SLIDE 1
q r t q - - PowerPoint PPT Presentation
q r t q - - PowerPoint PPT Presentation
q r t q s r ssstt t s rr t rrt
SLIDE 2
SLIDE 3
❈♦q ✐s ♥♦t✿
◮ ❛ ❢❛st✴❞✐str✐❜✉t❡❞✴❜✐t❝♦✐♥✲♦r✐❡♥t❡❞ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ ◮ ❛ ❚✉r✐♥❣✲❝♦♠♣❧❡t❡ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ ◮ ❛ ♠♦❞❡❧✲❝❤❡❝❦❡r ◮ ❛♥ ❛✉t♦♠❛t✐❝ ♣r♦✈❡r ◮ ❛♥ ♦r❛❝❧❡ ◮ s♦♠❡t❤✐♥❣ ❡❛s② t♦ ✇♦r❦ ✇✐t❤
SLIDE 4
Pr✐♥❝✐♣❧❡s✿ P♦✐♥❝❛ré
◮ ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦♦❢s ❝❛♥ ❜❡ ❛r❜✐tr❛r✐❧② ❝♦♠♣❧❡①
✭❛♥❞ t❤✉s ❞✐✣❝✉❧t t♦ ✜♥❞✮
◮ ♣r♦♦❢r❡❛❞✐♥❣ ✐s ❡❛s②✳ ✳ ✳
✭❛♥❞ t❤✉s ❜♦r✐♥❣✮
✳ ✳ ✳ ♦♥❝❡ ✇❡ ❛❣r❡❡ ❛❜♦✉t ✇❤❛t ❛ ♣r♦♦❢ ✐s
SLIDE 5
Pr✐♥❝✐♣❧❡s✿ P♦✐♥❝❛ré
◮ ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦♦❢s ❝❛♥ ❜❡ ❛r❜✐tr❛r✐❧② ❝♦♠♣❧❡①
✭❛♥❞ t❤✉s ❞✐✣❝✉❧t t♦ ✜♥❞✮
◮ ♣r♦♦❢r❡❛❞✐♥❣ ✐s ❡❛s②✳ ✳ ✳
✭❛♥❞ t❤✉s ❜♦r✐♥❣✮
✳ ✳ ✳ ♦♥❝❡ ✇❡ ❛❣r❡❡ ❛❜♦✉t ✇❤❛t ❛ ♣r♦♦❢ ✐s
SLIDE 6
Pr✐♥❝✐♣❧❡s ✲ ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❛♥❝❡ ✏♣r♦♦❢s ❛r❡ ♣r♦❣r❛♠s✑
(A → B) ∧ (B → C) ∧ A → C ♣r♦♣❡rt② t②♣❡ ✭✐♥t❡r❢❛❝❡✮ ♣r♦♦❢ t❡r♠ ✭✐♠♣❧❡♠❡♥t❛t✐♦♥✮ ♣r♦♦❢✲❝❤❡❝❦✐♥❣ t②♣❡✲❝❤❡❝❦✐♥❣
SLIDE 7
