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 HaskProofCategory.
39 Require Import HaskStrongCategory.
40 Require Import ReificationsEquivalentToGeneralizedArrows.
41 Require Import ProgrammingLanguage.
44 Open Scope string_scope.
45 Extraction Language Haskell.
47 (*Extract Inductive vec => "([])" [ "([])" "(:)" ].*)
48 (*Extract Inductive Tree => "([])" [ "([])" "(:)" ].*)
49 (*Extract Inlined Constant map => "Prelude.map".*)
51 (* I try to reuse Haskell types mostly to get the "deriving Show" aspect *)
52 Extract Inductive option => "Prelude.Maybe" [ "Prelude.Just" "Prelude.Nothing" ].
53 Extract Inductive list => "([])" [ "([])" "(:)" ].
54 Extract Inductive string => "Prelude.String" [ "[]" "(:)" ].
55 Extract Inductive prod => "(,)" [ "(,)" ].
56 Extract Inductive sum => "Prelude.Either" [ "Prelude.Left" "Prelude.Right" ].
57 Extract Inductive sumbool => "Prelude.Bool" [ "Prelude.True" "Prelude.False" ].
58 Extract Inductive bool => "Prelude.Bool" [ "Prelude.True" "Prelude.False" ].
59 Extract Inductive unit => "()" [ "()" ].
60 Extract Inlined Constant string_dec => "(==)".
61 Extract Inlined Constant ascii_dec => "(==)".
63 (* adapted from ExtrOcamlString.v *)
64 Extract Inductive ascii => "Char" [ "bin2ascii" ] "bin2ascii'".
65 Extract Constant zero => "'\000'".
66 Extract Constant one => "'\001'".
67 Extract Constant shift => "shiftAscii".
69 Unset Extraction Optimize.
70 Unset Extraction AutoInline.
72 Variable Name : Type. Extract Inlined Constant Name => "Name.Name".
73 Variable mkSystemName : Unique -> string -> nat -> Name.
74 Extract Inlined Constant mkSystemName =>
75 "(\u s d -> Name.mkSystemName u (OccName.mkOccName (OccName.varNameDepth (nat2int d)) s))".
76 Variable mkTyVar : Name -> Kind -> CoreVar.
77 Extract Inlined Constant mkTyVar => "(\n k -> Var.mkTyVar n (kindToCoreKind k))".
78 Variable mkCoVar : Name -> CoreType -> CoreType -> CoreVar.
79 Extract Inlined Constant mkCoVar => "(\n t1 t2 -> Var.mkCoVar n (Coercion.mkCoKind t1 t2))".
80 Variable mkExVar : Name -> CoreType -> CoreVar.
81 Extract Inlined Constant mkExVar => "Id.mkLocalId".
84 Context (ce:@CoreExpr CoreVar).
86 Definition Γ : TypeEnv := nil.
88 Definition Δ : CoercionEnv Γ := nil.
90 Definition φ : TyVarResolver Γ :=
91 fun cv => Error ("unbound tyvar: " +++ toString (cv:CoreVar)).
92 (*fun tv => error ("tried to get the representative of an unbound tyvar:" +++ (getCoreVarOccString tv)).*)
94 Definition ψ : CoVarResolver Γ Δ :=
95 fun cv => Error ("tried to get the representative of an unbound covar!" (*+++ (getTypeVarOccString cv)*)).
97 (* We need to be able to resolve unbound exprvars, but we can be sure their types will have no
98 * free tyvars in them *)
99 Definition ξ (cv:CoreVar) : LeveledHaskType Γ ★ :=
100 match coreVarToWeakVar cv with
101 | WExprVar wev => match weakTypeToTypeOfKind φ wev ★ with
102 | Error s => Prelude_error ("Error in top-level xi: " +++ s)
105 | WTypeVar _ => Prelude_error "top-level xi got a type variable"
106 | WCoerVar _ => Prelude_error "top-level xi got a coercion variable"
110 (* core-to-string (-dcoqpass) *)
112 Definition header : string :=
113 "\documentclass[9pt]{article}"+++eol+++
114 "\usepackage{amsmath}"+++eol+++
115 "\usepackage{amssymb}"+++eol+++
116 "\usepackage{proof}"+++eol+++
117 "\usepackage{mathpartir} % http://cristal.inria.fr/~remy/latex/"+++eol+++
118 "\usepackage{trfrac} % http://www.utdallas.edu/~hamlen/trfrac.sty"+++eol+++
119 "\def\code#1#2{\Box_{#1} #2}"+++eol+++
120 "\usepackage[paperwidth=200in,centering]{geometry}"+++eol+++
121 "\usepackage[displaymath,tightpage,active]{preview}"+++eol+++
122 "\begin{document}"+++eol+++
123 "\begin{preview}"+++eol.
