source: Deliverables/D4.1/Matita/ @ 234

Last change on this file since 234 was 234, checked in by mulligan, 9 years ago

Division and modulus implemented. All necessary orders on naturals
completed. More operations on bitvectors (and general operations that
apply to all vectors) implemented.

File size: 1.3 KB
1include "".
2include "".
3include "".
4include "".
6ndefinition BitVector ≝ λn: Nat. Vector Bool n.
7ndefinition Bit ≝ BitVector (S Z).
8ndefinition Nibble ≝ BitVector (S (S (S (S Z)))).
9ndefinition Byte7 ≝ BitVector (S (S (S (S (S (S (S Z))))))).
10ndefinition Byte ≝ BitVector (S (S (S (S (S (S (S (S Z)))))))).
11ndefinition Word ≝ BitVector (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S (S Z)))))))))))))))).
13ndefinition zero ≝
14  λn: Nat.
15    replicate Bool n False.
17ndefinition conjunction ≝
18  λn: Nat.
19  λb: BitVector n.
20  λc: BitVector n.
21    zip Bool Bool Bool n conjunction b c.
23ndefinition inclusive_disjunction ≝
24  λn: Nat.
25  λb: BitVector n.
26  λc: BitVector n.
27    zip Bool Bool Bool n inclusive_disjunction b c.
29ndefinition exclusive_disjunction ≝
30  λn: Nat.
31  λb: BitVector n.
32  λc: BitVector n.
33    zip Bool Bool Bool n exclusive_disjunction b c.
35ndefinition complement ≝
36  λn: Nat.
37  λb: BitVector n.
38    map Bool Bool n (negation) b.
40ndefinition divide_with_remainder ≝
41  λm, n: Nat.
42    mk_Cartesian Nat Nat (m ÷ n) (modulus m n).
44nlet rec bitvector_of_nat_aux (n: Nat): List Nat ≝
45  let div_rem ≝ divide_with_remainder n (S (S Z)) in
46  let div ≝ first Nat Nat div_rem in
47  let rem ≝ second Nat Nat div_rem in
48    Empty Nat.
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