Pr✐♥❝✐♣❧❡s ✲ ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❛♥❝❡ ✏♣r♦♦❢s ❛r❡ ♣r♦❣r❛♠s✑
p : (A → B) ∧ (B → C) ∧ A → C (f , g, x) → ♣r♦♣❡rt② t②♣❡ ✭✐♥t❡r❢❛❝❡✮ ♣r♦♦❢ t❡r♠ ✭✐♠♣❧❡♠❡♥t❛t✐♦♥✮ ♣r♦♦❢✲❝❤❡❝❦✐♥❣ t②♣❡✲❝❤❡❝❦✐♥❣
SLIDE 8
Pr✐♥❝✐♣❧❡s ✲ ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❛♥❝❡ ✏♣r♦♦❢s ❛r❡ ♣r♦❣r❛♠s✑
p : (A → B) ∧ (B → C) ∧ A → C (f , g, x) → g(f (x)) ♣r♦♣❡rt② t②♣❡ ✭✐♥t❡r❢❛❝❡✮ ♣r♦♦❢ t❡r♠ ✭✐♠♣❧❡♠❡♥t❛t✐♦♥✮ ♣r♦♦❢✲❝❤❡❝❦✐♥❣ t②♣❡✲❝❤❡❝❦✐♥❣
SLIDE 9
Pr✐♥❝✐♣❧❡s ✲ ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❛♥❝❡ ✏♣r♦♦❢s ❛r❡ ♣r♦❣r❛♠s✑
p : (A → B) ∧ (B → C) ∧ A → C (f , g, x) → g(f (x)) ♣r♦♣❡rt② P t②♣❡ T ✭✐♥t❡r❢❛❝❡✮ ♣r♦♦❢ p t❡r♠ t ✭✐♠♣❧❡♠❡♥t❛t✐♦♥✮ ♣r♦♦❢✲❝❤❡❝❦✐♥❣ t②♣❡✲❝❤❡❝❦✐♥❣ p ⊢ P ⊢ t : T
SLIDE 10
❖✉t❧✐♥❡
◗✉✐❝❦ t♦✉r ♦❢ s②♥t❛① ❛♥❞ ❜❛s✐❝ ♣r✐♥❝✐♣❧❡s ❚❤r❡❡ ❦✐♥❞s ♦❢ ✉s❡ Pr♦✈❡✴❝❡rt✐❢② ♠❛t❤❡♠❛t✐❝❛❧ t❤❡♦r❡♠s ❈❡rt✐❢② ❡①✐st✐♥❣ s♦❢t✇❛r❡ ❇✉✐❧❞ ❝❡rt✐✜❡❞ s♦❢t✇❛r❡ ❈♦♥❝❧✉s✐♦♥s
SLIDE 11
❙②♥t❛①
▲❡t✬s ♣❧❛② ✇✐t❤ ❈♦q✳
SLIDE 12
❲❤❛t ❞✐❞ ✇❡ ❧❡❛r♥❄
◮ ❚❤❡r❡ ✐s ❛ s✐♥❣❧❡ ❧❛♥❣✉❛❣❡ ✭❣❛❧❧✐♥❛✮✱ ❢♦r✿
◮ ♣r♦❣r❛♠s✴❢✉♥❝t✐♦♥s✱ ◮ s♣❡❝✐✜❝❛t✐♦♥s✱ ◮ ♣r♦♦❢s✳
