Is expression evaluated before assigning type?Proving that $Omega = (lambda x.xx)(lambda x.xx)$ is not typable in the simply typed lambda calculusHas a Dependent Type always a Type?If $f(x)=g(x)$ for all $x:A$, why is it not true that $lambda x.f(x)=lambda x.g(x)$?Proving that $Omega = (lambda x.xx)(lambda x.xx)$ is not typable in the simply typed lambda calculusQuestions regarding well formed expressions in the Theory of typesWikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no senseThe place of lambda abstraction in internal and Mitchell-Bénabou languagesBasic problem with lambda-calculus syntaxHow should I type this lambda expression?Variable Condition in Typed Lambda Calculus“Type dependence” in type theory and category theory?
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Is expression evaluated before assigning type?
Proving that $Omega = (lambda x.xx)(lambda x.xx)$ is not typable in the simply typed lambda calculusHas a Dependent Type always a Type?If $f(x)=g(x)$ for all $x:A$, why is it not true that $lambda x.f(x)=lambda x.g(x)$?Proving that $Omega = (lambda x.xx)(lambda x.xx)$ is not typable in the simply typed lambda calculusQuestions regarding well formed expressions in the Theory of typesWikipedia's explanation of the lambda-calclulus form of Curry's paradox makes no senseThe place of lambda abstraction in internal and Mitchell-Bénabou languagesBasic problem with lambda-calculus syntaxHow should I type this lambda expression?Variable Condition in Typed Lambda Calculus“Type dependence” in type theory and category theory?
$begingroup$
I am assigning type to an $lambda$-expression: if false then M else N
where if A then B else C and false have their usual meanings (read: not specified).
The problem arises because M and N have different types. While clearly the expression evaluates to N & hence should be assigned type(N) but apparently it is expected that for if-else, the types for B & C should be same.
How to proceed on this? Should I use conjuncted type?
lambda-calculus type-theory
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
$endgroup$
add a comment |
$begingroup$
I am assigning type to an $lambda$-expression: if false then M else N
where if A then B else C and false have their usual meanings (read: not specified).
The problem arises because M and N have different types. While clearly the expression evaluates to N & hence should be assigned type(N) but apparently it is expected that for if-else, the types for B & C should be same.
How to proceed on this? Should I use conjuncted type?
lambda-calculus type-theory
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
$endgroup$
$begingroup$
What do you mean by conjuncted type?
$endgroup$
– Potato44
Mar 30 at 12:00
$begingroup$
I may have used the word "conjunction" incorrectly. I'm referring to this answer
$endgroup$
– Sudutt Harne
Mar 31 at 17:41
$begingroup$
That sounds like intersection types. Do you also have union types?
$endgroup$
– Potato44
Mar 31 at 17:42
$begingroup$
No, I don't think we have covered them yet.
$endgroup$
– Sudutt Harne
Mar 31 at 17:46
add a comment |
$begingroup$
I am assigning type to an $lambda$-expression: if false then M else N
where if A then B else C and false have their usual meanings (read: not specified).
The problem arises because M and N have different types. While clearly the expression evaluates to N & hence should be assigned type(N) but apparently it is expected that for if-else, the types for B & C should be same.
How to proceed on this? Should I use conjuncted type?
lambda-calculus type-theory
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
$endgroup$
I am assigning type to an $lambda$-expression: if false then M else N
where if A then B else C and false have their usual meanings (read: not specified).
The problem arises because M and N have different types. While clearly the expression evaluates to N & hence should be assigned type(N) but apparently it is expected that for if-else, the types for B & C should be same.
How to proceed on this? Should I use conjuncted type?
lambda-calculus type-theory
lambda-calculus type-theory
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
asked Mar 30 at 5:18
Sudutt HarneSudutt Harne
33
33
$begingroup$
What do you mean by conjuncted type?
$endgroup$
– Potato44
Mar 30 at 12:00
$begingroup$
I may have used the word "conjunction" incorrectly. I'm referring to this answer
$endgroup$
– Sudutt Harne
Mar 31 at 17:41
$begingroup$
That sounds like intersection types. Do you also have union types?
$endgroup$
– Potato44
Mar 31 at 17:42
$begingroup$
No, I don't think we have covered them yet.
$endgroup$
– Sudutt Harne
Mar 31 at 17:46
add a comment |
$begingroup$
What do you mean by conjuncted type?
$endgroup$
– Potato44
Mar 30 at 12:00
$begingroup$
I may have used the word "conjunction" incorrectly. I'm referring to this answer
$endgroup$
– Sudutt Harne
Mar 31 at 17:41
$begingroup$
That sounds like intersection types. Do you also have union types?
$endgroup$
– Potato44
Mar 31 at 17:42
$begingroup$
No, I don't think we have covered them yet.
$endgroup$
– Sudutt Harne
Mar 31 at 17:46
$begingroup$
What do you mean by conjuncted type?
$endgroup$
– Potato44
Mar 30 at 12:00
$begingroup$
What do you mean by conjuncted type?
$endgroup$
– Potato44
Mar 30 at 12:00
$begingroup$
I may have used the word "conjunction" incorrectly. I'm referring to this answer
$endgroup$
– Sudutt Harne
Mar 31 at 17:41
$begingroup$
I may have used the word "conjunction" incorrectly. I'm referring to this answer
$endgroup$
– Sudutt Harne
Mar 31 at 17:41
$begingroup$
That sounds like intersection types. Do you also have union types?
$endgroup$
– Potato44
Mar 31 at 17:42
$begingroup$
That sounds like intersection types. Do you also have union types?
$endgroup$
– Potato44
Mar 31 at 17:42
$begingroup$
No, I don't think we have covered them yet.
$endgroup$
– Sudutt Harne
Mar 31 at 17:46
$begingroup$
No, I don't think we have covered them yet.
$endgroup$
– Sudutt Harne
Mar 31 at 17:46
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Type checking is something that happens before evaluation.
In most common type systems for lambda calculus, including simply typed lambda calculus and System F, if false then M else N is ill typed if N and M have different types. Unless you have been told otherwise you are probably working with one of these.
There are extensions such as union types and certain forms of subtyping that allow if false then M else N to be well formed with N and Mhaving different types.
answered Mar 31 at 18:14
Potato44Potato44
1185
$endgroup$
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
add a comment |
Your Answer
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Type checking is something that happens before evaluation.
In most common type systems for lambda calculus, including simply typed lambda calculus and System F, if false then M else N is ill typed if N and M have different types. Unless you have been told otherwise you are probably working with one of these.
There are extensions such as union types and certain forms of subtyping that allow if false then M else N to be well formed with N and Mhaving different types.
answered Mar 31 at 18:14
Potato44Potato44
1185
$endgroup$
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
add a comment |
$begingroup$
Type checking is something that happens before evaluation.
In most common type systems for lambda calculus, including simply typed lambda calculus and System F, if false then M else N is ill typed if N and M have different types. Unless you have been told otherwise you are probably working with one of these.
There are extensions such as union types and certain forms of subtyping that allow if false then M else N to be well formed with N and Mhaving different types.
answered Mar 31 at 18:14
Potato44Potato44
1185
$endgroup$
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
add a comment |
$begingroup$
Type checking is something that happens before evaluation.
In most common type systems for lambda calculus, including simply typed lambda calculus and System F, if false then M else N is ill typed if N and M have different types. Unless you have been told otherwise you are probably working with one of these.
There are extensions such as union types and certain forms of subtyping that allow if false then M else N to be well formed with N and Mhaving different types.
answered Mar 31 at 18:14
Potato44Potato44
1185
$endgroup$
Type checking is something that happens before evaluation.
In most common type systems for lambda calculus, including simply typed lambda calculus and System F, if false then M else N is ill typed if N and M have different types. Unless you have been told otherwise you are probably working with one of these.
There are extensions such as union types and certain forms of subtyping that allow if false then M else N to be well formed with N and Mhaving different types.
answered Mar 31 at 18:14
Potato44Potato44
1185
answered Mar 31 at 18:14
Potato44Potato44
1185
answered Mar 31 at 18:14
Potato44Potato44
1185
answered Mar 31 at 18:14
Potato44Potato44
1185
1185
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
add a comment |
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
Thanks for the explanation! Could you suggest some books/authoritative references to study this further from?
$endgroup$
– Sudutt Harne
Mar 31 at 18:34
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
$begingroup$
I haven't read either myself, but two I have seen recommended by others are " Practical Foundations for Programming Languages" by Robert Harper and " Types and Programming Languages" by Benjamin Pierce.
$endgroup$
– Potato44
Mar 31 at 20:43
add a comment |
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$begingroup$
What do you mean by conjuncted type?
$endgroup$
– Potato44
Mar 30 at 12:00
$begingroup$
I may have used the word "conjunction" incorrectly. I'm referring to this answer
$endgroup$
– Sudutt Harne
Mar 31 at 17:41
$begingroup$
That sounds like intersection types. Do you also have union types?
$endgroup$
– Potato44
Mar 31 at 17:42
$begingroup$
No, I don't think we have covered them yet.
$endgroup$
– Sudutt Harne
Mar 31 at 17:46