1 | (* *********************************************************************) |
---|
2 | (* *) |
---|
3 | (* The Compcert verified compiler *) |
---|
4 | (* *) |
---|
5 | (* Xavier Leroy, INRIA Paris-Rocquencourt *) |
---|
6 | (* *) |
---|
7 | (* Copyright Institut National de Recherche en Informatique et en *) |
---|
8 | (* Automatique. All rights reserved. This file is distributed *) |
---|
9 | (* under the terms of the GNU General Public License as published by *) |
---|
10 | (* the Free Software Foundation, either version 2 of the License, or *) |
---|
11 | (* (at your option) any later version. This file is also distributed *) |
---|
12 | (* under the terms of the INRIA Non-Commercial License Agreement. *) |
---|
13 | (* *) |
---|
14 | (* *********************************************************************) |
---|
15 | |
---|
16 | (* * Abstract syntax for the Clight language *) |
---|
17 | |
---|
18 | (*include "Integers.ma".*) |
---|
19 | include "common/AST.ma". |
---|
20 | include "utilities/Coqlib.ma". |
---|
21 | include "common/Errors.ma". |
---|
22 | include "common/CostLabel.ma". |
---|
23 | |
---|
24 | (* * * Abstract syntax *) |
---|
25 | |
---|
26 | (* * ** Types *) |
---|
27 | |
---|
28 | (* * The syntax of type expressions. Some points to note: |
---|
29 | - Array types [Tarray n] carry the size [n] of the array. |
---|
30 | Arrays with unknown sizes are represented by pointer types. |
---|
31 | - Function types [Tfunction targs tres] specify the number and types |
---|
32 | of the function arguments (list [targs]), and the type of the |
---|
33 | function result ([tres]). Variadic functions and old-style unprototyped |
---|
34 | functions are not supported. |
---|
35 | - In C, struct and union types are named and compared by name. |
---|
36 | This enables the definition of recursive struct types such as |
---|
37 | << |
---|
38 | struct s1 { int n; struct * s1 next; }; |
---|
39 | >> |
---|
40 | Note that recursion within types must go through a pointer type. |
---|
41 | For instance, the following is not allowed in C. |
---|
42 | << |
---|
43 | struct s2 { int n; struct s2 next; }; |
---|
44 | >> |
---|
45 | In Clight, struct and union types [Tstruct id fields] and |
---|
46 | [Tunion id fields] are compared by structure: the [fields] |
---|
47 | argument gives the names and types of the members. The identifier |
---|
48 | [id] is a local name which can be used in conjuction with the |
---|
49 | [Tcomp_ptr] constructor to express recursive types. [Tcomp_ptr rg id] |
---|
50 | stands for a pointer type to the nearest enclosing [Tstruct] |
---|
51 | or [Tunion] type named [id] in memory region [rg]. For instance. |
---|
52 | the structure [s1] defined above in C is expressed by |
---|
53 | << |
---|
54 | Tstruct "s1" (Fcons "n" (Tint I32 Signed) |
---|
55 | (Fcons "next" (Tcomp_ptr Any "id") |
---|
56 | Fnil)) |
---|
57 | >> |
---|
58 | Note that the incorrect structure [s2] above cannot be expressed at |
---|
59 | all, since [Tcomp_ptr] lets us refer to a pointer to an enclosing |
---|
60 | structure or union, but not to the structure or union directly. |
---|
61 | *) |
---|
62 | |
---|
63 | inductive type : Type[0] ≝ |
---|
64 | | Tvoid: type (**r the [void] type *) |
---|
65 | | Tint: intsize → signedness → type (**r integer types *) |
---|
66 | | Tpointer: (*region →*) type → type (**r pointer types ([*ty]) *) |
---|
67 | | Tarray: (*region →*) type → nat → type (**r array types ([ty[len]]) *) |
---|
68 | | Tfunction: typelist → type → type (**r function types *) |
---|
69 | | Tstruct: ident → fieldlist → type (**r struct types *) |
---|
70 | | Tunion: ident → fieldlist → type (**r union types *) |
---|
71 | | Tcomp_ptr: (*region →*) ident → type (**r pointer to named struct or union *) |
---|
72 | |
---|
73 | with typelist : Type[0] ≝ |
---|
74 | | Tnil: typelist |
