1311e36a98
This adds support for mutual structural recursive functions. For now this is opt-in: The functions must have a `termination_by structural …` annotation (new since #4542) for this to work: ```lean mutual inductive A | self : A → A | other : B → A | empty inductive B | self : B → B | other : A → B | empty end mutual def A.size : A → Nat | .self a => a.size + 1 | .other b => b.size + 1 | .empty => 0 termination_by structural x => x def B.size : B → Nat | .self b => b.size + 1 | .other a => a.size + 1 | .empty => 0 termination_by structural x => x end ``` The recursive functions don’t have to be in a one-to-one relation to a set of mutually recursive inductive data types. It is possible to ignore some of the types: ```lean def A.self_size : A → Nat | .self a => a.self_size + 1 | .other _ => 0 | .empty => 0 termination_by structural x => x ``` or have more than one function per argument type: ```lean def isEven : Nat → Prop | 0 => True | n+1 => ¬ isOdd n termination_by structural x => x def isOdd : Nat → Prop | 0 => False | n+1 => ¬ isEven n termination_by structural x => x ``` This does not include * Support for nested inductive data types or nested recursion * Inferring mutual structural recursion in the absence of `termination_by`. * Functional induction principles for these. * Mutually recursive functions that live in different universes. This may be possible, maybe after beefing up the `.below` and `.brecOn` functions; we can look into this some other time, maybe when there are concrete use cases. --------- Co-authored-by: Richard Kiss <him@richardkiss.com> Co-authored-by: Tobias Grosser <tobias@grosser.es>
20 lines
478 B
Text
20 lines
478 B
Text
set_option linter.constructorNameAsVariable false
|
|
|
|
inductive A (n : Nat) : Type
|
|
| a : A n
|
|
| b : A n → A n
|
|
|
|
/--
|
|
error: its type is an inductive datatype
|
|
A n
|
|
and the datatype parameter
|
|
n
|
|
depends on the function parameter
|
|
n
|
|
which does not come before the varying parameters and before the indices of the recursion parameter.
|
|
-/
|
|
#guard_msgs in
|
|
def A.size (acc n : Nat) : A n → Nat
|
|
| .a => acc
|
|
| .b a' => 1 + A.size (acc + 1) n a'
|
|
termination_by structural a => a
|