The document discusses Coq and Gallina, the language used for formal proofs in Coq. It provides examples of proof goals, such as proving that reversing a list twice returns the original list, and that decoding and encoding with base64 returns the original string. It also lists several Coq-based projects, including CompCert for formally verified C code generation, and links to learning resources for Coq.

1. 2011/11/05 LL.
Coq/Gallina
mzp /
1

2. 2011/11/05 LL.
Coq/Gallina
mzp /
2

3. @mzp /
LL
‣
→
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4. Coq
INRIA
OCaml
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5. LL ?
Gallina : Coq
5

6. (2011/09/17)
Coq by
‣ http://www.slideshare.net/ltf14/
coq-9306231
Q
...
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7. ( )

8. (1)
Goal forall (A B C: Prop),
(A -> B) -> (B -> C) -> A -> C.
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9. SNS
9

10. (2)
Goal forall A (xs : list A),
reverse (reverse xs) = xs.
1
?
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11. ( )

12. ‣ ↑
‣ ↑↑
12

13. (1)
Goal forall A (xs : list A),
reverse xs = reverse_iter [] xs.
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14. (2)
JSON Base64
Goal forall (s : string),
decode (encode s) = s.
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15. ‣ ?
‣ ?
15

16. “ ”
Coq
‣ OK
Goal forall A (xs : list A),
reverse xs = reverse_iter [] xs.
16

17. CompCert
‣ C
iZE Smart Desktop
‣ D-Bus JSON
Msgpack for OCaml
‣
OCamltter
‣ Twitter
‣ Base64
17

18. Coq
‣ http://www.iij-ii.co.jp/lab/techdoc/
coqt/
Software Foundation
‣ http://proofcafe.org/sf/
Proof Cafe
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19. Coq
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