125 Definition footer : string :=
126 eol+++"\end{preview}"+++
127 eol+++"\end{document}"+++
131 Definition coreToStringExpr' (ce:@CoreExpr CoreVar) : ???string :=
132 addErrorMessage ("input CoreSyn: " +++ toString ce)
133 (addErrorMessage ("input CoreType: " +++ toString (coreTypeOfCoreExpr ce)) (
134 coreExprToWeakExpr ce >>= fun we =>
135 addErrorMessage ("WeakExpr: " +++ toString we)
136 ((addErrorMessage ("CoreType of WeakExpr: " +++ toString (coreTypeOfCoreExpr (weakExprToCoreExpr we)))
137 ((weakTypeOfWeakExpr we) >>= fun t =>
138 (addErrorMessage ("WeakType: " +++ toString t)
139 ((weakTypeToTypeOfKind φ t ★) >>= fun τ =>
140 addErrorMessage ("HaskType: " +++ toString τ)
141 ((weakExprToStrongExpr Γ Δ φ ψ ξ (fun _ => false) τ nil we) >>= fun e =>
142 OK (eol+++"$$"+++ toString (nd_ml_toLatexMath (@expr2proof _ _ _ _ _ _ e))+++"$$"+++eol)
145 Definition coreToStringExpr (ce:@CoreExpr CoreVar) : string :=
146 match coreToStringExpr' ce with
148 | Error s => Prelude_error s
151 Definition coreToStringBind (binds:@CoreBind CoreVar) : string :=
153 | CoreNonRec _ e => coreToStringExpr e
154 | CoreRec lbe => fold_left (fun x y => x+++eol+++eol+++y) (map (fun x => coreToStringExpr (snd x)) lbe) ""
157 Definition coqPassCoreToString (lbinds:list (@CoreBind CoreVar)) : string :=
159 (fold_left (fun x y => x+++eol+++eol+++y) (map coreToStringBind lbinds) "")
163 (* core-to-core (-fcoqpass) *)
166 Definition mkWeakTypeVar (u:Unique)(k:Kind) : WeakTypeVar :=
167 weakTypeVar (mkTyVar (mkSystemName u "tv" O) k) k.
168 Definition mkWeakCoerVar (u:Unique)(k:Kind)(t1 t2:WeakType) : WeakCoerVar :=
169 weakCoerVar (mkCoVar (mkSystemName u "cv" O) (weakTypeToCoreType t1) (weakTypeToCoreType t2)) k t1 t2.
170 Definition mkWeakExprVar (u:Unique)(t:WeakType) : WeakExprVar :=
171 weakExprVar (mkExVar (mkSystemName u "ev" O) (weakTypeToCoreType t)) t.
173 Context (hetmet_brak : WeakExprVar).
174 Context (hetmet_esc : WeakExprVar).
175 Context (uniqueSupply : UniqSupply).
177 Definition useUniqueSupply {T}(ut:UniqM T) : ???T :=
180 f uniqueSupply >>= fun x => OK (snd x)
183 Definition larger : forall ln:list nat, { n:nat & forall n', In n' ln -> gt n n' }.
189 destruct IHln as [n pf].
190 exists (plus (S n) a).
194 fold (@In _ n' ln) in H.
199 Definition FreshNat : @FreshMonad nat.
200 refine {| FMT := fun T => nat -> prod nat T
206 set (larger tl) as q.
207 destruct q as [n' pf].
213 refine {| returnM := fun a (v:a) => _ |}.
214 intro n. exact (n,v).
217 destruct q as [n' v].
222 Definition unFresh {T} : @FreshM _ FreshNat T -> T.
229 Definition env := ★::nil.
230 Definition freshTV : HaskType env ★ := haskTyVarToType (FreshHaskTyVar _).
231 Definition idproof0 : ND Rule [] [env > nil > [] |- [freshTV--->freshTV @@ nil]].
237 eapply (RURule _ _ _ _ (RuCanL _ _)) .
