Misusing the Type System for & Ian Dees @undees PNSQC 2015 - PowerPoint PPT Presentation

> rewrite (plusSuccRightSucc y x) ---------- Other goals: ---------- { hole 3 } { hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- x : Nat y : Nat hypothesis : plus x y = plus y x ---------- Goal: ---------- { hole 4 }: S (plus x y) = S (plus y x)

> rewrite hypothesis ---------- Other goals: ---------- { hole 4 } { hole 3 } { hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- x : Nat y : Nat hypothesis : plus x y = plus y x ---------- Goal: ---------- { hole 5 }: S (plus x y) = S (plus x y)

> rewrite hypothesis ---------- Other goals: ---------- { hole 4 } { hole 3 } { hole 2 } { hole 1 } { hole 0 } ---------- Assumptions: ---------- x : Nat y : Nat hypothesis : plus x y = plus y x ---------- Goal: ---------- { hole 5 }: S (plus x y) = S (plus x y)

> trivial inductive: No more goals. > qed Proof completed! Math.inductive = proof intros rewrite (plusSuccRightSucc y x) rewrite hypothesis trivial

3. Applying the ideas 
 in the real world

Mission: 
 Edit audio clips

class Audio { public: };

class Audio { public: size_t count() const; };

class Audio { public: size_t count() const; int16_t operator[](size_t i) const; int16_t& operator[](size_t i); };

class Audio { public: size_t count() const; int16_t operator[](size_t i) const; int16_t& operator[](size_t i); double timeAtZero() const; double sampleRate() const; };

class Audio { public: size_t count() const; int16_t operator[](size_t i) const; int16_t& operator[](size_t i); double timeAtZero() const; double sampleRate() const; double verticalScale() const; };

Audio audio; double time = 0.5; size_t index = (time - audio.timeAtZero()) / audio.sampleRate();

Audio audio; double time = 0.5; size_t index = (time - audio.timeAtZero()) / audio.sampleRate(); int16_t value = audio[index]; double level = static_cast<double>(value) * audio.verticalScale();

class Audio { public: size_t count() const; int16_t operator[](size_t i) const; int16_t& operator[](size_t i); double timeAtZero() const; double sampleRate() const; double verticalScale() const; };

class Audio { public: size_t count() const; int16_t operator[](size_t i) const; int16_t& operator[](size_t i); double timeAtZero() const; double sampleRate() const; double verticalScale() const; std::string fileName() const; std::string comments() const; bool isStereo() const; void loadFromFile(const std::string& filename); void saveToFile(const std::string& filename); };

What is an audio clip?