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
23317
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
23317
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
yesterday
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
23317
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
23317
asked Nov 20 at 1:22
Matt
23317
asked Nov 20 at 1:22
Matt
23317
asked Nov 20 at 1:22
Matt
23317
asked Nov 20 at 1:22
Matt
23317
23317
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
yesterday
add a comment |
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
yesterday
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
yesterday
I don't see a difference between the two terms besides the dot, which has no meaning.
– Couchy311
yesterday
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
yesterday