---|
75 | | Tcons: type → typelist → typelist |
---|
76 | |
---|
77 | with fieldlist : Type[0] ≝ |
---|
78 | | Fnil: fieldlist |
---|
79 | | Fcons: ident → type → fieldlist → fieldlist. |
---|
80 | |
---|
81 | (* XXX: no induction scheme! *) |
---|
82 | let rec type_ind |
---|
83 | (P:type → Prop) |
---|
84 | (vo:P Tvoid) |
---|
85 | (it:∀i,s. P (Tint i s)) |
---|
86 | (pt:∀t. P t → P (Tpointer t)) |
---|
87 | (ar:∀t,n. P t → P (Tarray t n)) |
---|
88 | (fn:∀tl,t. P t → P (Tfunction tl t)) |
---|
89 | (st:∀i,fl. P (Tstruct i fl)) |
---|
90 | (un:∀i,fl. P (Tunion i fl)) |
---|
91 | (cp:∀i. P (Tcomp_ptr i)) |
---|
92 | (t:type) on t : P t ≝ |
---|
93 | match t return λt'.P t' with |
---|
94 | [ Tvoid ⇒ vo |
---|
95 | | Tint i s ⇒ it i s |
---|
96 | | Tpointer t' ⇒ pt t' (type_ind P vo it pt ar fn st un cp t') |
---|
97 | | Tarray t' n ⇒ ar t' n (type_ind P vo it pt ar fn st un cp t') |
---|
98 | | Tfunction tl t' ⇒ fn tl t' (type_ind P vo it pt ar fn st un cp t') |
---|
99 | | Tstruct i fs ⇒ st i fs |
---|
100 | | Tunion i fs ⇒ un i fs |
---|
101 | | Tcomp_ptr i ⇒ cp i |
---|
102 | ]. |
---|
103 | |
---|
104 | let rec fieldlist_ind |
---|
105 | (P:fieldlist → Prop) |
---|
106 | (nl:P Fnil) |
---|
107 | (cs:∀i,t,fs. P fs → P (Fcons i t fs)) |
---|
108 | (fs:fieldlist) on fs : P fs ≝ |
---|
109 | match fs with |
---|
110 | [ Fnil ⇒ nl |
---|
111 | | Fcons i t fs' ⇒ cs i t fs' (fieldlist_ind P nl cs fs') |
---|
112 | ]. |
---|
113 | |
---|
114 | (* * ** Expressions *) |
---|
115 | |
---|
116 | (* * Arithmetic and logical operators. *) |
---|
117 | |
---|
118 | inductive unary_operation : Type[0] ≝ |
---|
119 | | Onotbool : unary_operation (**r boolean negation ([!] in C) *) |
---|
120 | | Onotint : unary_operation (**r integer complement ([~] in C) *) |
---|
121 | | Oneg : unary_operation. (**r opposite (unary [-]) *) |
---|
122 | |
---|
123 | inductive binary_operation : Type[0] ≝ |
---|
124 | | Oadd : binary_operation (**r addition (binary [+]) *) |
---|
125 | | Osub : binary_operation (**r subtraction (binary [-]) *) |
---|
126 | | Omul : binary_operation (**r multiplication (binary [*]) *) |
---|
127 | | Odiv : binary_operation (**r division ([/]) *) |
---|
128 | | Omod : binary_operation (**r remainder ([%]) *) |
---|
129 | | Oand : binary_operation (**r bitwise and ([&]) *) |
---|
130 | | Oor : binary_operation (**r bitwise or ([|]) *) |
---|
131 | | Oxor : binary_operation (**r bitwise xor ([^]) *) |
---|
132 | | Oshl : binary_operation (**r left shift ([<<]) *) |
---|
133 | | Oshr : binary_operation (**r right shift ([>>]) *) |
---|
134 | | Oeq: binary_operation (**r comparison ([==]) *) |
---|
135 | | One: binary_operation (**r comparison ([!=]) *) |
---|
136 | | Olt: binary_operation (**r comparison ([<]) *) |
---|
137 | | Ogt: binary_operation (**r comparison ([>]) *) |
---|
138 | | Ole: binary_operation (**r comparison ([<=]) *) |
---|
139 | | Oge: binary_operation. (**r comparison ([>=]) *) |
---|
140 | |
---|
141 | (* * Clight expressions are a large subset of those of C. |
---|
142 | The main omissions are string literals and assignment operators |
---|
143 | ([=], [+=], [++], etc). In Clight, assignment is a statement, |
---|
144 | not an expression. |
---|
145 | |
---|
146 | All expressions are annotated with their types. An expression |
---|
147 | (type [expr]) is therefore a pair of a type and an expression |
---|
148 | description (type [expr_descr]). |
---|
149 | *) |
---|
150 | |
---|
151 | inductive expr : Type[0] ≝ |
---|
152 | | Expr: expr_descr → type → expr |
---|
153 | |
---|
154 | with expr_descr : Type[0] ≝ |
---|
155 | | Econst_int: ∀sz:intsize. bvint sz → expr_descr (**r integer literal *) |
---|
156 | | Evar: ident → expr_descr (**r variable *) |
---|
157 | | Ederef: expr → expr_descr (**r pointer dereference (unary [*]) *) |
---|
