beta reduction: order of substitution
up vote
1
down vote
favorite
Do we always apply our input to the left most term in a lamda expression?
For instance, take the expressions:
$λP λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP λQ[ ∀x P(x)→Q(x)]]$
$λP. λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP [λQ[ ∀x P(x)→Q(x)]]]$
If we apply an input to each expression, would the input in both expressions replace P? But if that's the case, wouldn't that make the two expressions equivalent?
first-order-logic lambda-calculus
asked Nov 20 at 1:22
Matt
23318
add a comment |
up vote
1
down vote
favorite
Do we always apply our input to the left most term in a lamda expression?
For instance, take the expressions:
$λP λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP λQ[ ∀x P(x)→Q(x)]]$
$λP. λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP [λQ[ ∀x P(x)→Q(x)]]]$
If we apply an input to each expression, would the input in both expressions replace P? But if that's the case, wouldn't that make the two expressions equivalent?
first-order-logic lambda-calculus
asked Nov 20 at 1:22
Matt
23318
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
Nov 21 at 7:23
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Do we always apply our input to the left most term in a lamda expression?
For instance, take the expressions:
$λP λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP λQ[ ∀x P(x)→Q(x)]]$
$λP. λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP [λQ[ ∀x P(x)→Q(x)]]]$
If we apply an input to each expression, would the input in both expressions replace P? But if that's the case, wouldn't that make the two expressions equivalent?
first-order-logic lambda-calculus
asked Nov 20 at 1:22
Matt
23318
Do we always apply our input to the left most term in a lamda expression?
For instance, take the expressions:
$λP λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP λQ[ ∀x P(x)→Q(x)]]$
$λP. λQ. ∀x P(x)→Q(x)$ which we can rewrite as $[λP [λQ[ ∀x P(x)→Q(x)]]]$
If we apply an input to each expression, would the input in both expressions replace P? But if that's the case, wouldn't that make the two expressions equivalent?
first-order-logic lambda-calculus
first-order-logic lambda-calculus
asked Nov 20 at 1:22
Matt
23318
asked Nov 20 at 1:22
Matt
23318
asked Nov 20 at 1:22
Matt
23318
asked Nov 20 at 1:22
Matt
23318
asked Nov 20 at 1:22
Matt
23318
23318
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
Nov 21 at 7:23
add a comment |
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
Nov 21 at 7:23
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
Nov 21 at 7:23
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
Nov 21 at 7:23
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3005797%2fbeta-reduction-order-of-substitution%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
Nov 21 at 7:23