1 (*********************************************************************************************************************************)
4 (* This module is the "top level" for extraction *)
6 (*********************************************************************************************************************************)
8 Require Import Coq.Strings.Ascii.
9 Require Import Coq.Strings.String.
10 Require Import Coq.Lists.List.
12 Require Import Preamble.
13 Require Import General.
15 Require Import NaturalDeduction.
16 Require Import NaturalDeductionToLatex.
18 Require Import HaskKinds.
19 Require Import HaskLiteralsAndTyCons.
20 Require Import HaskCoreVars.
21 Require Import HaskCoreTypes.
22 Require Import HaskCore.
23 Require Import HaskWeakVars.
24 Require Import HaskWeakTypes.
25 Require Import HaskWeak.
26 Require Import HaskStrongTypes.
27 Require Import HaskStrong.
28 Require Import HaskProof.
29 Require Import HaskCoreToWeak.
30 Require Import HaskWeakToStrong.
31 Require Import HaskStrongToProof.
32 Require Import HaskProofToLatex.
33 Require Import HaskStrongToWeak.
34 Require Import HaskWeakToCore.
35 Require Import HaskProofToStrong.
37 Require Import ProgrammingLanguage.
39 Require Import HaskProofCategory.
41 Require Import HaskStrongCategory.
43 Require Import ReificationsEquivalentToGeneralizedArrows.
45 Open Scope string_scope.
46 Extraction Language Haskell.
48 (*Extract Inductive vec => "([])" [ "([])" "(:)" ].*)
49 (*Extract Inductive Tree => "([])" [ "([])" "(:)" ].*)
50 (*Extract Inlined Constant map => "Prelude.map".*)
52 (* I try to reuse Haskell types mostly to get the "deriving Show" aspect *)
53 Extract Inductive option => "Prelude.Maybe" [ "Prelude.Just" "Prelude.Nothing" ].
54 Extract Inductive list => "([])" [ "([])" "(:)" ].
55 Extract Inductive string => "Prelude.String" [ "[]" "(:)" ].
56 Extract Inductive prod => "(,)" [ "(,)" ].
57 Extract Inductive sum => "Prelude.Either" [ "Prelude.Left" "Prelude.Right" ].
58 Extract Inductive sumbool => "Prelude.Bool" [ "Prelude.True" "Prelude.False" ].
59 Extract Inductive bool => "Prelude.Bool" [ "Prelude.True" "Prelude.False" ].
60 Extract Inductive unit => "()" [ "()" ].
61 Extract Inlined Constant string_dec => "(==)".
62 Extract Inlined Constant ascii_dec => "(==)".
64 (* adapted from ExtrOcamlString.v *)
65 Extract Inductive ascii => "Char" [ "bin2ascii" ] "bin2ascii'".
66 Extract Constant zero => "'\000'".
67 Extract Constant one => "'\001'".
68 Extract Constant shift => "shiftAscii".
70 Unset Extraction Optimize.
71 Unset Extraction AutoInline.
73 Variable Name : Type. Extract Inlined Constant Name => "Name.Name".
74 Variable mkSystemName : Unique -> string -> nat -> Name.
75 Extract Inlined Constant mkSystemName =>
76 "(\u s d -> Name.mkSystemName u (OccName.mkOccName (OccName.varNameDepth (nat2int d)) s))".
77 Variable mkTyVar : Name -> Kind -> CoreVar.
78 Extract Inlined Constant mkTyVar => "(\n k -> Var.mkTyVar n (kindToCoreKind k))".
79 Variable mkCoVar : Name -> CoreType -> CoreType -> CoreVar.
80 Extract Inlined Constant mkCoVar => "(\n t1 t2 -> Var.mkCoVar n (Coercion.mkCoKind t1 t2))".
81 Variable mkExVar : Name -> CoreType -> CoreVar.
82 Extract Inlined Constant mkExVar => "Id.mkLocalId".
85 Context (ce:@CoreExpr CoreVar).
87 Definition Γ : TypeEnv := nil.
89 Definition Δ : CoercionEnv Γ := nil.
91 Definition φ : TyVarResolver Γ :=
92 fun cv => Error ("unbound tyvar: " +++ toString (cv:CoreVar)).
93 (*fun tv => error ("tried to get the representative of an unbound tyvar:" +++ (getCoreVarOccString tv)).*)
95 Definition ψ : CoVarResolver Γ Δ :=
96 fun cv => Error ("tried to get the representative of an unbound covar!" (*+++ (getTypeVarOccString cv)*)).