❚❤✐s ✐s ❛ ♣✉r❡❧② ❢✉♥❝t✐♦♥♥❛❧ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡✳ ❚❤❡r❡ ✐s ❛♥♦t❤❡r ❧❛♥❣✉❛❣❡ ✭t❛❝t✐❝s✿ ▲t❛❝✮✿
❢♦r ❜✉✐❧❞✐♥❣✴s❡❛r❝❤✐♥❣ ♣r♦♦❢s✱ t❤❛t ❝❛♥ ❜❡ ✉s❡❞ ✐♥t❡r❛❝t✐✈❡❧②✳
❚❤❡r❡ ❛r❡ ♣r✐♠✐t✐✈❡ t❛❝t✐❝s ✭✐♥tr♦s✱ ❛♣♣❧②✱ ✐♥❞✉❝t✐♦♥✮✱ ❛♥❞ r❛t❤❡r ❝♦♠♣❧❡① ♦♥❡s ✭t❛✉t♦✱ r✐♥❣✮✳
SLIDE 13
❲❤❛t ❞✐❞ ✇❡ ❧❡❛r♥❄
◮ ❚❤❡r❡ ✐s ❛ s✐♥❣❧❡ ❧❛♥❣✉❛❣❡ ✭❣❛❧❧✐♥❛✮✱ ❢♦r✿
◮ ♣r♦❣r❛♠s✴❢✉♥❝t✐♦♥s✱ ◮ s♣❡❝✐✜❝❛t✐♦♥s✱ ◮ ♣r♦♦❢s✳
❚❤✐s ✐s ❛ ♣✉r❡❧② ❢✉♥❝t✐♦♥♥❛❧ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡✳ ◮ ❚❤❡r❡ ✐s ❛♥♦t❤❡r ❧❛♥❣✉❛❣❡ ✭t❛❝t✐❝s✿ ▲t❛❝✮✿
◮ ❢♦r ❜✉✐❧❞✐♥❣✴s❡❛r❝❤✐♥❣ ♣r♦♦❢s✱ ◮ t❤❛t ❝❛♥ ❜❡ ✉s❡❞ ✐♥t❡r❛❝t✐✈❡❧②✳
❚❤❡r❡ ❛r❡ ♣r✐♠✐t✐✈❡ t❛❝t✐❝s ✭✐♥tr♦s✱ ❛♣♣❧②✱ ✐♥❞✉❝t✐♦♥✮✱ ❛♥❞ r❛t❤❡r ❝♦♠♣❧❡① ♦♥❡s ✭t❛✉t♦✱ r✐♥❣✮✳
SLIDE 14
Pr✐♥❝✐♣❧❡s ✲ ●❛❧❧✐♥❛
◮ ❈❤❡❝❦✐♥❣ ❛ ♣r♦♦❢ ✐s ❡❛s②✿ t❤✐s ✐s ❥✉st t②♣❡✲❝❤❡❝❦✐♥❣✳ ✳ ✳ ✳ ✳ ✳ ❜✉t ✇❡ ♥❡❡❞ t♦ tr✉st t❤❡ t②♣❡✲❝❤❡❝❦❡r✳ ◮ ●❛❧❧✐♥❛ ✐s ❛ s♠❛❧❧ ❧❛♥❣✉❛❣❡✱
◮ ❢♦r ✇❤✐❝❤ t②♣❡✲❝❤❡❝❦✐♥❣ ✐s ✭❡❛s✐❧②✮ ❞❡❝✐❞❛❜❧❡❀ ◮ ❛♥❞ st✐❧❧ r❡♠❛✐♥s r❡❛❧❧② ❡①♣r❡ss✐✈❡✳
◮ ■t r❡❧✐❡s ♦♥ ❛ str♦♥❣ t❤❡♦r❡t✐❝❛❧ ❜❛❝❦❣r♦✉♥❞✿
◮ t❤❡ ✏❈❛❧❝✉❧✉s ♦❢ ■♥❞✉❝t✐✈❡ ❈♦♥str✉❝t✐♦♥s✑✱ ◮ ✇❤✐❝❤ ❝♦♠❡s ❢r♦♠ t❤❡ λ✲❝❛❧❝✉❧✉s✳
SLIDE 15
Pr✐♥❝✐♣❧❡s ✲ ▲t❛❝
