat)(Γ:TypeEnv)(Δ:CoercionEnv Γ) : ProgrammingLanguageSMME. - refine {| plsmme_pl := PCF n Γ Δ |}. - admit. - Defined. - - Definition SystemFCa_SMME (n:nat)(Γ:TypeEnv)(Δ:CoercionEnv Γ) : ProgrammingLanguageSMME. - refine {| plsmme_pl := SystemFCa n Γ Δ |}. - admit. - Defined. - - Definition ReificationFunctorMonoidal n : MonoidalFunctor (JudgmentsN n) (JudgmentsN (S n)) (ReificationFunctor n). - admit. - Defined. - - (* 5.1.4 *) - Definition PCF_SystemFCa_two_level n Γ Δ : TwoLevelLanguage (PCF_SMME n Γ Δ) (SystemFCa_SMME (S n) Γ Δ). - admit. - Defined. -*) - (* ... and the retraction exists *) - -End HaskProofFlattener. -