Mercurial > urweb
view src/coq/Syntax.v @ 1381:bf58ca871c00
Detect missing 'database' directive; don't compile garbage C files
author | Adam Chlipala <adam@chlipala.net> |
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date | Thu, 06 Jan 2011 09:14:06 -0500 |
parents | 75c7a69354d6 |
children |
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(* Copyright (c) 2009, Adam Chlipala * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions are met: * * - Redistributions of source code must retain the above copyright notice, * this list of conditions and the following disclaimer. * - Redistributions in binary form must reproduce the above copyright notice, * this list of conditions and the following disclaimer in the documentation * and/or other materials provided with the distribution. * - The names of contributors may not be used to endorse or promote products * derived from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. *) Require Import Name. Export Name. Set Implicit Arguments. (** Syntax of Featherweight Ur *) Inductive kind : Type := | KType : kind | KName : kind | KArrow : kind -> kind -> kind | KRecord : kind -> kind. Section vars. Variable cvar : kind -> Type. Inductive con : kind -> Type := | CVar : forall k, cvar k -> con k | Arrow : con KType -> con KType -> con KType | Poly : forall k, (cvar k -> con KType) -> con KType | CAbs : forall k1 k2, (cvar k1 -> con k2) -> con (KArrow k1 k2) | CApp : forall k1 k2, con (KArrow k1 k2) -> con k1 -> con k2 | Name : name -> con KName | TRecord : con (KRecord KType) -> con KType | CEmpty : forall k, con (KRecord k) | CSingle : forall k, con KName -> con k -> con (KRecord k) | CConcat : forall k, con (KRecord k) -> con (KRecord k) -> con (KRecord k) | CMap : forall k1 k2, con (KArrow (KArrow k1 k2) (KArrow (KRecord k1) (KRecord k2))) | TGuarded : forall k, con (KRecord k) -> con (KRecord k) -> con KType -> con KType. Variable dvar : forall k, con (KRecord k) -> con (KRecord k) -> Type. Section subs. Variable k1 : kind. Variable c1 : con k1. Inductive subs : forall k2, (cvar k1 -> con k2) -> con k2 -> Type := | S_Unchanged : forall k2 (c2 : con k2), subs (fun _ => c2) c2 | S_CVar : subs (fun x => CVar x) c1 | S_Arrow : forall c2 c3 c2' c3', subs c2 c2' -> subs c3 c3' -> subs (fun x => Arrow (c2 x) (c3 x)) (Arrow c2' c3') | S_Poly : forall k (c2 : cvar k1 -> cvar k -> _) (c2' : cvar k -> _), (forall x', subs (fun x => c2 x x') (c2' x')) -> subs (fun x => Poly (c2 x)) (Poly c2') | S_CAbs : forall k2 k3 (c2 : cvar k1 -> cvar k2 -> con k3) (c2' : cvar k2 -> _), (forall x', subs (fun x => c2 x x') (c2' x')) -> subs (fun x => CAbs (c2 x)) (CAbs c2') | S_CApp : forall k1 k2 (c2 : _ -> con (KArrow k1 k2)) c3 c2' c3', subs c2 c2' -> subs c3 c3' -> subs (fun x => CApp (c2 x) (c3 x)) (CApp c2' c3') | S_TRecord : forall c2 c2', subs c2 c2' -> subs (fun x => TRecord (c2 x)) (TRecord c2') | S_CSingle : forall k2 c2 (c3 : _ -> con k2) c2' c3', subs c2 c2' -> subs c3 c3' -> subs (fun x => CSingle (c2 x) (c3 x)) (CSingle c2' c3') | S_CConcat : forall k2 (c2 c3 : _ -> con (KRecord k2)) c2' c3', subs c2 c2' -> subs c3 c3' -> subs (fun x => CConcat (c2 x) (c3 x)) (CConcat c2' c3') | S_TGuarded : forall k2 (c2 c3 : _ -> con (KRecord k2)) c4 c2' c3' c4', subs c2 c2' -> subs c3 c3' -> subs c4 c4' -> subs (fun