◮ ❙❡q✉❡♥❝❡s ♦❢ t❛❝t✐❝s ❞♦ ♥♦t ❝♦♥st✐t✉t❡ ♣r♦♦❢s✿ t❛❝t✐❝s ♣r♦❞✉❝❡ ❣❛❧❧✐♥❛ t❡r♠s t❤❛t ❝❛♥ ❜❡ ❝❤❡❝❦❡❞ ❜② ❈♦q✳ ◮ ❲❡ ❞♦♥✬t ♥❡❡❞ t♦ tr✉st t❛❝t✐❝s✿ ❛♥② ✇❛② t♦ ♦❜t❛✐♥ ❛ ♣r♦♦❢ ✐s ✈❛❧✐❞ s✐♥❝❡ t❤❡ ♣r♦♦❢ ✇✐❧❧ ❜❡ ❝❤❡❝❦❡❞✳ ◮ Pr♦♦❢s ❝❛♥ ❛❝t✉❛❧❧② ❜❡ s❡❛r❝❤❡❞ ❜② ♦t❤❡r ♠❡❛♥s t❤❛♥ ▲t❛❝✳
SLIDE 16
❖✉t❧✐♥❡
◗✉✐❝❦ t♦✉r ♦❢ s②♥t❛① ❛♥❞ ❜❛s✐❝ ♣r✐♥❝✐♣❧❡s ❚❤r❡❡ ❦✐♥❞s ♦❢ ✉s❡ Pr♦✈❡✴❝❡rt✐❢② ♠❛t❤❡♠❛t✐❝❛❧ t❤❡♦r❡♠s ❈❡rt✐❢② ❡①✐st✐♥❣ s♦❢t✇❛r❡ ❇✉✐❧❞ ❝❡rt✐✜❡❞ s♦❢t✇❛r❡ ❈♦♥❝❧✉s✐♦♥s
SLIDE 17
Pr♦✈❡✴❝❡rt✐❢② ♠❛t❤❡♠❛t✐❝❛❧ t❤❡♦r❡♠s
◮ ❲❡ ❥✉st ♣r♦✈❡❞ s♦♠❡ ❡❧❡♠❡♥t❛r② t❤❡♦r❡♠s✱ ♠♦r❡ ❝♦♠♣❧❡① ♦♥❡s ❝❛♥ ❜❡ ♣r♦✈❡❞ t♦♦✦ ◮ ❚✇♦ ♠❛❥♦r ❡①❛♠♣❧❡s✿
◮ ●❡♦r❣❡s ●♦♥t❤✐❡r ❡t ❛❧✳✬s ♣r♦♦❢ ♦❢ ❢♦✉r✲❝♦❧♦✉rs t❤❡♦r❡♠❀ ◮ ❋❡✐t✲❚❤♦♠♣s♦♥✬s t❤❡♦r❡♠ ✭✜♥✐t❡ ❣r♦✉♣s ❝❧❛ss✐✜❝❛t✐♦♥✮
SLIDE 18
❈❡rt✐❢② ❡①✐st✐♥❣ s♦❢t✇❛r❡
◮ ●✐✈❡♥ ❛♥ ❡①✐st✐♥❣ ♣r♦❣r❛♠✱ ✇❡ ♠✐❣❤t ✇❛♥t t♦ ♣r♦✈❡✿
◮ t❤❡ ❛❜s❡♥❝❡ ♦❢ r✉♥t✐♠❡ ❡rr♦rs✱ ◮ t❡r♠✐♥❛t✐♦♥✱ ◮ ❜❡❤❛✈✐♦✉r❛❧ ❝♦rr❡❝t♥❡ss✳
Pr♦❜❧❡♠✿ s♦♠❡t✐♠❡s✱ ♣r♦❣r❛♠s ❛r❡ ♥♦t ✇r✐tt❡♥ ✐♥ ❈♦q✳ ✳ ✳ ❆ s♦❧✉t✐♦♥✿ ❲❤② ❛♥❞ ❑r❛❦❛t♦❛✴❈❛❞✉❝❡✉s t♦♦❧s✳
✭s❡❡ ❏❡❛♥✲❈❤r✐st♦♣❤❡ ❋✐❧❧✐âtr❡✬ ❣❛❧❧❡r② ♦❢ ❝❡rt✐✜❡❞ ♣r♦❣r❛♠s✿ ❤tt♣✿✴✴✇❤②✳❧r✐✳❢r✴❡①❛♠♣❧❡s✴✮
SLIDE 19
❈❡rt✐❢② ❡①✐st✐♥❣ s♦❢t✇❛r❡
◮ ●✐✈❡♥ ❛♥ ❡①✐st✐♥❣ ♣r♦❣r❛♠✱ ✇❡ ♠✐❣❤t ✇❛♥t t♦ ♣r♦✈❡✿
◮ t❤❡ ❛❜s❡♥❝❡ ♦❢ r✉♥t✐♠❡ ❡rr♦rs✱ ◮ t❡r♠✐♥❛t✐♦♥✱ ◮ ❜❡❤❛✈✐♦✉r❛❧ ❝♦rr❡❝t♥❡ss✳
◮ Pr♦❜❧❡♠✿ s♦♠❡t✐♠❡s✱ ♣r♦❣r❛♠s ❛r❡ ♥♦t ✇r✐tt❡♥ ✐♥ ❈♦q✳ ✳ ✳ ❆ s♦❧✉t✐♦♥✿ ❲❤② ❛♥❞ ❑r❛❦❛t♦❛✴❈❛❞✉❝❡✉s t♦♦❧s✳
✭s❡❡ ❏❡❛♥✲❈❤r✐st♦♣❤❡ ❋✐❧❧✐âtr❡✬ ❣❛❧❧❡r② ♦❢ ❝❡rt✐✜❡❞ ♣r♦❣r❛♠s✿ ❤tt♣✿✴✴✇❤②✳❧r✐✳❢r✴❡①❛♠♣❧❡s✴✮
SLIDE 20
❈❡rt✐❢② ❡①✐st✐♥❣ s♦❢t✇❛r❡
◮ ●✐✈❡♥ ❛♥ ❡①✐st✐♥❣ ♣r♦❣r❛♠✱ ✇❡ ♠✐❣❤t ✇❛♥t t♦ ♣r♦✈❡✿
◮ t❤❡ ❛❜s❡♥❝❡ ♦❢ r✉♥t✐♠❡ ❡rr♦rs✱ ◮ t❡r♠✐♥❛t✐♦♥✱ ◮ ❜❡❤❛✈✐♦✉r❛❧ ❝♦rr❡❝t♥❡ss✳
◮ Pr♦❜❧❡♠✿ s♦♠❡t✐♠❡s✱ ♣r♦❣r❛♠s ❛r❡ ♥♦t ✇r✐tt❡♥ ✐♥ ❈♦q✳ ✳ ✳ ◮ ❆ s♦❧✉t✐♦♥✿ ❲❤② ❛♥❞ ❑r❛❦❛t♦❛✴❈❛❞✉❝❡✉s t♦♦❧s✳
✭s❡❡ ❏❡❛♥✲❈❤r✐st♦♣❤❡ ❋✐❧❧✐âtr❡✬ ❣❛❧❧❡r② ♦❢ ❝❡rt✐✜❡❞ ♣r♦❣r❛♠s✿ ❤tt♣✿✴✴✇❤②✳❧r✐✳❢r✴❡①❛♠♣❧❡s✴✮
SLIDE 21
SLIDE 22
❇✉✐❧❞ ❝❡rt✐✜❡❞ s♦❢t✇❛r❡
◮ ■❢ ✇❡ ❤❛✈❡ t♦ ✇r✐t❡ ❛ ♥❡✇ ♣r♦❣r❛♠✱ ✇❤② ♥♦t ✇r✐t✐♥❣ ✐t ❛♥❞ ❝❡rt✐❢②✐♥❣ ✐t ✇✐t❤✐♥ ❈♦q❄ ◮ ◆♦t s♦ r❡❛❧✐st✐❝✱ ❈♦q ✐s ❞❡✜♥✐t❡❧② t♦♦ s❧♦✇✿
◮ ✐t✬s ✐♥t❡r♣r❡t❡❞❀ ◮ ✐♥t❡❣❡rs✱ ✢♦❛ts✳ ✳ ✳ ❛r❡ ♥♦t ❵♥❛t✐✈❡✬✳
◮ ❍♦✇❡✈❡r✱ ❈♦q ♣r♦❣r❛♠s ❝❛♥ ❜❡ ❡①tr❛❝t❡❞ t♦ ♦t❤❡r ❧❛♥❣✉❛❣❡s✿ ❖❈❛♠❧✱ ❍❛s❦❡❧❧ ❛♥❞ ❙❝❤❡♠❡✳ ◮ ❚❤✐s ✐s ❤♦✇ ❳❛✈✐❡r ▲❡r♦② ❛♥❞ ❙❛♥❞r✐♥❡ ❇❧❛③② ♦❜t❛✐♥❡❞ t❤❡✐r ❝❡rt✐✜❡❞ ❝♦♠♣✐❧❡r ❢♦r ❈✿ ❤tt♣✿✴✴❝♦♠♣❝❡rt✳✐♥r✐❛✳❢r✴
