1 | include "cerco/Util.ma". |
---|
2 | include "cerco-intermediate-languages/utilities/BitVectorTrieSet.ma". |
---|
3 | include "cerco-intermediate-languages/LIN/LIN.ma". |
---|
4 | |
---|
5 | let rec association (i: Identifier) (l: list (Identifier × nat)) |
---|
6 | on l: member i (eq_bv ?) l → nat ≝ |
---|
7 | match l return λl. member i (eq_bv ?) l → nat with |
---|
8 | [ nil ⇒ λabsd. ? |
---|
9 | | cons hd tl ⇒ |
---|
10 | λprf: member i (eq_bv ?) (cons ? hd tl). |
---|
11 | (match eq_bv ? (\fst hd) i return λb. eq_bv ? (\fst hd) i = b → nat with |
---|
12 | [ true ⇒ λeq_prf. \snd hd |
---|
13 | | false ⇒ λeq_prf. association i tl ? |
---|
14 | ]) (refl ? (eq_bv ? (\fst hd) i)) |
---|
15 | ]. |
---|
16 | [ cases absd |
---|
17 | | cases prf |
---|
18 | [ > eq_prf |
---|
19 | # H |
---|
20 | cases H |
---|
21 | | # H |
---|
22 | assumption |
---|
23 | ] |
---|
24 | ] |
---|
25 | qed. |
---|
26 | |
---|
27 | definition statement_labels ≝ |
---|
28 | λg: list (Identifier × nat). |
---|
29 | λs: LINStatement g. |
---|
30 | match s with |
---|
31 | [ LIN_St_Goto lbl ⇒ set_insert ? lbl (set_empty ?) |
---|
32 | | LIN_St_Label lbl ⇒ set_insert ? lbl (set_empty ?) |
---|
33 | | LIN_St_CostLabel lbl ⇒ set_insert ? lbl (set_empty ?) |
---|
34 | | LIN_St_CondAcc lbl ⇒ set_insert ? lbl (set_empty ?) |
---|
35 | | _ ⇒ set_empty ? |
---|
36 | ]. |
---|
37 | |
---|
38 | definition function_labels_internal ≝ |
---|
39 | λglobals: list (Identifier × nat). |
---|
40 | λlabels: BitVectorTrieSet 8. |
---|
41 | λstatement: LINStatement globals. |
---|
42 | set_union ? labels (statement_labels globals statement). |
---|
43 | |
---|
44 | (* dpm: A = Identifier *) |
---|
45 | definition function_labels: ∀A. ∀globals. ∀f. BitVectorTrieSet 8 ≝ |
---|
46 | λA: Type[0]. |
---|
47 | λglobals: list (Identifier × nat). |
---|
48 | λf: A × (LINFunctionDefinition globals). |
---|
49 | let 〈ignore, fun_def〉 ≝ f in |
---|
50 | match fun_def return λ_. BitVectorTrieSet 8 with |
---|
51 | [ LIN_Fu_Internal stmts ⇒ |
---|
52 | foldl ? ? (function_labels_internal globals) (set_empty 8) stmts |
---|
53 | | LIN_Fu_External _ ⇒ set_empty ? |
---|
54 | ]. |
---|
55 | |
---|
56 | definition program_labels_internal: ∀A. ∀globals. ∀labels. ∀funct. BitVectorTrieSet 8 ≝ |
---|
57 | λA: Type[0]. |
---|
58 | λglobals: list (Identifier × nat). |
---|
59 | λlabels: BitVectorTrieSet 8. |
---|
60 | λfunct: A × (LINFunctionDefinition globals). |
---|
61 | set_union ? labels (function_labels ? globals funct). |
---|
62 | |
---|
63 | definition program_labels ≝ |
---|
64 | λglobals: list (Identifier × nat). |
---|
65 | λprogram. |
---|
66 | foldl ? ? (program_labels_internal ? globals) |
---|
67 | (set_empty 8) (LIN_Pr_funs globals program). |
---|
68 | |
---|
69 | definition data_of_int ≝ λbv. DATA bv. |
---|
70 | definition data16_of_int ≝ λbv. DATA16 (bitvector_of_nat 16 bv). |
---|
71 | definition accumulator_address ≝ DIRECT (bitvector_of_nat 8 224). |
---|
72 | |
---|
73 | axiom ImplementedInRuntime: False. |
---|
74 | |
---|
75 | definition translate_statements ≝ |
---|
76 | λglobals: list (Identifier × nat). |
---|
77 | λlin_statement: LINStatement globals. |
---|
78 | match lin_statement with |
---|
79 | [ LIN_St_Goto lbl ⇒ [ Jmp lbl ] |
---|
80 | | LIN_St_Label lbl ⇒ [ Label lbl ] |
---|
81 | | LIN_St_Comment _ ⇒ [ ] |
---|
82 | | LIN_St_CostLabel lbl ⇒ [ Cost lbl ] |
---|
83 | | LIN_St_Pop ⇒ [ Instruction (POP ? accumulator_address) ] |
---|