158 | | Eaddrof: expr → expr_descr (**r address-of operator ([&]) *) |
---|
159 | | Eunop: unary_operation → expr → expr_descr (**r unary operation *) |
---|
160 | | Ebinop: binary_operation → expr → expr → expr_descr (**r binary operation *) |
---|
161 | | Ecast: type → expr → expr_descr (**r type cast ([(ty) e]) *) |
---|
162 | | Econdition: expr → expr → expr → expr_descr (**r conditional ([e1 ? e2 : e3]) *) |
---|
163 | | Eandbool: expr → expr → expr_descr (**r sequential and ([&&]) *) |
---|
164 | | Eorbool: expr → expr → expr_descr (**r sequential or ([||]) *) |
---|
165 | | Esizeof: type → expr_descr (**r size of a type *) |
---|
166 | | Efield: expr → ident → expr_descr (**r access to a member of a struct or union *) |
---|
167 | | Ecost: costlabel → expr → expr_descr. |
---|
168 | |
---|
169 | |
---|
170 | |
---|
171 | |
---|
172 | (* * Extract the type part of a type-annotated Clight expression. *) |
---|
173 | |
---|
174 | definition typeof : expr → type ≝ λe. |
---|
175 | match e with [ Expr de te ⇒ te ]. |
---|
176 | |
---|
177 | (* * ** Statements *) |
---|
178 | |
---|
179 | (* * Clight statements include all C statements. |
---|
180 | Only structured forms of [switch] are supported; moreover, |
---|
181 | the [default] case must occur last. Blocks and block-scoped declarations |
---|
182 | are not supported. *) |
---|
183 | |
---|
184 | definition label ≝ ident. |
---|
185 | |
---|
186 | inductive statement : Type[0] ≝ |
---|
187 | | Sskip : statement (**r do nothing *) |
---|
188 | | Sassign : expr → expr → statement (**r assignment [lvalue = rvalue] *) |
---|
189 | | Scall: option expr → expr → list expr → statement (**r function call *) |
---|
190 | | Ssequence : statement → statement → statement (**r sequence *) |
---|
191 | | Sifthenelse : expr → statement → statement → statement (**r conditional *) |
---|
192 | | Swhile : expr → statement → statement (**r [while] loop *) |
---|
193 | | Sdowhile : expr → statement → statement (**r [do] loop *) |
---|
194 | | Sfor: statement → expr → statement → statement → statement (**r [for] loop *) |
---|
195 | | Sbreak : statement (**r [break] statement *) |
---|
196 | | Scontinue : statement (**r [continue] statement *) |
---|
197 | | Sreturn : option expr → statement (**r [return] statement *) |
---|
198 | | Sswitch : expr → labeled_statements → statement (**r [switch] statement *) |
---|
199 | | Slabel : label → statement → statement |
---|
200 | | Sgoto : label → statement |
---|
201 | | Scost : costlabel → statement → statement |
---|
202 | |
---|
203 | with labeled_statements : Type[0] ≝ (**r cases of a [switch] *) |
---|
204 | | LSdefault: statement → labeled_statements |
---|
205 | | LScase: ∀sz:intsize. bvint sz → statement → labeled_statements → labeled_statements. |
---|
206 | |
---|
207 | let rec labeled_statements_ind |
---|
208 | (P:labeled_statements → Prop) |
---|
209 | (LSd:∀s. P (LSdefault s)) |
---|
210 | (LSc:∀sz,i,s,tl. P tl → P (LScase sz i s tl)) |
---|
211 | ls on ls : P ls ≝ |
---|
212 | match ls with |
---|
213 | [ LSdefault s ⇒ LSd s |
---|
214 | | LScase sz i s tl ⇒ LSc sz i s tl (labeled_statements_ind P LSd LSc tl) |
---|
215 | ]. |
---|
216 | |
---|
217 | let rec statement_ind2 |
---|
218 | (P:statement → Prop) (Q:labeled_statements → Prop) |
---|
219 | (Ssk:P Sskip) |
---|
220 | (Sas:∀e1,e2. P (Sassign e1 e2)) |
---|
221 | (Sca:∀eo,e,args. P (Scall eo e args)) |
---|
222 | (Ssq:∀s1,s2. P s1 → P s2 → P (Ssequence s1 s2)) |
---|
223 | (Sif:∀e,s1,s2. P s1 → P s2 → P (Sifthenelse e s1 s2)) |
---|
224 | (Swh:∀e,s. P s → P (Swhile e s)) |
---|
225 | (Sdo:∀e,s. P s → P (Sdowhile e s)) |
---|
226 | (Sfo:∀s1,e,s2,s3. P s1 → P s2 → P s3 → P (Sfor s1 e s2 s3)) |
---|
227 | (Sbr:P Sbreak) |
---|
228 | (Sco:P Scontinue) |
---|
229 | (Sre:∀eo. P (Sreturn eo)) |
---|
230 | (Ssw:∀e,ls. Q ls → P (Sswitch e ls)) |
---|
