[PDF] • Question #1: What is the value of the following expression? {+ 1 2}





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Unit 7 Conditional Sentences (Type 0-3)

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• Question #1: What is the value of the following expression? {+ 1 2}

expression? {+ 1 2}. • Wrong answer: 0. • Wrong answer: 42. 3 Conditional Type Rules. <MFAE>1 : bool. <MFAE>2 ... {if <MFAE>1 <MFAE>2 <MFAE>3} : <type>0.



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Solutions to Exercises Marked with sG from the book Introduction to

birth orders are equally likely what is the probability that the 3 eldest children are the. 3 girls? Solution: Label the girls as 1

Quiz •Question #1: What is the value of the following expression? {+ 1 2}1 Quiz •Question #1: What is the value of the following expression? {+ 1 2} •Wrong answer: 0 2 Quiz •Question #1: What is the value of the following expression? {+ 1 2} •Wrong answer: 0 •Wrong answer: 42 3 Quiz •Question #1: What is the value of the following expression? {+ 1 2} •Wrong answer: 0 •Wrong answer: 42 •Answer: 3 4 Quiz •Question #2: What is the value of the following expression? {+ fun 17 8}5 Quiz •Question #2: What is the value of the following expression? {+ fun 17 8} •Wrong answer: error 6 Quiz •Question #2: What is the value of the following expression? {+ fun 17 8} •Wrong answer: error •Answer: Trick question! {+ fun 17 8} is not an expression 7

Language Grammar for Quiz

true false {+ } {- } {= } {fun { } } { {if }8 Quiz •Question #3: Is the following an expression? {{fun {x y} 1} 7}9 Quiz •Question #3: Is the following an expression? {{fun {x y} 1} 7} •Wrong answer: No 10 Quiz •Question #3: Is the following an expression? {{fun {x y} 1} 7} •Wrong answer: No •Answer: Yes (according to our grammar) 11 Quiz •Question #4: What is the value of the following expression? {{fun {x y} 1} 7}12 Quiz •Question #4: What is the value of the following expression? {{fun {x y} 1} 7} •Answer: {fun {y} 1} (according to some interpreters) 13 Quiz •Question #4: What is the value of the following expression? {{fun {x y} 1} 7} •Answer: {fun {y} 1} (according to some interpreters) •But no real language would accept {{fun {x y} 1} 7}14 Quiz •Question #4: What is the value of the following expression? {{fun {x y} 1} 7} •Answer: {fun {y} 1} (according to some interpreters) •But no real language would accept {{fun {x y} 1} 7} •Let's agree to call {{fun {x y} 1} 7} an ill-formed expression because {fun {x y} 1} should be used only with two arguments •Let's agree to never evaluate ill-formed expressions 15 Quiz •Question #5: What is the value of the following expression? {{fun {x y} 1} 7}16 Quiz •Question #5: What is the value of the following expression? {{fun {x y} 1} 7} •Answer: None - the expression is ill-formed 17 Quiz •Question #6: Is the following a well-formed expression? {+ {fun {} 1} 8}18 Quiz •Question #6: Is the following a well-formed expression? {+ {fun {} 1} 8} •Answer: Yes 19 Quiz •Question #7: What is the value of the following expression? {+ {fun {} 1} 8}20 Quiz •Question #7: What is the value of the following expression? {+ {fun {} 1} 8} •Answer: None - it produces an error: numeric operation expected number 21
Quiz •Question #7: What is the value of the following expression? {+ {fun {} 1} 8} •Answer: None - it produces an error: numeric operation expected number •Let's agree that a fun expression cannot be inside a form 22
Quiz •Question #8: Is the following a well-formed expression? {+ {fun {} 1} 8}23 Quiz •Question #8: Is the following a well-formed expression? {+ {fun {} 1} 8} •Answer: No 24
Quiz •Question #9: Is the following a well-formed expression? {+ {{fun {x} x} 7} 5}25 Quiz •Question #9: Is the following a well-formed expression? {+ {{fun {x} x} 7} 5} •Answer: Depends on what we meant by inside in our most recent agreement