x => TGuarded (c2 x) (c3 x) (c4 x)) (TGuarded c2' c3' c4'). End subs. Inductive disj : forall k, con (KRecord k) -> con (KRecord k) -> Prop := | DVar : forall k (c1 c2 : con (KRecord k)), dvar c1 c2 -> disj c1 c2 | DComm : forall k (c1 c2 : con (KRecord k)), disj c1 c2 -> disj c2 c1 | DEmpty : forall k c2, disj (CEmpty k) c2 | DSingleKeys : forall k X1 X2 (c1 c2 : con k), X1 <> X2 -> disj (CSingle (Name X1) c1) (CSingle (Name X2) c2) | DSingleValues : forall k n1 n2 (c1 c2 : con k) k' (c1' c2' : con k'), disj (CSingle n1 c1') (CSingle n2 c2') -> disj (CSingle n1 c1) (CSingle n2 c2) | DConcat : forall k (c1 c2 c : con (KRecord k)), disj c1 c -> disj c2 c -> disj (CConcat c1 c2) c | DEq : forall k (c1 c2 c1' : con (KRecord k)), disj c1 c2 -> deq c1' c1 -> disj c1' c2 with deq : forall k, con k -> con k -> Prop := | Eq_Beta : forall k1 k2 (c1 : cvar k1 -> con k2) c2 c1', subs c2 c1 c1' -> deq (CApp (CAbs c1) c2) c1' | Eq_Refl : forall k (c : con k), deq c c | Eq_Comm : forall k (c1 c2 : con k), deq c2 c1 -> deq c1 c2 | Eq_Trans : forall k (c1 c2 c3 : con k), deq c1 c2 -> deq c2 c3 -> deq c1 c3 | Eq_Cong : forall k1 k2 c1 c1' (c2 : cvar k1 -> con k2) c2' c2'', deq c1 c1' -> subs c1 c2 c2' -> subs c1' c2 c2'' -> deq c2' c2'' | Eq_Concat_Empty : forall k c, deq (CConcat (CEmpty k) c) c | Eq_Concat_Comm : forall k (c1 c2 c3 : con (KRecord k)), disj c1 c2 -> deq (CConcat c1 c2) (CConcat c2 c1) | Eq_Concat_Assoc : forall k (c1 c2 c3 : con (KRecord k)), deq (CConcat c1 (CConcat c2 c3)) (CConcat (CConcat c1 c2) c3) | Eq_Map_Empty : forall k1 k2 f, deq (CApp (CApp (CMap k1 k2) f) (CEmpty _)) (CEmpty _) | Eq_Map_Cons : forall k1 k2 f c1 c2 c3, disj (CSingle c1 c2) c3 -> deq (CApp (CApp (CMap k1 k2) f) (CConcat (CSingle c1 c2) c3)) (CConcat (CSingle c1 (CApp f c2)) (CApp (CApp (CMap k1 k2) f) c3)) | Eq_Map_Ident : forall k c, deq (CApp (CApp (CMap k k) (CAbs (fun x => CVar x))) c) c | Eq_Map_Dist : forall k1 k2 f c1 c2, deq (CApp (CApp (CMap k1 k2) f) (CConcat c1 c2)) (CConcat (CApp (CApp (CMap k1 k2) f) c1) (CApp (CApp (CMap k1 k2) f) c2)) | Eq_Map_Fuse : forall k1 k2 k3 f f' c, deq (CApp (CApp (CMap k2 k3) f') (CApp (CApp (CMap k1 k2) f) c)) (CApp (CApp (CMap k1 k3) (CAbs (fun x => CApp f' (CApp f (CVar x))))) c). Variable evar : con KType -> Type. Inductive exp : con KType -> Type := | Var : forall t, evar t -> exp t | App : forall dom ran, exp (Arrow dom ran) -> exp dom -> exp ran | Abs : forall dom ran, (evar dom -> exp ran) -> exp (Arrow dom ran) | ECApp : forall k (dom : con k) ran ran', exp (Poly ran) -> subs dom ran ran' -> exp ran' | ECAbs : forall k (ran : cvar k -> _), (forall X, exp (ran X)) -> exp (Poly ran) | Cast : forall t1 t2, deq t1 t2 -> exp t1 -> exp t2 | Empty : exp (TRecord (CEmpty _)) | Single : forall c t, exp t -> exp (TRecord (CConcat (CSingle c t) (CEmpty _))) | Proj : forall c t c', exp (TRecord (CConcat (CSingle c t) c')) -> exp t | Cut : forall c t c', disj (CSingle c t) c' -> exp (TRecord (CConcat (CSingle c t) c')) -> exp (TRecord c') | Concat : forall c1 c2, exp (TRecord c1) -> exp (TRecord c2) -> exp (TRecord (CConcat c1 c2)) | Guarded : forall k (c1 c2 : con (KRecord k)) c, (dvar c1 c2 -> exp c) -> exp (TGuarded c1 c2 c) | GuardedApp : forall k (c1 c2 : con (KRecord k)) t, exp (TGuarded c1 c2 t) -> disj c1 c2 -> exp t. End vars.