lean4-htt/tests/lean/unification_hints1.lean.expected.out
Leonardo de Moura 5cef84709f refactor(library): avoid auxiliary definitions such as add/mul/le/etc
See Section "Other goodies" at
https://github.com/leanprover/lean/wiki/Refactoring-structures

This commit also improves the support for projections in the
unifier/matcher.

Now, we consider the extra case-split for projections.
Given a projection `proj`, and the constraint `proj s =?= proj t`, we need to try first `s =?= t` and if it fails, then try to reduce.
This is needed in the standard library because we now have constraints such as:
```
@has_le.le ?A ?s ?a ?b  =?=  @has_le.le nat nat.has_add x y
```
If we reduce the right hand side, we get the unsolvable constraint
```
@has_le.le ?A ?s ?a ?b  =?=  nat.le x y
```
Before this change, the constraint was `@le ?A ?s ?a ?b  =?=  @le nat nat.has_add x y`, and we already perform a case-split in this case.
Moreover, projections were eagerly reduced whenever possible.
The extra case-split generates a performance problem in several tests. For example `fib 8 = 34` was timing out.
I worked around this issue by performing the case-split only when the constraint contains meta-variables.
There are also minor issues. Example. `<` is notation for `has_lt.lt`, but `>` is for `gt`.
2017-05-01 08:52:19 -07:00

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Text

g x y =?= f z
unification failed
g x y =?= f z
g x y =?= f z
unification successful
unification hints:
(has_add.add, nat.succ) #2 + succ #1 =?= succ #0 {#0 =?= #2 + #1}
(toy.f, toy.g) f z =?= g #1 #0 {}
Canonical.carrier A_canonical =?= A
unification failed
Canonical.carrier A_canonical =?= A
Canonical.carrier A_canonical =?= A
unification successful
unification hints:
(has_add.add, nat.succ) #2 + succ #1 =?= succ #0 {#0 =?= #2 + #1}
(toy.f, toy.g) toy.f toy.z =?= toy.g #1 #0 {}
(canonical.A, canonical.Canonical.carrier) A =?= Canonical.carrier #0 {#0 =?= A_canonical}