84 | | LIN_St_Push ⇒ [ Instruction (PUSH ? accumulator_address) ] |
---|
85 | | LIN_St_ClearCarry ⇒ [ Instruction (CLR ? CARRY) ] |
---|
86 | | LIN_St_Return ⇒ [ Instruction (RET ?) ] |
---|
87 | | LIN_St_CallId f ⇒ [ Call f ] |
---|
88 | | LIN_St_OpAccs accs ⇒ |
---|
89 | match accs with |
---|
90 | [ Mul ⇒ [ Instruction (MUL ? ACC_A ACC_B) ] |
---|
91 | | Divu ⇒ [ Instruction (DIV ? ACC_A ACC_B) ] |
---|
92 | | Modu ⇒ ? |
---|
93 | ] |
---|
94 | | LIN_St_Op1 op1 ⇒ |
---|
95 | match op1 with |
---|
96 | [ Cmpl ⇒ [ Instruction (CPL ? ACC_A) ] |
---|
97 | | Inc ⇒ [ Instruction (INC ? ACC_A) ] |
---|
98 | ] |
---|
99 | | LIN_St_Op2 op2 reg ⇒ |
---|
100 | match op2 with |
---|
101 | [ Add ⇒ |
---|
102 | let reg' ≝ register_address reg in |
---|
103 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
104 | direct; |
---|
105 | register ]] x) → ? with |
---|
106 | [ ACC_A ⇒ λacc_a: True. |
---|
107 | [ Instruction (ADD ? ACC_A accumulator_address) ] |
---|
108 | | DIRECT d ⇒ λdirect1: True. |
---|
109 | [ Instruction (ADD ? ACC_A (DIRECT d)) ] |
---|
110 | | REGISTER r ⇒ λregister1: True. |
---|
111 | [ Instruction (ADD ? ACC_A (REGISTER r)) ] |
---|
112 | | _ ⇒ λother: False. ⊥ |
---|
113 | ] (subaddressing_modein … reg') |
---|
114 | | Addc ⇒ |
---|
115 | let reg' ≝ register_address reg in |
---|
116 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
117 | direct; |
---|
118 | register ]] x) → ? with |
---|
119 | [ ACC_A ⇒ λacc_a: True. |
---|
120 | [ Instruction (ADDC ? ACC_A accumulator_address) ] |
---|
121 | | DIRECT d ⇒ λdirect2: True. |
---|
122 | [ Instruction (ADDC ? ACC_A (DIRECT d)) ] |
---|
123 | | REGISTER r ⇒ λregister2: True. |
---|
124 | [ Instruction (ADDC ? ACC_A (REGISTER r)) ] |
---|
125 | | _ ⇒ λother: False. ⊥ |
---|
126 | ] (subaddressing_modein … reg') |
---|
127 | | Sub ⇒ |
---|
128 | let reg' ≝ register_address reg in |
---|
129 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
130 | direct; |
---|
131 | register ]] x) → ? with |
---|
132 | [ ACC_A ⇒ λacc_a: True. |
---|
133 | [ Instruction (SUBB ? ACC_A accumulator_address) ] |
---|
134 | | DIRECT d ⇒ λdirect3: True. |
---|
135 | [ Instruction (SUBB ? ACC_A (DIRECT d)) ] |
---|
136 | | REGISTER r ⇒ λregister3: True. |
---|
137 | [ Instruction (SUBB ? ACC_A (REGISTER r)) ] |
---|
138 | | _ ⇒ λother: False. ⊥ |
---|
139 | ] (subaddressing_modein … reg') |
---|
140 | | And ⇒ |
---|
141 | let reg' ≝ register_address reg in |
---|
142 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
143 | direct; |
---|
144 | register ]] x) → ? with |
---|
145 | [ ACC_A ⇒ λacc_a: True. |
---|
146 | [ Instruction (NOP ?) ] |
---|
147 | | DIRECT d ⇒ λdirect4: True. |
---|
148 | [ Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))) ] |
---|
149 | | REGISTER r ⇒ λregister4: True. |
---|
150 | [ Instruction (ANL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))) ] |
---|
151 | | _ ⇒ λother: False. ⊥ |
---|
152 | ] (subaddressing_modein … reg') |
---|
153 | | Or ⇒ |
---|
154 | let reg' ≝ register_address reg in |
---|
155 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
156 | direct; |
---|
157 | register ]] x) → ? with |
---|
158 | [ ACC_A ⇒ λacc_a: True. |
---|
159 | [ Instruction (NOP ?) ] |
---|
160 | | DIRECT d ⇒ λdirect5: True. |
---|
161 | [ Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉))) ] |
---|
162 | | REGISTER r ⇒ λregister5: True. |
---|
163 | [ Instruction (ORL ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉))) ] |
---|
164 | | _ ⇒ λother: False. ⊥ |