231 | (Sla:∀l,s. P s → P (Slabel l s)) |
---|
232 | (Sgo:∀l. P (Sgoto l)) |
---|
233 | (Scs:∀l,s. P s → P (Scost l s)) |
---|
234 | (LSd:∀s. P s → Q (LSdefault s)) |
---|
235 | (LSc:∀sz,i,s,t. P s → Q t → Q (LScase sz i s t)) |
---|
236 | (s:statement) on s : P s ≝ |
---|
237 | match s with |
---|
238 | [ Sskip ⇒ Ssk |
---|
239 | | Sassign e1 e2 ⇒ Sas e1 e2 |
---|
240 | | Scall eo e args ⇒ Sca eo e args |
---|
241 | | Ssequence s1 s2 ⇒ Ssq s1 s2 |
---|
242 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s1) |
---|
243 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s2) |
---|
244 | | Sifthenelse e s1 s2 ⇒ Sif e s1 s2 |
---|
245 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s1) |
---|
246 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s2) |
---|
247 | | Swhile e s ⇒ Swh e s |
---|
248 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s) |
---|
249 | | Sdowhile e s ⇒ Sdo e s |
---|
250 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s) |
---|
251 | | Sfor s1 e s2 s3 ⇒ Sfo s1 e s2 s3 |
---|
252 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s1) |
---|
253 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s2) |
---|
254 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s3) |
---|
255 | | Sbreak ⇒ Sbr |
---|
256 | | Scontinue ⇒ Sco |
---|
257 | | Sreturn eo ⇒ Sre eo |
---|
258 | | Sswitch e ls ⇒ Ssw e ls |
---|
259 | (labeled_statements_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc ls) |
---|
260 | | Slabel l s ⇒ Sla l s |
---|
261 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s) |
---|
262 | | Sgoto l ⇒ Sgo l |
---|
263 | | Scost l s ⇒ Scs l s |
---|
264 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s) |
---|
265 | ] |
---|
266 | and labeled_statements_ind2 |
---|
267 | (P:statement → Prop) (Q:labeled_statements → Prop) |
---|
268 | (Ssk:P Sskip) |
---|
269 | (Sas:∀e1,e2. P (Sassign e1 e2)) |
---|
270 | (Sca:∀eo,e,args. P (Scall eo e args)) |
---|
271 | (Ssq:∀s1,s2. P s1 → P s2 → P (Ssequence s1 s2)) |
---|
272 | (Sif:∀e,s1,s2. P s1 → P s2 → P (Sifthenelse e s1 s2)) |
---|
273 | (Swh:∀e,s. P s → P (Swhile e s)) |
---|
274 | (Sdo:∀e,s. P s → P (Sdowhile e s)) |
---|
275 | (Sfo:∀s1,e,s2,s3. P s1 → P s2 → P s3 → P (Sfor s1 e s2 s3)) |
---|
276 | (Sbr:P Sbreak) |
---|
277 | (Sco:P Scontinue) |
---|
278 | (Sre:∀eo. P (Sreturn eo)) |
---|
279 | (Ssw:∀e,ls. Q ls → P (Sswitch e ls)) |
---|
280 | (Sla:∀l,s. P s → P (Slabel l s)) |
---|
281 | (Sgo:∀l. P (Sgoto l)) |
---|
282 | (Scs:∀l,s. P s → P (Scost l s)) |
---|
283 | (LSd:∀s. P s → Q (LSdefault s)) |
---|
284 | (LSc:∀sz,i,s,t. P s → Q t → Q (LScase sz i s t)) |
---|
285 | (ls:labeled_statements) on ls : Q ls ≝ |
---|
286 | match ls with |
---|
287 | [ LSdefault s ⇒ LSd s |
---|
288 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s) |
---|
289 | | LScase sz i s t ⇒ LSc sz i s t |
---|
290 | (statement_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc s) |
---|
291 | (labeled_statements_ind2 P Q Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs LSd LSc t) |
---|
292 | ]. |
---|
293 | |
---|
294 | definition statement_ind ≝ λP,Ssk,Sas,Sca,Ssq,Sif,Swh,Sdo,Sfo,Sbr,Sco,Sre,Ssw,Sla,Sgo,Scs. |
---|
295 | statement_ind2 P (λ_.True) Ssk Sas Sca Ssq Sif Swh Sdo Sfo Sbr Sco Sre Ssw Sla Sgo Scs |
---|
296 | (λ_,_. I) (λ_,_,_,_,_,_.I). |
---|
297 | |
---|
298 | (* * ** Functions *) |
---|
299 | |
---|
300 | (* * A function definition is composed of its return type ([fn_return]), |
---|
301 | the names and types of its parameters ([fn_params]), the names |
---|
302 | and types of its local variables ([fn_vars]), and the body of the |
---|
303 | function (a statement, [fn_body]). *) |
---|
304 | |
---|
305 | record function : Type[0] ≝ { |
---|
306 | fn_return: type; |
---|
307 | fn_params: list (ident × type); |
---|
308 | fn_vars: list (ident × type); |
---|
309 | fn_body: statement |
---|
