How to define a recursive function in the (pure) calculus of constructions? I do not see any fixpoint combinator there.
Recursion in the calculus of construction
389 Views Asked by Bob At
1
There are 1 best solutions below
Related Questions in RECURSION
- Angular Show All When No Filter Is Supplied
- Why does a function show up as not defined
- I count the time the user takes to solve my quiz using Javascript but I want the same time displayed on another page
- Set "More" "Less" font size
- Using pagination on a table in AngularJS
- How to sort these using Javascript or Jquery Most effectively
- how to fill out the table with next values in array with one button
- State with different subviews
- Ajax jQuery firing multiple time display event for the same result
- Getting and passing MVC Model data to AngularJS controller
Related Questions in FUNCTIONAL-PROGRAMMING
- Angular Show All When No Filter Is Supplied
- Why does a function show up as not defined
- I count the time the user takes to solve my quiz using Javascript but I want the same time displayed on another page
- Set "More" "Less" font size
- Using pagination on a table in AngularJS
- How to sort these using Javascript or Jquery Most effectively
- how to fill out the table with next values in array with one button
- State with different subviews
- Ajax jQuery firing multiple time display event for the same result
- Getting and passing MVC Model data to AngularJS controller
Related Questions in COQ
- Angular Show All When No Filter Is Supplied
- Why does a function show up as not defined
- I count the time the user takes to solve my quiz using Javascript but I want the same time displayed on another page
- Set "More" "Less" font size
- Using pagination on a table in AngularJS
- How to sort these using Javascript or Jquery Most effectively
- how to fill out the table with next values in array with one button
- State with different subviews
- Ajax jQuery firing multiple time display event for the same result
- Getting and passing MVC Model data to AngularJS controller
Related Questions in LAMBDA-CALCULUS
- Angular Show All When No Filter Is Supplied
- Why does a function show up as not defined
- I count the time the user takes to solve my quiz using Javascript but I want the same time displayed on another page
- Set "More" "Less" font size
- Using pagination on a table in AngularJS
- How to sort these using Javascript or Jquery Most effectively
- how to fill out the table with next values in array with one button
- State with different subviews
- Ajax jQuery firing multiple time display event for the same result
- Getting and passing MVC Model data to AngularJS controller
Related Questions in TYPED-LAMBDA-CALCULUS
- Angular Show All When No Filter Is Supplied
- Why does a function show up as not defined
- I count the time the user takes to solve my quiz using Javascript but I want the same time displayed on another page
- Set "More" "Less" font size
- Using pagination on a table in AngularJS
- How to sort these using Javascript or Jquery Most effectively
- how to fill out the table with next values in array with one button
- State with different subviews
- Ajax jQuery firing multiple time display event for the same result
- Getting and passing MVC Model data to AngularJS controller
Trending Questions
- UIImageView Frame Doesn't Reflect Constraints
- Is it possible to use adb commands to click on a view by finding its ID?
- How to create a new web character symbol recognizable by html/javascript?
- Why isn't my CSS3 animation smooth in Google Chrome (but very smooth on other browsers)?
- Heap Gives Page Fault
- Connect ffmpeg to Visual Studio 2008
- Both Object- and ValueAnimator jumps when Duration is set above API LvL 24
- How to avoid default initialization of objects in std::vector?
- second argument of the command line arguments in a format other than char** argv or char* argv[]
- How to improve efficiency of algorithm which generates next lexicographic permutation?
- Navigating to the another actvity app getting crash in android
- How to read the particular message format in android and store in sqlite database?
- Resetting inventory status after order is cancelled
- Efficiently compute powers of X in SSE/AVX
- Insert into an external database using ajax and php : POST 500 (Internal Server Error)
Popular # Hahtags
Popular Questions
- How do I undo the most recent local commits in Git?
- How can I remove a specific item from an array in JavaScript?
- How do I delete a Git branch locally and remotely?
- Find all files containing a specific text (string) on Linux?
- How do I revert a Git repository to a previous commit?
- How do I create an HTML button that acts like a link?
- How do I check out a remote Git branch?
- How do I force "git pull" to overwrite local files?
- How do I list all files of a directory?
- How to check whether a string contains a substring in JavaScript?
- How do I redirect to another webpage?
- How can I iterate over rows in a Pandas DataFrame?
- How do I convert a String to an int in Java?
- Does Python have a string 'contains' substring method?
- How do I check if a string contains a specific word?
People in the CS stack exchange might be able to provide some more insight, but here is an attempt.
Inductive data types are defined in the calculus of constructions with a Church encoding: the data type is the type of its fold function. The most basic example are the natural numbers, which are defined as follows, using a Coq-like notation:
This encoding yields two things: (1) terms
zero : nat
andsucc : nat -> nat
for constructing natural numbers, and (2) an operatornat_rec
for writing recursive functions.If we pose
F := nat_rec T x f
for termsx : T
andf : T -> T
, we see that the following equations are valid:Thus,
nat_rec
allows us to define recursive functions by specifying a return valuex
for the base case, and a functionf
to process the value of the recursive call. Note that this does not allow us to define arbitrary recursive functions on the natural numbers, but only those that perform recursive calls on the predecessor of their argument. Allowing arbitrary recursion would open the door to partial functions, which would compromise the soundness of the calculus.This example can be generalized to other inductive data types. For instance, we can define the type of lists of natural numbers as the type of their fold right function: