Quiz on Language Grammar and Types, Quizzes of Programming Languages

Download Quiz on Language Grammar and Types and more Quizzes Programming Languages in PDF only on Docsity! Quiz • Question #1: What is the value of the following expression? {+ 1 2} • Wrong answer: 0 • Wrong answer: 42 • Answer: 3 1-4 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 5-7 Quiz • Question #4: What is the value of the following expression? {{fun {} 1} 7} • Answer: 1 (according to some interpreters) • But no real language would accept {{fun {} 1} 7} • Let's agree to call {{fun {} 1} 7} an ill-formed expression because {fun {} 1} should be used with only zero arguments • Let's agree to never evaluate ill-formed expressions 12-15 Quiz • Question #5: What is the value of the following expression? {{fun {} 1} 7} • Answer: None - the expression is ill-formed 16-17 Quiz • Question #6: Is the following a well-formed expression? {+ {fun {} 1} 8} • Answer: Yes 18-19 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 25-27 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! 28-29 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! 30-31 Types 1 : num true : bool {+ 1 2} num num num {+ 1 false} num bool no type 37-45 Type Rules <num> : num true : bool false : bool <MFAE>1 : num <MFAE>2 : num {+ <MFAE>1 <MFAE>2} : num 1 : num true : bool 1 : num 2 : num {+ 1 2} : num 1 : num false : bool {+ 1 false} : no type 46-49 Type Rules <num> : num true : bool false : bool <MFAE>1 : num <MFAE>2 : num {+ <MFAE>1 <MFAE>2} : num 1 : num 2 : num {+ 1 2} : num 3 : num {+ {+ 1 2} 3} : num 50 Types: Variables and Functions x : no type {fun {x : bool} x} bool (bool → bool) {if x 1 2}{fun {x : bool} } bool num num num (bool → num) 70-79 Variable and Function Type Rules [ ... <id>←τ ... ] <id> : τ Γ[ <id>←τ1 ] e : τ2 Γ {fun {<id> : τ1} e} : (τ1 → τ2) Abbreviations: τ = <type> e = <MFAE> Γ = <env> 80 Variable and Function Type Rules [ ... <id>←τ ... ] <id> : τ Γ[ <id>←τ1 ] e : τ2 Γ {fun {<id> : τ1} e} : (τ1 → τ2) ∅ x : no type [ x←bool ] x : bool ∅ {fun {x : bool} x} : (bool → bool) [ x←bool ] x : bool [ x←bool ] 1 : num [ x←bool ] 2 : num [ x←bool ] {if x 1 2} : num ∅ {fun {x : bool} {if x 1 2}} : (bool → num) 81-83 Function Call Type Rule Γ e1 : (τ2 → τ3) Γ e2 : τ2 Γ {e1 e2} : τ3 ∅ {fun {x : bool} {if x 1 2}} : (bool → num) ∅ true : bool ∅ {{fun {x : bool} {if x 1 2}} true} : num ∅ {fun {x : bool} {if x 1 2}} : (bool → num) ∅ 5 : num ∅ {{fun {x : bool} {if x 1 2}} 5} : no type ∅ 7 : num ∅ 5 : num ∅ {7 5} : no type 97-100 Types: Multiple Arguments {+ x y}{fun {x : num y : num} } num num num (num num → num) {{fun {x : num y : num} {+ x y}} 5 6} (num num → num) num num num {{fun {x : num y : num} {+ x y}} 5} (num num → num) num no type 101-114 Revised Function and Call Rules Γ[ <id>1←τ1 ... <id>n←τn ] e : τ0 Γ {fun {<id>1 : τ1 ... <id>n : τn} e} : (τ1 ... τn → τ0) Γ e0 : (τ1 ... τn → τ0) Γ e1 : τ1 ... Γ en : τn Γ {e0 e1 ... en} : τ0 115