310 | }. |
---|
311 | |
---|
312 | (* * Functions can either be defined ([CL_Internal]) or declared as |
---|
313 | external functions ([CL_External]). Similar to the AST definition, but |
---|
314 | with high level type information for external functions. *) |
---|
315 | |
---|
316 | inductive clight_fundef : Type[0] ≝ |
---|
317 | | CL_Internal: function → clight_fundef |
---|
318 | | CL_External: ident → typelist → type → clight_fundef. |
---|
319 | |
---|
320 | (* * ** Programs *) |
---|
321 | |
---|
322 | (* * A program is a collection of named functions, plus a collection |
---|
323 | of named global variables, carrying their types and optional initialization |
---|
324 | data. See module [AST] for more details. *) |
---|
325 | |
---|
326 | definition clight_program : Type[0] ≝ program (λ_.clight_fundef) (list init_data × type). |
---|
327 | |
---|
328 | (* * * Operations over types *) |
---|
329 | |
---|
330 | (* * The type of a function definition. *) |
---|
331 | |
---|
332 | let rec type_of_params (params: list (ident × type)) : typelist ≝ |
---|
333 | match params with |
---|
334 | [ nil ⇒ Tnil |
---|
335 | | cons h rem ⇒ let 〈id,ty〉 ≝ h in Tcons ty (type_of_params rem) |
---|
336 | ]. |
---|
337 | |
---|
338 | definition type_of_function : function → type ≝ λf. |
---|
339 | Tfunction (type_of_params (fn_params f)) (fn_return f). |
---|
340 | |
---|
341 | definition type_of_fundef : clight_fundef → type ≝ λf. |
---|
342 | match f with |
---|
343 | [ CL_Internal fd ⇒ type_of_function fd |
---|
344 | | CL_External id args res ⇒ Tfunction args res |
---|
345 | ]. |
---|
346 | |
---|
347 | (* * Natural alignment of a type, in bytes. *) |
---|
348 | let rec alignof (t: type) : nat ≝ (*1*) |
---|
349 | (* these are old values for 32 bit machines *) |
---|
350 | match t with |
---|
351 | [ Tvoid ⇒ 1 |
---|
352 | | Tint sz _ ⇒ match sz with [ I8 ⇒ 1 | I16 ⇒ 2 | I32 ⇒ 4 ] |
---|
353 | | Tpointer _ ⇒ 4 |
---|
354 | | Tarray t' n ⇒ alignof t' |
---|
355 | | Tfunction _ _ ⇒ 1 |
---|
356 | | Tstruct _ fld ⇒ alignof_fields fld |
---|
357 | | Tunion _ fld ⇒ alignof_fields fld |
---|
358 | | Tcomp_ptr _ ⇒ 4 |
---|
359 | ] |
---|
360 | |
---|
361 | and alignof_fields (f: fieldlist) : nat ≝ |
---|
362 | match f with |
---|
363 | [ Fnil ⇒ 1 |
---|
364 | | Fcons id t f' ⇒ max (alignof t) (alignof_fields f') |
---|
365 | ]. |
---|
366 | |
---|
367 | (* |
---|
368 | Scheme type_ind2 := Induction for type Sort Prop |
---|
369 | with fieldlist_ind2 := Induction for fieldlist Sort Prop. |
---|
370 | *) |
---|
371 | |
---|
372 | (* XXX: automatic generation? *) |
---|
373 | let rec type_ind2 |
---|
374 | (P:type → Prop) (Q:fieldlist → Prop) |
---|
375 | (vo:P Tvoid) |
---|
376 | (it:∀i,s. P (Tint i s)) |
---|
377 | (pt:∀t. P t → P (Tpointer t)) |
---|
378 | (ar:∀t,n. P t → P (Tarray t n)) |
---|
379 | (fn:∀tl,t. P t → P (Tfunction tl t)) |
---|
380 | (st:∀i,fl. Q fl → P (Tstruct i fl)) |
---|
381 | (un:∀i,fl. Q fl → P (Tunion i fl)) |
---|
382 | (cp:∀i. P (Tcomp_ptr i)) |
---|
383 | (nl:Q Fnil) |
---|
384 | (cs:∀i,t,f'. P t → Q f' → Q (Fcons i t f')) |
---|
385 | (t:type) on t : P t ≝ |
---|
386 | match t return λt'.P t' with |
---|
387 | [ Tvoid ⇒ vo |
---|
388 | | Tint i s ⇒ it i s |
---|
389 | | Tpointer t' ⇒ pt t' (type_ind2 P Q vo it pt ar fn st un cp nl cs t') |
---|
390 | | Tarray t' n ⇒ ar t' n (type_ind2 P Q vo it pt ar fn st un cp nl cs t') |
---|
391 | | Tfunction tl t' ⇒ fn tl t' (type_ind2 P Q vo it pt ar fn st un cp nl cs t') |
---|
392 | | Tstruct i fs ⇒ st i fs (fieldlist_ind2 P Q vo it pt ar fn st un cp nl cs fs) |
---|
393 | | Tunion i fs ⇒ un i fs (fieldlist_ind2 P Q vo it pt ar fn st un cp nl cs fs) |
---|
394 | | Tcomp_ptr i ⇒ cp i |
---|
395 | ] |
---|
396 | and fieldlist_ind2 |
---|
397 | (P:type → Prop) (Q:fieldlist → Prop) |
---|
398 | (vo:P Tvoid) |
---|
399 | (it:∀i,s. P (Tint i s)) |