Anywhere inside - No

Immediately inside - Yes

26
Quiz •Question #9: Is the following a well-formed expression? {+ {{fun {x} x} 7} 5} •Answer: Depends on what we meant by inside in our most recent agreement

Anywhere inside - No

Immediately inside - Yes

•Since our intrepreter produces 12, and since that result makes sense, let's agree on immediately inside 27
Quiz •Question #10: Is the following a well-formed expression? {+ {{fun {x} x} {fun {y} y}} 5}28 Quiz •Question #10: Is the following a well-formed expression? {+ {{fun {x} x} {fun {y} y}} 5} •Answer: Yes, but we don't want it to be! 29
Quiz •Question #11: Is it possible to define well-formed (as a decidable property) so that we reject all expressions that produce errors? 30
Quiz •Question #11: Is it possible to define well-formed (as a decidable property) so that we reject all expressions that produce errors? •Answer: Yes: reject all expressions! 31
Quiz •Question #12: Is it possible to define well-formed (as a decidable property) so that we reject only expressions that produce errors? 32
Quiz •Question #12: Is it possible to define well-formed (as a decidable property) so that we reject only expressions that produce errors? •Answer: No 33
Quiz •Question #12: Is it possible to define well-formed (as a decidable property) so that we reject only expressions that produce errors? •Answer: No {+ 1 {if ... 1 {fun {x} x}}} •If we always knew whether produces true or false, we could solve the halting problem 34
Types •Solution to our dilemma

In the process of rejecting expressions that are

certainly bad, also reject some expressions that are good {+ 1 {if {prime? 131101} 1 {fun {x} x}}}35 Types •Solution to our dilemma

In the process of rejecting expressions that are

certainly bad, also reject some expressions that are good {+ 1 {if {prime? 131101} 1 {fun {x} x}}} •Overall strategy: Assign a type to each expression without evaluating

Compute the type of a complex expression based

on the types of its subexpressions 36
Types

1 : numtrue : bool37

Types

1 : numtrue : bool{+ 1 2}38

Types

1 : numtrue : bool{+ 1 2}num39

Types

1 : numtrue : bool{+ 1 2}numnum40

Types

1 : numtrue : bool{+ 1 2}numnumnum41

Types

1 : numtrue : bool{+ 1 2}numnumnum{+ 1 false}42

Types

1 : numtrue : bool{+ 1 2}numnumnum{+ 1 false}num43

Types

1 : numtrue : bool{+ 1 2}numnumnum{+ 1 false}numbool44

Types

1 : numtrue : bool{+ 1 2}numnumnum{+ 1 false}numbool

no type 45

Type Rules

: numtrue : boolfalse : bool 1 : num 2 : num{+ 1 2 } : num46

Type Rules

: numtrue : boolfalse : bool 1 : num 2 : num{+ 1 2 } : num1 : numtrue : bool47

Type Rules

: numtrue : boolfalse : bool 1 : num 2 : num{+ 1 2 } : num1 : numtrue : bool1:num2:num{+ 1 2}:num48

Type Rules

: numtrue : boolfalse : bool 1 : num 2 : num{+ 1 2 } : num1 : numtrue : bool1:num2:num{+ 1 2}:num1:numfalse:bool{+ 1 false}: no type 49

Type Rules

: numtrue : boolfalse : bool 1 : num 2 : num{+ 1 2 } : num1 : num2 : num{+ 1 2} : num3 : num{+ {+ 1 2} 3} : num50

Types: Conditionals

{if true 1 2}51

Types: Conditionals

{if true 1 2}bool52

Types: Conditionals

{if true 1 2}boolnum53

Types: Conditionals

{if true 1 2}boolnumnum54

Types: Conditionals

{if true 1 2}boolnumnumnum55

Types: Conditionals

{if true 1 2}boolnumnumnum{if {+ 1 2} 1 2}56

Types: Conditionals

{if true 1 2}boolnumnumnum{if {+ 1 2} 1 2}num57

Types: Conditionals

quotesdbs_dbs50.pdfusesText_50
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