1 | include "ASM/I8051.ma". |
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2 | include "common/Registers.ma". |
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3 | |
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4 | record register_set: Type[1] ≝ |
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5 | { |
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6 | rs_set: Type[0]; |
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7 | rs_empty: rs_set; |
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8 | rs_singleton: Register → rs_set; |
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9 | rs_fold: ∀A: Type[0]. (Register → A → A) → rs_set → A → A; |
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10 | rs_insert: Register → rs_set → rs_set; |
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11 | rs_exists: Register → rs_set → bool; |
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12 | rs_union: rs_set → rs_set → rs_set; |
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13 | rs_subset: rs_set → rs_set → bool; |
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14 | rs_to_list: rs_set → list Register; |
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15 | rs_from_list: list Register → rs_set |
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16 | }. |
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17 | |
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18 | (* dpm: horrendously inefficient, but will do for now *) |
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19 | |
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20 | definition rs_list_set_empty: list Register ≝ [ ]. |
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21 | |
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22 | definition rs_list_set_singleton: Register → list Register ≝ λr. [ r ]. |
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23 | |
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24 | definition rs_list_set_fold ≝ |
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25 | λA: Type[0]. |
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26 | λf: Register → A → A. |
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27 | λl: list Register. |
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28 | λa: A. |
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29 | foldr ? ? f a l. |
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30 | |
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31 | definition rs_list_set_insert ≝ |
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32 | λr: Register. |
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33 | λs: list Register. |
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34 | match member ? eq_Register r s with |
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35 | [ true ⇒ r :: s |
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36 | | false ⇒ s |
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37 | ]. |
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38 | |
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39 | definition rs_list_set_exists ≝ |
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40 | λr: Register. |
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41 | λs: list Register. |
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42 | member ? eq_Register r s. |
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43 | |
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44 | definition rs_list_set_union ≝ |
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45 | λr: list Register. |
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46 | λs: list Register. |
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47 | nub_by ? eq_Register (r @ s). |
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48 | |
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49 | definition rs_list_set_subset ≝ |
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50 | λr: list Register. |
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51 | λs: list Register. |
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52 | forall … (λx. member … eq_Register x s) r. |
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53 | |
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54 | definition rs_list_set_from_list ≝ |
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55 | λr: list Register. |
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56 | nub_by ? eq_Register r. |
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57 | |
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58 | definition register_list_set: register_set ≝ |
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59 | mk_register_set (list Register) rs_list_set_empty |
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60 | rs_list_set_singleton rs_list_set_fold |
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61 | rs_list_set_insert rs_list_set_exists |
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62 | rs_list_set_union |
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63 | rs_list_set_subset |
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64 | (λx. x) rs_list_set_from_list. |
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