---|
400 | (pt:∀t. P t → P (Tpointer t)) |
---|
401 | (ar:∀t,n. P t → P (Tarray t n)) |
---|
402 | (fn:∀tl,t. P t → P (Tfunction tl t)) |
---|
403 | (st:∀i,fl. Q fl → P (Tstruct i fl)) |
---|
404 | (un:∀i,fl. Q fl → P (Tunion i fl)) |
---|
405 | (cp:∀i. P (Tcomp_ptr i)) |
---|
406 | (nl:Q Fnil) |
---|
407 | (cs:∀i,t,f'. P t → Q f' → Q (Fcons i t f')) |
---|
408 | (fs:fieldlist) on fs : Q fs ≝ |
---|
409 | match fs return λfs'.Q fs' with |
---|
410 | [ Fnil ⇒ nl |
---|
411 | | Fcons i t f' ⇒ cs i t f' (type_ind2 P Q vo it pt ar fn st un cp nl cs t) |
---|
412 | (fieldlist_ind2 P Q vo it pt ar fn st un cp nl cs f') |
---|
413 | ]. |
---|
414 | |
---|
415 | lemma alignof_fields_pos: |
---|
416 | ∀f. alignof_fields f > 0. |
---|
417 | @fieldlist_ind //; |
---|
418 | #i #t #fs' #IH @max_r @IH qed. |
---|
419 | |
---|
420 | lemma alignof_pos: |
---|
421 | ∀t. alignof t > 0. |
---|
422 | #t elim t; normalize; //; |
---|
423 | [ 1,2: #z cases z; /2/; |
---|
424 | | 3,4: #i @alignof_fields_pos |
---|
425 | ] qed. |
---|
426 | |
---|
427 | (* * Size of a type, in bytes. *) |
---|
428 | |
---|
429 | let rec sizeof (t: type) : nat ≝ |
---|
430 | match t with |
---|
431 | [ Tvoid ⇒ 1 |
---|
432 | | Tint i _ ⇒ match i with [ I8 ⇒ 1 | I16 ⇒ 2 | I32 ⇒ 4 ] |
---|
433 | | Tpointer _ ⇒ size_pointer |
---|
434 | | Tarray t' n ⇒ sizeof t' * max 1 n |
---|
435 | | Tfunction _ _ ⇒ 1 |
---|
436 | | Tstruct _ fld ⇒ align (max 1 (sizeof_struct fld 0)) (alignof t) |
---|
437 | | Tunion _ fld ⇒ align (max 1 (sizeof_union fld)) (alignof t) |
---|
438 | | Tcomp_ptr _ ⇒ size_pointer |
---|
439 | ] |
---|
440 | |
---|
441 | and sizeof_struct (fld: fieldlist) (pos: nat) on fld : nat ≝ |
---|
442 | match fld with |
---|
443 | [ Fnil ⇒ pos |
---|
444 | | Fcons id t fld' ⇒ sizeof_struct fld' (align pos (alignof t) + sizeof t) |
---|
445 | ] |
---|
446 | |
---|
447 | and sizeof_union (fld: fieldlist) : nat ≝ |
---|
448 | match fld with |
---|
449 | [ Fnil ⇒ 0 |
---|
450 | | Fcons id t fld' ⇒ max (sizeof t) (sizeof_union fld') |
---|
451 | ]. |
---|
452 | (* TODO: needs some Z_times results |
---|
453 | lemma sizeof_pos: |
---|
454 | ∀t. sizeof t > 0. |
---|
455 | #t0 |
---|
456 | napply (type_ind2 (λt. sizeof t > 0) |
---|
457 | (λf. sizeof_union f ≥ 0 ∧ ∀pos:Z. pos ≥ 0 → sizeof_struct f pos ≥ 0)); |
---|
458 | [ 1,4,6,9: //; |
---|
459 | | #i cases i;#s //; |
---|
460 | | #f cases f;// |
---|
461 | | #t #n #H whd in ⊢ (?%?); |
---|
462 | Proof. |
---|
463 | intro t0. |
---|
464 | apply (type_ind2 (fun t => sizeof t > 0) |
---|
465 | (fun f => sizeof_union f >= 0 /\ forall pos, pos >= 0 -> sizeof_struct f pos >= 0)); |
---|
466 | intros; simpl; auto; try omega. |
---|
467 | destruct i; omega. |
---|
468 | destruct f; omega. |
---|
469 | apply Zmult_gt_0_compat. auto. generalize (Zmax1 1 z); omega. |
---|
470 | destruct H. |
---|
471 | generalize (align_le (Zmax 1 (sizeof_struct f 0)) (alignof_fields f) (alignof_fields_pos f)). |
---|
472 | generalize (Zmax1 1 (sizeof_struct f 0)). omega. |
---|
473 | generalize (align_le (Zmax 1 (sizeof_union f)) (alignof_fields f) (alignof_fields_pos f)). |
---|
474 | generalize (Zmax1 1 (sizeof_union f)). omega. |
---|
475 | split. omega. auto. |
---|
476 | destruct H0. split; intros. |
---|
477 | generalize (Zmax2 (sizeof t) (sizeof_union f)). omega. |
---|
478 | apply H1. |
---|
479 | generalize (align_le pos (alignof t) (alignof_pos t)). omega. |
---|
480 | Qed. |
---|
481 | |
---|
482 | Lemma sizeof_struct_incr: |
---|
483 | forall fld pos, pos <= sizeof_struct fld pos. |
---|
484 | Proof. |
---|
485 | induction fld; intros; simpl. omega. |
---|
486 | eapply Zle_trans. 2: apply IHfld. |
---|
487 | apply Zle_trans with (align pos (alignof t)). |
---|
488 | apply align_le. apply alignof_pos. |
---|
489 | assert (sizeof t > 0) by apply sizeof_pos. omega. |
---|
490 | Qed. |
