Agda 入門@ProofSummit 2011
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Agda 入門@ProofSummit 2011

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対話的定理証明支援系 Agda の紹介です

対話的定理証明支援系 Agda の紹介です

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    Agda 入門@ProofSummit 2011 Agda 入門@ProofSummit 2011 Presentation Transcript

    • Agda @ikegami _ _Proof Summit 2011 2011-09-25
    • Agda• • = • =• • tactic
    • Agda• tactic • = • = • = • Agda • Agda
    • UniverseUnicode subscriptSet1 Set1
    • TAB
    • TAB
    • TAB
    • TAB
    • TAB
    • TAB
    • TAB
    • ℕ ℕ ℕ ℕ
    • ℕ ℕtotal
    • Hidden arguments
    • lambda
    • Unicode / ASCII UTF8
    • mixfix ℕ ℕ ℕ
    • mixfix
    • ℕ∷ ℕ
    • ℕ∷ ℕ
    • ℕ∷ ℕ
    • Agda AgdaA BAA BA B
    • Proposition as Set• • proof object •
    • A B• • •
    • :A A
    • Agda AgdaA BAA BA B
    • A• • •
    • Agda AgdaA BAA BA B
    • disjoint union ⊎ ⊎ ⊎
    • Agda AgdaA BAA B ⊎A B
    • sigma
    • times
    • Agda AgdaA BAA B ⊎A B
    • • double negation elimination •• Law of the excluded middle • ⊎•• etc.
    • ℕ ℕ
    • Agda
    • forall ℕ ℕ ℕ
    • forall ℕ ℕ ℕ
    • Hidden argument ℕ m
    • Hidden argument ℕ m
    • let where
    • ()
    • wildcard
    • with
    • dot ℕ ℕ
    • dot ℕ ℕ ℕ
    • dot ℕ ℕ ℕm
    • dot ℕ ℕ ℕ
    • dot ℕ ℕ ℕ
    • dot ℕ ℕ ℕ
    • dot ℕ ℕ ℕ
    • mutual Agda 2.2.12
    • mutual Agda 2.2.12
    • mutual Agda 2.2.12
    • postulateAgda
    • postulateAgda
    • postulateAgda
    • parametrized module
    • Agda moduleUlf (2006) 30 …
    • module lib/src/Data/Nat.agda (add-to-list ʻagda2-include-dirs “.../lib/src”)Agda .../lib/src
    • module MyProject/Foo.agda(add-to-list ʻagda2-include-dirs “.../MyProject”)
    • open import• import • Nat.zero• open import • zero
    • module using
    • module renaming
    • module hiding ℕ
    • module as
    • Agda
    • agda2-goal-and-context Ctrl-c Ctrl-,
    • agda2-goal-and-context- and-inferred Ctrl-c Ctrl-.
    • agda2-refine Ctrl-c Ctrl-r
    • agda2-refine Ctrl-c Ctrl-r
    • /• Ctrl-C Ctrl-l (agda2-load)• Ctrl-C Ctrl-x Ctrl-r (agda2-restart)
    • compile ⊤C-c C-x C-c (agda2-compile) MAlonzo
    • automation proving Ctrl-c Ctrl-a Agsy
    • automation proving Ctrl-c Ctrl-a Agsy
    • automation proving Ctrl-c Ctrl-a Agsy
    • advanced topic
    • equalityLeibnitz equality
    • rewrite ℕ
    • rewrite ℕ
    • rewrite ℕ
    • rewriteℕ
    • rewriteℕ
    • rewriteℕ
    • rewrite
    • equality reasoning ⟨ ⟩∎
    • equality reasoning ⟨ ⟩∎
    • equality reasoning ⟨ ⟩∎
    • tactic
    • emptiness check ℕ ℕ Agda 2.2.12 Feature
    • --universe-polymorphism Universe AgdaAgda 2.2.12
    • agda• --compile • MAlonzo• --html • HTML• •• etc.
    • Agda release notes• Agda 2-2-0 (2009-03-18) • Sized type
    • sized typesℕ ℕ ℕℕ ℕ ℕ
    • sized typesℕ ℕ ℕℕ ℕ ℕ
    • Sized Type
    • Agda release notes• Agda 2.2.10 (2011-02-21) • --without-K flag • irrelevant declarations • termination checker with projections • compiler backend • Epic • MAlonzo
    • Epic• Epic • http://www.cs.st-andrews.ac.uk/~eb/ epic.php• Agda Epic• Epic C
    • MAlonzo • Agda • Haskell (!?)Agda Haskell
    • (experimental)• JavaScript Compiler Backend• Ruby Compiler Backend • https://github.com/larrytheliquid/agda-rb
    • Agda release notes• Agda 2.2.12 (current development) • coming soon (maybe within this week?) • instance arguments {{ }} • pattern matching lambda
    • Agda in browser• Agda + JavaScript Compiler• Functional Reactive Programming• Example : Clock
    • DemoKeyCastr.appEmacs.app (Command + T )[1B_Maze-Black 25pt font]
    • • Agda standard library • irrelevant declaration • projection and termination • well-founded induction • instance arguments • coinduction • pattern matching lambda• --without-K • reflection • etc. (too much)