---|
165 | ] (subaddressing_modein … reg') |
---|
166 | | Xor ⇒ |
---|
167 | let reg' ≝ register_address reg in |
---|
168 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
169 | direct; |
---|
170 | register ]] x) → ? with |
---|
171 | [ ACC_A ⇒ λacc_a: True. |
---|
172 | [ Instruction (XRL ? (inr ? ? 〈accumulator_address, ACC_A〉)) ] |
---|
173 | | DIRECT d ⇒ λdirect6: True. |
---|
174 | [ Instruction (XRL ? (inl ? ? 〈ACC_A, DIRECT d〉)) ] |
---|
175 | | REGISTER r ⇒ λregister6: True. |
---|
176 | [ Instruction (XRL ? (inl ? ? 〈ACC_A, REGISTER r〉)) ] |
---|
177 | | _ ⇒ λother: False. ⊥ |
---|
178 | ] (subaddressing_modein … reg') |
---|
179 | ] |
---|
180 | | LIN_St_Int reg byte ⇒ |
---|
181 | let reg' ≝ register_address reg in |
---|
182 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
183 | direct; |
---|
184 | register ]] x) → ? with |
---|
185 | [ REGISTER r ⇒ λregister7: True. |
---|
186 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, (data_of_int byte)〉)))))) ] |
---|
187 | | ACC_A ⇒ λacc: True. |
---|
188 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, (data_of_int byte)〉)))))) ] |
---|
189 | | DIRECT d ⇒ λdirect7: True. |
---|
190 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, (data_of_int byte)〉))))) ] |
---|
191 | | _ ⇒ λother: False. ⊥ |
---|
192 | ] (subaddressing_modein … reg') |
---|
193 | | LIN_St_FromAcc reg ⇒ |
---|
194 | let reg' ≝ register_address reg in |
---|
195 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
196 | direct; |
---|
197 | register ]] x) → ? with |
---|
198 | [ REGISTER r ⇒ λregister8: True. |
---|
199 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈REGISTER r, ACC_A〉)))))) ] |
---|
200 | | ACC_A ⇒ λacc: True. |
---|
201 | [ Instruction (NOP ?) ] |
---|
202 | | DIRECT d ⇒ λdirect8: True. |
---|
203 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inr ? ? 〈DIRECT d, ACC_A〉))))) ] |
---|
204 | | _ ⇒ λother: False. ⊥ |
---|
205 | ] (subaddressing_modein … reg') |
---|
206 | | LIN_St_ToAcc reg ⇒ |
---|
207 | let reg' ≝ register_address reg in |
---|
208 | match reg' return λx. bool_to_Prop (is_in … [[ acc_a; |
---|
209 | direct; |
---|
210 | register ]] x) → ? with |
---|
211 | [ REGISTER r ⇒ λregister9: True. |
---|
212 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, REGISTER r〉)))))) ] |
---|
213 | | DIRECT d ⇒ λdirect9: True. |
---|
214 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? (inl ? ? 〈ACC_A, DIRECT d〉)))))) ] |
---|
215 | | ACC_A ⇒ λacc_a: True. |
---|
216 | [ Instruction (NOP ?) ] |
---|
217 | | _ ⇒ λother: False. ⊥ |
---|
218 | ] (subaddressing_modein … reg') |
---|
219 | | LIN_St_Load ⇒ [ Instruction (MOVX ? (inl ? ? 〈ACC_A, EXT_INDIRECT_DPTR〉)) ] |
---|
220 | | LIN_St_Store ⇒ [ Instruction (MOVX ? (inr ? ? 〈EXT_INDIRECT_DPTR, ACC_A〉)) ] |
---|
221 | | LIN_St_Address addr proof ⇒ |
---|
222 | let look ≝ association addr globals proof in |
---|
223 | [ Instruction (MOV ? (inl ? ? (inl ? ? (inr ? ? (〈DPTR, (data16_of_int look)〉))))) ] |
---|
224 | | LIN_St_CondAcc lbl ⇒ |
---|
225 | (* dpm: this should be handled in translate_code! *) |
---|
226 | [ WithLabel (JNZ ? lbl) ] |
---|
227 | ]. |
---|
228 | try assumption |
---|
229 | try @ I |
---|
230 | cases ImplementedInRuntime |
---|
231 | qed. |
---|
232 | |
---|
233 | definition translate_code ≝ |
---|
234 | λglobals: list (Identifier × nat). |
---|
235 | λcode: list (LINStatement globals). |
---|
236 | flatten ? (map ? ? (translate_statements globals) code). |
---|