SLIDE 23
❖✉t❧✐♥❡
◗✉✐❝❦ t♦✉r ♦❢ s②♥t❛① ❛♥❞ ❜❛s✐❝ ♣r✐♥❝✐♣❧❡s ❚❤r❡❡ ❦✐♥❞s ♦❢ ✉s❡ Pr♦✈❡✴❝❡rt✐❢② ♠❛t❤❡♠❛t✐❝❛❧ t❤❡♦r❡♠s ❈❡rt✐❢② ❡①✐st✐♥❣ s♦❢t✇❛r❡ ❇✉✐❧❞ ❝❡rt✐✜❡❞ s♦❢t✇❛r❡ ❈♦♥❝❧✉s✐♦♥s
SLIDE 24
❙✉♠♠❛r②
◮ ❈♦q ✐s ❛ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡✿
◮ ♣✉r❡❧② ❢✉♥❝t✐♦♥♥❛❧❀ ◮ ✐♥t❡r♣r❡t❡❞ ✭r❛t❤❡r s❧♦✇✮✱ ❜✉t ♣r♦❣r❛♠s ❝❛♥ ❜❡ ❡①tr❛❝t❡❞ t♦ ❢❛st✱ ❝♦♠♣✐❧❡❞✱ ❧❛♥❣✉❛❣❡s❀
◮ ❈♦q ✐s ❛♥ ❡①♣r❡ss✐✈❡ s♣❡❝✐✜❝❛t✐♦♥ ❧❛♥❣✉❛❣❡✿
◮ ❛♥② ♠❛t❤❡♠❛t✐❝❛❧ ♣r♦♣❡rt② ❝❛♥ ❜❡ st❛t❡❞✳
◮ ❈♦q ❝❡rt✐✜❡s ♣r♦♦❢s ❜② ❛ s✐♠♣❧❡ t②♣❡✲❝❤❡❝❦✐♥❣ ❛❧❣♦r✐t❤♠✳ ◮ ❈♦q ✐s ❛ ♣r♦♦❢ ❛ss✐st❛♥t✿
◮ t❤❡ ✐♥t❡r❛❝t✐✈❡ ♠♦❞❡ ❛❧❧♦✇s ✉s t♦ ♣r♦✈❡ ❛ t❤❡♦r❡♠ ♣r♦❣r❡ss✐✈❡❧②✱ ❜② ✉s✐♥❣ t❛❝t✐❝s❀ ◮ t❛❝t✐❝s ❝❛♥ ❜❡ ♠♦r❡ ♦r ❧❡ss ❡❧❛❜♦r❛t❡❞✱ ❛♥❞ ❝❛♥ ❜❡ ❞❡✜♥❡❞ ❜② t❤❡ ✉s❡r✳
SLIDE 25
❘❡❧❛t❡❞ s♦❢t✇❛r❡
◮ ❲❤②✱ ❑r❛❦❛t♦❛✴❈❛❞✉❝❡✉s✱
◮ ❢♦r t❤❡ ❛♥❛❧②s✐s ♦❢ ❏❛✈❛ ❛♥❞ ❈ ♣r♦❣r❛♠s✳
◮ ■s❛❜❡❧❧❡✴❍❖▲
◮ ▲❛rr② P❛✉❧s♦♥ ✲ ❯✳ ♦❢ ❈❛♠❜r✐❞❣❡ ✫ ❚♦❜✐❛s ◆✐♣❦♦✇ ✲ ❯✳ ♦❢ ▼ü♥❝❤❡♥
◮ P❱❙
◮ ❙❛♠ ❖✇r❡✱ ◆❛t❛r❛❥❛♥ ❙❤❛♥❦❛r✱ ❏♦❤♥ ❘✉s❤❜②
◮ ❚✇❡❧❢
◮ ❑❛r❧ ❈r❛r② ✫ ❘♦❜❡rt ❍❛r♣❡r ✲ ❈❛r♥❡❣✐❡ ▼❡❧❧♦♥ ❯✳✱ ❯❙❆
SLIDE 26