Add support for inductively defined functions

[stevenraphael]

Following substantial discussion with Andrew Adams and Alex Reinking, I have implemented a first draft of their idea of inductively defined functions. A full description is in src/Inductive.h. This pull includes correctness and error tests. Please suggest any additional changes I need to make. The basic idea is to have pure functions that are defined with self-references, e.g. f(x) = select(x <= 0, input(0), input(x) + f(x - 1)), which allows for optimizations that are currently impossible to do with reduction domains.

[zvookin]

Given the constraints on the definition, I'm wondering if this should be its own syntax. E.g. f(x) = inductive(cond, expr1, expr2) Could also try to put it all in the construction, similar to how RDom is done, but given the arguments need to be specified, function definition syntax seems better.

Main goal is to avoid confusion around the lack of generality in the definition. If it is envisioned that this will become more general, the current design might be the right way to go. (And by confusion, I mean that this makes it look like normal programming language recursion expectations are supported.)

[abadams]

The goal is definitely to become more general over time. The thinking was that if we fail to solve for a base case, we could tell the user to write things in a particular form that is known to work, but first we'd try to handle any recursive RHS.

[alexreinking]

We are likely to merge #8877 before this, so consider using the new APIs to simplify visitors/mutators here. I see two here: RecursiveHelper in is_inductive, and maybe BaseCaseSolver as it has just one visit overload.

[codecov]

Codecov Report

❌ Patch coverage is 65.14523% with 84 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (main@7e2ecf2). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/Function.cpp	69.38%	19 Missing and 11 partials ⚠️
src/IROperator.cpp	35.13%	11 Missing and 13 partials ⚠️
src/Inductive.cpp	77.77%	9 Missing and 5 partials ⚠️
src/Func.cpp	54.54%	1 Missing and 4 partials ⚠️
src/IRPrinter.cpp	0.00%	4 Missing and 1 partial ⚠️
src/Schedule.h	0.00%	2 Missing ⚠️
src/Type.h	50.00%	2 Missing ⚠️
src/BoundsInference.cpp	87.50%	0 Missing and 1 partial ⚠️
src/ScheduleFunctions.cpp	75.00%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #8878   +/-   ##
=======================================
  Coverage        ?   69.24%           
=======================================
  Files           ?      255           
  Lines           ?    78436           
  Branches        ?    18782           
=======================================
  Hits            ?    54316           
  Misses          ?    18532           
  Partials        ?     5588           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.