The document discusses using the Coq proof assistant to implement and verify algorithms in Ruby. It mentions encoding a Base64 algorithm in Coq and extracting it to OCaml, Haskell, Scheme and potentially Ruby. It provides examples of defining and proving properties of a factorial function in Coq and extracting implementations to other languages. It also discusses using Coq to model and verify other algorithms like sorting before generating Ruby implementations.

1. Coq to Ruby
@mzp - CSNagoya
2011/2/26 Ruby 02
1

2. • @mzp /
• SE
•
2

3. Ruby
• Ruby = ruby-lang.org
(2004/5)
3

4. • HTML5 + Rails3.0 ” ”
• #101 Redmine
4

5. Reject
14:50-15:10 A realtime chat application for
Developers : AsakusaSattelite
5

6. D
Reject
TE
C
JE
14:50-15:10 A realtime chat application for
RE
Developers : AsakusaSattelite
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7. 6

8. 7

9. ?
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10. 9

11. ?
10

12. :)
11

13. ‘‘
Coq Merge Sort -
http://d.hatena.ne.jp/yoshihiro503/20090923/p1
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14. 13

15. Base64
• encode() decode() OK
•
#
encode "abc" # => “YWJj”
decode "YWJj" # => “abc
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16. TDD
• encode decode
•
: Test::Unit
assert_equal "", decode(encode(""))
assert_equal "foo", decode(encode("foo"))
assert_equal "bar", decode(encode("bar"))
assert_equal "baz", decode(encode("baz"))
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17. NG
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18. •
: RushCheck
http://rushcheck.rubyforge.org/index.html
$ cat test.rb
Assertion.new(String) do |s|
s == decode(encode(s))
end.check
(* 100 *)
$ ruby test.rb
OK, passed 100 tests.
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19. 18

20. •
Goal forall ( s : string),
decode (encode s) = s.
•
•
19

21. •=
•6 => => 8
•
• “OCamltter”
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22. 21

23. ×
TDD
✓
✓
PDD ×
✓
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24. Unison
OCamltter Twitter Base64
MessagePack for
Ocaml
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25. 24

26. Coq
•
• OCaml / F#
•
•
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27. Coq
• Haskell/OCaml/F#
Fixpoint fact (n : nat) :=
match n with
| O => 1
| S m => n * fact m
end.
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28. Coq
• Base64
Theorem soundness : forall s,
decode (encode s) = s.
Proof.
intro s; unfold encode; unfold
decode.
....
Qed.
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29. (* OCaml *)
Extraction "file.ml" fact.
(* Haskell *)
Extraction Language Haskell.
Extraction "file.hs" fact.
(* Scheme *)
• ? Ruby ?
Extraction Language Scheme.
Extraction "file.scm" fact.
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30. (* OCaml *)
Extraction "file.ml" fact.
(* Haskell *)
Extraction Language Haskell.
Extraction "file.hs" fact.
(* Scheme
•
*)
? Ruby ?
? Ruby ?
Extraction Language Scheme.
Extraction "file.scm" fact.
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31. 29

32. Coq
29

33. @
Coq 5
Scala 5
Python 4
C# 3
Agda 1
Android 1
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34. &
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35. :)
def mult
lambda{|n|lambda{|m|match(n,[:O,
lambda{[:O,[]]}],
Text [:S, lambda{|p|
plus[m][mult[p][m]]}])}}
end
def fact
lambda{|n|match(n,[:O, lambda{[:S,[[:O,
[]]]]}],
[:S, lambda{|m|mult[n]
[fact[m]]}])} 32

36. •
• Coq
• Coq Ruby
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37. •
(15:30 15:50)
•
34

38. D
•
TE
(15:30 15:50)
• C
JE
RE
34

39. $ git clone git://github.com/mzp/coq-ruby.git
$ cd coq-ruby
#
$ git diff dbc4ad4
#
$ make bin/coqc states/initial.coq
#
$ ./bin/coqc -coqlib . fact.v
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