98 (* We need to be able to resolve unbound exprvars, but we can be sure their types will have no
99 * free tyvars in them *)
100 Definition ξ (cv:CoreVar) : LeveledHaskType Γ ★ :=
101 match coreVarToWeakVar cv with
102 | WExprVar wev => match weakTypeToTypeOfKind φ wev ★ with
103 | Error s => Prelude_error ("Error in top-level xi: " +++ s)
106 | WTypeVar _ => Prelude_error "top-level xi got a type variable"
107 | WCoerVar _ => Prelude_error "top-level xi got a coercion variable"
111 (* core-to-string (-dcoqpass) *)
113 Definition header : string :=
114 "\documentclass[9pt]{article}"+++eol+++
115 "\usepackage{amsmath}"+++eol+++
116 "\usepackage{amssymb}"+++eol+++
117 "\usepackage{proof}"+++eol+++
118 "\usepackage{mathpartir} % http://cristal.inria.fr/~remy/latex/"+++eol+++
119 "\usepackage{trfrac} % http://www.utdallas.edu/~hamlen/trfrac.sty"+++eol+++
120 "\def\code#1#2{\Box_{#1} #2}"+++eol+++
121 "\usepackage[paperwidth=200in,centering]{geometry}"+++eol+++
122 "\usepackage[displaymath,tightpage,active]{preview}"+++eol+++
123 "\begin{document}"+++eol+++
124 "\begin{preview}"+++eol.
126 Definition footer : string :=
127 eol+++"\end{preview}"+++
128 eol+++"\end{document}"+++
132 Definition coreToStringExpr' (ce:@CoreExpr CoreVar) : ???string :=
133 addErrorMessage ("input CoreSyn: " +++ toString ce)
134 (addErrorMessage ("input CoreType: " +++ toString (coreTypeOfCoreExpr ce)) (
135 coreExprToWeakExpr ce >>= fun we =>
136 addErrorMessage ("WeakExpr: " +++ toString we)
137 ((addErrorMessage ("CoreType of WeakExpr: " +++ toString (coreTypeOfCoreExpr (weakExprToCoreExpr we)))
138 ((weakTypeOfWeakExpr we) >>= fun t =>
139 (addErrorMessage ("WeakType: " +++ toString t)
140 ((weakTypeToTypeOfKind φ t ★) >>= fun τ =>
141 addErrorMessage ("HaskType: " +++ toString τ)
142 ((weakExprToStrongExpr Γ Δ φ ψ ξ (fun _ => false) τ nil we) >>= fun e =>
143 OK (eol+++"$$"+++ toString (nd_ml_toLatexMath (@expr2proof _ _ _ _ _ _ e))+++"$$"+++eol)
146 Definition coreToStringExpr (ce:@CoreExpr CoreVar) : string :=
147 match coreToStringExpr' ce with
149 | Error s => Prelude_error s
152 Definition coreToStringBind (binds:@CoreBind CoreVar) : string :=
154 | CoreNonRec _ e => coreToStringExpr e
155 | CoreRec lbe => fold_left (fun x y => x+++eol+++eol+++y) (map (fun x => coreToStringExpr (snd x)) lbe) ""
158 Definition coqPassCoreToString (lbinds:list (@CoreBind CoreVar)) : string :=
160 (fold_left (fun x y => x+++eol+++eol+++y) (map coreToStringBind lbinds) "")
164 (* core-to-core (-fcoqpass) *)
167 Definition mkWeakTypeVar (u:Unique)(k:Kind) : WeakTypeVar :=
168 weakTypeVar (mkTyVar (mkSystemName u "tv" O) k) k.
169 Definition mkWeakCoerVar (u:Unique)(k:Kind)(t1 t2:WeakType) : WeakCoerVar :=
170 weakCoerVar (mkCoVar (mkSystemName u "cv" O) (weakTypeToCoreType t1) (weakTypeToCoreType t2)) k t1 t2.
171 Definition mkWeakExprVar (u:Unique)(t:WeakType) : WeakExprVar :=
172 weakExprVar (mkExVar (mkSystemName u "ev" O) (weakTypeToCoreType t)) t.
174 Context (hetmet_brak : WeakExprVar).
175 Context (hetmet_esc : WeakExprVar).
176 Context (uniqueSupply : UniqSupply).
178 Definition useUniqueSupply {T}(ut:UniqM T) : ???T :=
181 f uniqueSupply >>= fun x => OK (snd x)
184 Definition larger : forall ln:list nat, { n:nat & forall n', In n' ln -> gt n n' }.
190 destruct IHln as [n pf].
191 exists (plus (S n) a).
195 fold (@In _ n' ln) in H.
200 Definition FreshNat : @FreshMonad nat.
201 refine {| FMT := fun T => nat -> prod nat T
207 set (larger tl) as q.
208 destruct q as [n' pf].
214 refine {| returnM := fun a (v:a) => _ |}.
215 intro n. exact (n,v).
218 destruct q as [n' v].
223 Definition unFresh {T} : @FreshM _ FreshNat T -> T.
230 Definition env := ★::nil.
231 Definition freshTV : HaskType env ★ := haskTyVarToType (FreshHaskTyVar _).
232 Definition idproof0 : ND Rule [] [env > nil > [] |- [freshTV--->freshTV @@ nil]].
238 eapply (RURule _ _ _ _ (RuCanL _ _)) .