---|
491 | |
---|
492 | (** Byte offset for a field in a struct or union. |
---|
493 | Field are laid out consecutively, and padding is inserted |
---|
494 | to align each field to the natural alignment for its type. *) |
---|
495 | |
---|
496 | Open Local Scope string_scope. |
---|
497 | *) |
---|
498 | |
---|
499 | let rec field_offset_rec (id: ident) (fld: fieldlist) (pos: nat) |
---|
500 | on fld : res nat ≝ |
---|
501 | match fld with |
---|
502 | [ Fnil ⇒ Error ? [MSG UnknownField (*"Unknown field "*); CTX ? id] |
---|
503 | | Fcons id' t fld' ⇒ |
---|
504 | match ident_eq id id' with |
---|
505 | [ inl _ ⇒ OK ? (align pos (alignof t)) |
---|
506 | | inr _ ⇒ field_offset_rec id fld' (align pos (alignof t) + sizeof t) |
---|
507 | ] |
---|
508 | ]. |
---|
509 | |
---|
510 | definition field_offset ≝ λid: ident. λfld: fieldlist. |
---|
511 | field_offset_rec id fld 0. |
---|
512 | |
---|
513 | let rec field_type (id: ident) (fld: fieldlist) on fld : res type := |
---|
514 | match fld with |
---|
515 | [ Fnil ⇒ Error ? [MSG UnknownField (*"Unknown field "*); CTX ? id] |
---|
516 | | Fcons id' t fld' ⇒ match ident_eq id id' with [ inl _ ⇒ OK ? t | inr _ ⇒ field_type id fld'] |
---|
517 | ]. |
---|
518 | |
---|
519 | (* * Some sanity checks about field offsets. First, field offsets are |
---|
520 | within the range of acceptable offsets. *) |
---|
521 | (* |
---|
522 | Remark field_offset_rec_in_range: |
---|
523 | forall id ofs ty fld pos, |
---|
524 | field_offset_rec id fld pos = OK ofs → field_type id fld = OK ty → |
---|
525 | pos <= ofs /\ ofs + sizeof ty <= sizeof_struct fld pos. |
---|
526 | Proof. |
---|
527 | intros until ty. induction fld; simpl. |
---|
528 | congruence. |
---|
529 | destruct (ident_eq id i); intros. |
---|
530 | inv H. inv H0. split. apply align_le. apply alignof_pos. apply sizeof_struct_incr. |
---|
531 | exploit IHfld; eauto. intros [A B]. split; auto. |
---|
532 | eapply Zle_trans; eauto. apply Zle_trans with (align pos (alignof t)). |
---|
533 | apply align_le. apply alignof_pos. generalize (sizeof_pos t). omega. |
---|
534 | Qed. |
---|
535 | |
---|
536 | Lemma field_offset_in_range: |
---|
537 | forall id fld ofs ty, |
---|
538 | field_offset id fld = OK ofs → field_type id fld = OK ty → |
---|
539 | 0 <= ofs /\ ofs + sizeof ty <= sizeof_struct fld 0. |
---|
540 | Proof. |
---|
541 | intros. eapply field_offset_rec_in_range. unfold field_offset in H; eauto. eauto. |
---|
542 | Qed. |
---|
543 | |
---|
544 | (** Second, two distinct fields do not overlap *) |
---|
545 | |
---|
546 | Lemma field_offset_no_overlap: |
---|
547 | forall id1 ofs1 ty1 id2 ofs2 ty2 fld, |
---|
548 | field_offset id1 fld = OK ofs1 → field_type id1 fld = OK ty1 → |
---|
549 | field_offset id2 fld = OK ofs2 → field_type id2 fld = OK ty2 → |
---|
550 | id1 <> id2 → |
---|
551 | ofs1 + sizeof ty1 <= ofs2 \/ ofs2 + sizeof ty2 <= ofs1. |
---|
552 | Proof. |
---|
553 | intros until ty2. intros fld0 A B C D NEQ. |
---|
554 | assert (forall fld pos, |
---|
555 | field_offset_rec id1 fld pos = OK ofs1 -> field_type id1 fld = OK ty1 -> |
---|
556 | field_offset_rec id2 fld pos = OK ofs2 -> field_type id2 fld = OK ty2 -> |
---|
557 | ofs1 + sizeof ty1 <= ofs2 \/ ofs2 + sizeof ty2 <= ofs1). |
---|
558 | induction fld; intro pos; simpl. congruence. |
---|
559 | destruct (ident_eq id1 i); destruct (ident_eq id2 i). |
---|
560 | congruence. |
---|
561 | subst i. intros. inv H; inv H0. |
---|
562 | exploit field_offset_rec_in_range. eexact H1. eauto. tauto. |
---|
563 | subst i. intros. inv H1; inv H2. |
---|
564 | exploit field_offset_rec_in_range. eexact H. eauto. tauto. |
---|
565 | intros. eapply IHfld; eauto. |
---|
566 | |
---|
567 | apply H with fld0 0; auto. |
---|
568 | Qed. |
---|
569 | |
---|
570 | (** Third, if a struct is a prefix of another, the offsets of fields |
---|
