"Good" vs. "Bad" Expressions. ; interp-expr FAE... -> FAE-Value
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1 "Good" vs. "Bad" Expressions ; interp-expr FAE... -> FAE-Value 1
2 "Good" vs. "Bad" Expressions ; interp-expr FAE... -> FAE-Value Does interp-expr produce a value for all expressions? 2
3 "Good" vs. "Bad" Expressions ; interp-expr FAE... -> FAE-Value Does interp-expr produce a value for all expressions? Of course not! 3
4 "Good" vs. "Bad" Expressions ; interp-expr FAE... -> FAE-Value Does interp-expr produce a value for all expressions? Of course not! (interp-expr (parse '{5 5})) etc... 4
5 "Good" vs. "Bad" Expressions ; interp-expr FAE... -> FAE-Value Does interp-expr produce a value for all expressions? Of course not! (interp-expr (parse '{5 5})) etc... But do we know enough about expressions to tell before actually calling interp-expr? 5
6 Question #1: What is the value of the following expression? {+ 1 2} 6
7 Question #1: What is the value of the following expression? {+ 1 2} Wrong answer: 0 7
8 Question #1: What is the value of the following expression? {+ 1 2} Wrong answer: 0 Wrong answer: 42 8
9 Question #1: What is the value of the following expression? {+ 1 2} Wrong answer: 0 Wrong answer: 42 Answer: 3 9
10 Question #2: What is the value of the following expression? {+ fun 17 8} 10
11 Question #2: What is the value of the following expression? {+ fun 17 8} Wrong answer: error 11
12 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 12
13 Language Grammar for <MFAE> ::= <num> true false {+ <MFAE> <MFAE>} {- <MFAE> <MFAE>} {= <MFAE> <MFAE>} <id> {fun {<id>*} <MFAE>} {<MFAE> <MFAE>*} {if <MFAE> <MFAE> <MFAE>} 13
14 Question #3: Is the following an expression? {{fun {x y} 1} 7} 14
15 Question #3: Is the following an expression? {{fun {x y} 1} 7} Wrong answer: No 15
16 Question #3: Is the following an expression? {{fun {x y} 1} 7} Wrong answer: No Answer: Yes (according to our grammar) 16
17 Question #4: What is the value of the following expression? {{fun {x y} 1} 7} 17
18 Question #4: What is the value of the following expression? {{fun {x y} 1} 7} Answer: {fun {y} 1} (according to some interpreters) 18
19 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} 19
20 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 20
21 Question #5: What is the value of the following expression? {{fun {x y} 1} 7} 21
22 Question #5: What is the value of the following expression? {{fun {x y} 1} 7} Answer: None - the expression is ill-formed 22
23 Question #6: Is the following a well-formed expression? {+ {fun {} 1} 8} 23
24 Question #6: Is the following a well-formed expression? {+ {fun {} 1} 8} Answer: Yes 24
25 Question #7: What is the value of the following expression? {+ {fun {} 1} 8} 25
26 Question #7: What is the value of the following expression? {+ {fun {} 1} 8} Answer: None - it produces an error: numeric operation expected number 26
27 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 27
28 Question #8: Is the following a well-formed expression? {+ {fun {} 1} 8} 28
29 Question #8: Is the following a well-formed expression? {+ {fun {} 1} 8} Answer: No 29
30 Question #9: Is the following a well-formed expression? {+ {{fun {x} x} 7} 5} 30
31 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 31
32 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 32
33 Question #10: Is the following a well-formed expression? {+ {{fun {x} x} {fun {y} y}} 5} 33
34 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! 34
35 Question #11: Is it possible to define well-formed (as a decidable property) so that we reject all expressions that produce errors? 35
36 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! 36
37 Question #12: Is it possible to define well-formed (as a decidable property) so that we reject only expressions that produce errors? 37
38 Question #12: Is it possible to define well-formed (as a decidable property) so that we reject only expressions that produce errors? Answer: No 38
39 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 39
40 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? } 1 {fun {x} x}}} 40
41 Types Overall strategy: Assign a type to each expression without evaluating Compute the type of a complex expression based on the types of its subexpressions 41
42 Types 1 : num true : bool 42
43 Types 1 : num true : bool {+ 1 2} 43
44 Types 1 : num true : bool {+ 1 2} num 44
45 Types 1 : num true : bool {+ 1 2} num num 45
46 Types 1 : num true : bool {+ 1 2} num num num 46
47 Types 1 : num true : bool {+ 1 2} num num num {+ 1 false} 47
48 Types 1 : num true : bool {+ 1 2} num num num {+ 1 false} num 48
49 Types 1 : num true : bool {+ 1 2} num num num {+ 1 false} num bool 49
50 Types 1 : num true : bool {+ 1 2} num num num {+ 1 false} num bool no type 50
Quiz. Question #1: What is the value of the following expression? {+ 1 2} Wrong answer: 0 Wrong answer: 42. Answer: 3 1-4
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