244 Definition coreToCoreExpr' (ce:@CoreExpr CoreVar) : ???(@CoreExpr CoreVar) :=
245 addErrorMessage ("input CoreSyn: " +++ toString ce)
246 (addErrorMessage ("input CoreType: " +++ toString (coreTypeOfCoreExpr ce)) (
247 coreExprToWeakExpr ce >>= fun we =>
248 addErrorMessage ("WeakExpr: " +++ toString we)
249 ((addErrorMessage ("CoreType of WeakExpr: " +++ toString (coreTypeOfCoreExpr (weakExprToCoreExpr we)))
250 ((weakTypeOfWeakExpr we) >>= fun t =>
251 (addErrorMessage ("WeakType: " +++ toString t)
252 ((weakTypeToTypeOfKind φ t ★) >>= fun τ =>
253 addErrorMessage ("HaskType: " +++ toString τ)
254 ((weakExprToStrongExpr Γ Δ φ ψ ξ (fun _ => true) τ nil we) >>= fun e =>
255 (let haskProof := @expr2proof _ _ _ _ _ _ e
256 in (* insert HaskProof-to-HaskProof manipulations here *)
257 (unFresh (@proof2expr nat _ FreshNat _ _ _ _ (fun _ => Prelude_error "unbound unique") _ haskProof))
258 >>= fun e' => Error (@toString _ (ExprToString _ _ _ _) (projT2 e'))
261 Prelude_error (@toString _ (@ExprToString nat _ _ _ _ _ _) (projT2 e'))
267 strongExprToWeakExpr hetmet_brak hetmet_esc mkWeakTypeVar mkWeakCoerVar mkWeakExprVar uniqueSupply
270 >>= fun q => Error (toString q)
275 Definition coreToCoreExpr' (ce:@CoreExpr CoreVar) : ???(@CoreExpr CoreVar) :=
276 addErrorMessage ("input CoreSyn: " +++ toString ce)
277 (addErrorMessage ("input CoreType: " +++ toString (coreTypeOfCoreExpr ce)) (
278 coreExprToWeakExpr ce >>= fun we =>
279 addErrorMessage ("WeakExpr: " +++ toString we)
280 ((addErrorMessage ("CoreType of WeakExpr: " +++ toString (coreTypeOfCoreExpr (weakExprToCoreExpr we)))
281 ((weakTypeOfWeakExpr we) >>= fun t =>
282 (addErrorMessage ("WeakType: " +++ toString t)
283 ((weakTypeToTypeOfKind φ t ★) >>= fun τ =>
285 ((weakExprToStrongExpr Γ Δ φ ψ ξ (fun _ => true) τ nil we) >>= fun e =>
287 (addErrorMessage ("HaskStrong...")
288 (let haskProof := @expr2proof _ _ _ _ _ _ e
289 in (* insert HaskProof-to-HaskProof manipulations here *)
290 OK ((@proof2expr nat _ FreshNat _ _ _ _ (fun _ => Prelude_error "unbound unique") _ haskProof) O)
292 (snd e') >>= fun e'' =>
293 strongExprToWeakExpr hetmet_brak hetmet_esc mkWeakTypeVar mkWeakCoerVar mkWeakExprVar uniqueSupply
296 OK (weakExprToCoreExpr q)
299 Definition coreToCoreExpr (ce:@CoreExpr CoreVar) : (@CoreExpr CoreVar) :=
300 match coreToCoreExpr' ce with
302 | Error s => Prelude_error s
305 Definition coreToCoreBind (binds:@CoreBind CoreVar) : @CoreBind CoreVar :=
307 | CoreNonRec v e => CoreNonRec v (coreToCoreExpr e)
308 | CoreRec lbe => CoreRec (map (fun ve => match ve with (v,e) => (v,coreToCoreExpr e) end) lbe)
311 Definition coqPassCoreToCore' (lbinds:list (@CoreBind CoreVar)) : list (@CoreBind CoreVar) :=
312 map coreToCoreBind lbinds.
316 Definition coqPassCoreToCore
317 (hetmet_brak : CoreVar)
318 (hetmet_esc : CoreVar)
319 (uniqueSupply : UniqSupply)
320 (lbinds:list (@CoreBind CoreVar)) : list (@CoreBind CoreVar) :=
321 match coreVarToWeakVar hetmet_brak with
322 | WExprVar hetmet_brak' => match coreVarToWeakVar hetmet_esc with
323 | WExprVar hetmet_esc' => coqPassCoreToCore' hetmet_brak' hetmet_esc' uniqueSupply lbinds
324 | _ => Prelude_error "IMPOSSIBLE"
326 | _ => Prelude_error "IMPOSSIBLE"