571 | in common is the same. *) |
---|
572 | |
---|
573 | Fixpoint fieldlist_app (fld1 fld2: fieldlist) {struct fld1} : fieldlist := |
---|
574 | match fld1 with |
---|
575 | | Fnil ⇒ fld2 |
---|
576 | | Fcons id ty fld ⇒ Fcons id ty (fieldlist_app fld fld2) |
---|
577 | end. |
---|
578 | |
---|
579 | Lemma field_offset_prefix: |
---|
580 | forall id ofs fld2 fld1, |
---|
581 | field_offset id fld1 = OK ofs → |
---|
582 | field_offset id (fieldlist_app fld1 fld2) = OK ofs. |
---|
583 | Proof. |
---|
584 | intros until fld2. |
---|
585 | assert (forall fld1 pos, |
---|
586 | field_offset_rec id fld1 pos = OK ofs -> |
---|
587 | field_offset_rec id (fieldlist_app fld1 fld2) pos = OK ofs). |
---|
588 | induction fld1; intros pos; simpl. congruence. |
---|
589 | destruct (ident_eq id i); auto. |
---|
590 | intros. unfold field_offset; auto. |
---|
591 | Qed. |
---|
592 | *) |
---|
593 | |
---|
594 | |
---|
595 | (* * Translating Clight types to Cminor types, function signatures, |
---|
596 | and external functions. *) |
---|
597 | |
---|
598 | definition typ_of_type : type → typ ≝ λt. |
---|
599 | match t with |
---|
600 | [ Tvoid ⇒ ASTint I32 Unsigned |
---|
601 | | Tint sz sg ⇒ ASTint sz sg |
---|
602 | | Tpointer _ ⇒ ASTptr |
---|
603 | | Tarray _ _ ⇒ ASTptr |
---|
604 | | Tfunction _ _ ⇒ ASTptr |
---|
605 | | Tcomp_ptr _ ⇒ ASTptr |
---|
606 | | _ ⇒ ASTint I32 Unsigned (* structs and unions shouldn't be converted? *) |
---|
607 | ]. |
---|
608 | |
---|
609 | definition opttyp_of_type : type → option typ ≝ λt. |
---|
610 | match t with |
---|
611 | [ Tvoid ⇒ None ? |
---|
612 | | Tint sz sg ⇒ Some ? (ASTint sz sg) |
---|
613 | | Tpointer _ ⇒ Some ? ASTptr |
---|
614 | | Tarray _ _ ⇒ Some ? ASTptr |
---|
615 | | Tfunction _ _ ⇒ Some ? ASTptr |
---|
616 | | Tcomp_ptr _ ⇒ Some ? ASTptr |
---|
617 | | _ ⇒ None ? (* structs and unions shouldn't be converted? *) |
---|
618 | ]. |
---|
619 | |
---|
620 | let rec typlist_of_typelist (tl: typelist) : list typ ≝ |
---|
621 | match tl with |
---|
622 | [ Tnil ⇒ nil ? |
---|
623 | | Tcons hd tl ⇒ typ_of_type hd :: typlist_of_typelist tl |
---|
624 | ]. |
---|
625 | |
---|
626 | |
---|
627 | (* * The [access_mode] function describes how a variable of the given |
---|
628 | type must be accessed: |
---|
629 | - [By_value ch]: access by value, i.e. by loading from the address |
---|
630 | of the variable using the memory chunk [ch]; |
---|
631 | - [By_reference]: access by reference, i.e. by just returning |
---|
632 | the address of the variable; |
---|
633 | - [By_nothing]: no access is possible, e.g. for the [void] type. |
---|
634 | |
---|
635 | We currently do not support 64-bit integers and 128-bit floats, so these |
---|
636 | have an access mode of [By_nothing]. |
---|
637 | *) |
---|
638 | |
---|
639 | inductive mode: typ → Type[0] ≝ |
---|
640 | | By_value: ∀t:typ. mode t |
---|
641 | | By_reference: (*∀r:region.*) mode ASTptr |
---|
642 | | By_nothing: ∀t. mode t. |
---|
643 | |
---|
644 | definition access_mode : ∀ty. mode (typ_of_type ty) ≝ λty. |
---|
645 | match ty return λty. mode (typ_of_type ty) with |
---|
646 | [ Tint i s ⇒ By_value (ASTint i s) |
---|
647 | | Tvoid ⇒ By_nothing … |
---|
648 | | Tpointer _ ⇒ By_value ASTptr |
---|
649 | | Tarray _ _ ⇒ By_reference |
---|
650 | | Tfunction _ _ ⇒ By_reference |
---|
651 | | Tstruct _ fList ⇒ By_nothing … |
---|
652 | | Tunion _ fList ⇒ By_nothing … |
---|
653 | | Tcomp_ptr _ ⇒ By_value ASTptr |
---|
654 | ]. |
---|
655 | |
---|
656 | definition signature_of_type : typelist → type → signature ≝ λargs. λres. |
---|
657 | mk_signature (typlist_of_typelist args) (opttyp_of_type res). |
---|
658 | |
---|
659 | definition external_function |
---|
660 | : ident → typelist → type → external_function ≝ λid. λtargs. λtres. |
---|
661 | mk_external_function id (signature_of_type targs tres). |
---|