243 Definition coreToCoreExpr' (ce:@CoreExpr CoreVar) : ???(@CoreExpr CoreVar) :=
244 addErrorMessage ("input CoreSyn: " +++ toString ce)
245 (addErrorMessage ("input CoreType: " +++ toString (coreTypeOfCoreExpr ce)) (
246 coreExprToWeakExpr ce >>= fun we =>
247 addErrorMessage ("WeakExpr: " +++ toString we)
248 ((addErrorMessage ("CoreType of WeakExpr: " +++ toString (coreTypeOfCoreExpr (weakExprToCoreExpr we)))
249 ((weakTypeOfWeakExpr we) >>= fun t =>
250 (addErrorMessage ("WeakType: " +++ toString t)
251 ((weakTypeToTypeOfKind φ t ★) >>= fun τ =>
252 addErrorMessage ("HaskType: " +++ toString τ)
253 ((weakExprToStrongExpr Γ Δ φ ψ ξ (fun _ => true) τ nil we) >>= fun e =>
254 (let haskProof := @expr2proof _ _ _ _ _ _ e
255 in (* insert HaskProof-to-HaskProof manipulations here *)
256 (unFresh (@proof2expr nat _ FreshNat _ _ _ _ (fun _ => Prelude_error "unbound unique") _ haskProof))
257 >>= fun e' => Error (@toString _ (ExprToString _ _ _ _) (projT2 e'))
260 Prelude_error (@toString _ (@ExprToString nat _ _ _ _ _ _) (projT2 e'))
266 strongExprToWeakExpr hetmet_brak hetmet_esc mkWeakTypeVar mkWeakCoerVar mkWeakExprVar uniqueSupply
269 >>= fun q => Error (toString q)
274 Definition coreToCoreExpr' (ce:@CoreExpr CoreVar) : ???(@CoreExpr CoreVar) :=
275 addErrorMessage ("input CoreSyn: " +++ toString ce)
276 (addErrorMessage ("input CoreType: " +++ toString (coreTypeOfCoreExpr ce)) (
277 coreExprToWeakExpr ce >>= fun we =>
278 addErrorMessage ("WeakExpr: " +++ toString we)
279 ((addErrorMessage ("CoreType of WeakExpr: " +++ toString (coreTypeOfCoreExpr (weakExprToCoreExpr we)))
280 ((weakTypeOfWeakExpr we) >>= fun t =>
281 (addErrorMessage ("WeakType: " +++ toString t)
282 ((weakTypeToTypeOfKind φ t ★) >>= fun τ =>
284 ((weakExprToStrongExpr Γ Δ φ ψ ξ (fun _ => true) τ nil we) >>= fun e =>
286 (addErrorMessage ("HaskStrong...")
287 (let haskProof := @expr2proof _ _ _ _ _ _ e
288 in (* insert HaskProof-to-HaskProof manipulations here *)
289 OK ((@proof2expr nat _ FreshNat _ _ _ _ (fun _ => Prelude_error "unbound unique") _ haskProof) O)
291 (snd e') >>= fun e'' =>
292 strongExprToWeakExpr hetmet_brak hetmet_esc mkWeakTypeVar mkWeakCoerVar mkWeakExprVar uniqueSupply
295 OK (weakExprToCoreExpr q)
298 Definition coreToCoreExpr (ce:@CoreExpr CoreVar) : (@CoreExpr CoreVar) :=
299 match coreToCoreExpr' ce with
301 | Error s => Prelude_error s
304 Definition coreToCoreBind (binds:@CoreBind CoreVar) : @CoreBind CoreVar :=
306 | CoreNonRec v e => CoreNonRec v (coreToCoreExpr e)
307 | CoreRec lbe => CoreRec (map (fun ve => match ve with (v,e) => (v,coreToCoreExpr e) end) lbe)
310 Definition coqPassCoreToCore' (lbinds:list (@CoreBind CoreVar)) : list (@CoreBind CoreVar) :=
311 map coreToCoreBind lbinds.
315 Definition coqPassCoreToCore
316 (hetmet_brak : CoreVar)
317 (hetmet_esc : CoreVar)
318 (uniqueSupply : UniqSupply)
319 (lbinds:list (@CoreBind CoreVar)) : list (@CoreBind CoreVar) :=
320 match coreVarToWeakVar hetmet_brak with
321 | WExprVar hetmet_brak' => match coreVarToWeakVar hetmet_esc with
322 | WExprVar hetmet_esc' => coqPassCoreToCore' hetmet_brak' hetmet_esc' uniqueSupply lbinds
323 | _ => Prelude_error "IMPOSSIBLE"
325 | _ => Prelude_error "IMPOSSIBLE"