[Agda] help explaining instance resolution

[Martin Stone Davis]

...which is now here 
<https://stackoverflow.com/questions/43195079/how-does-adding-an-instance-parameter-help-instance-search>.


On 04/03/2017 12:33 AM, Martin Stone Davis wrote:
> I realised just now that this question is probably more appropriately 
> posted on stackoverflow, so I'll post it there (after I check to see 
> if someone has already answered a similar question).
>
>
> On 04/01/2017 11:12 PM, Martin Stone Davis wrote:
>> {- Can someone explain why test2 succeeds but test1 fails (with 
>> unsolved metas & constraints)? How does the addition of the ⦃ 
>> isRelation ⦄ parameter to IsSymmetric2 help? I figure it must somehow 
>> have to do with some metas getting solved, therefore allowing 
>> instance search to succeed, but beyond that I'm quite foggy. -}
>>
>> {-# OPTIONS --show-implicit #-}
>>
>> record IsSymmetric1 {A : Set} (F : A → A → A) (Q : A → A → Set) : Set 
>> where
>>   field
>>     symmetry1 : ∀ {x y} → Q (F x y) (F y x)
>>
>> open IsSymmetric1 ⦃ … ⦄
>>
>> record IsRelation {A : Set} (Q : A → A → Set) : Set where
>>   no-eta-equality
>>
>> record IsSymmetric2 {A : Set} (F : A → A → A) (Q : A → A → Set) ⦃ 
>> isRelation : IsRelation Q ⦄ : Set where
>>   field
>>     symmetry2 : ∀ {x y} → Q (F x y) (F y x)
>>
>> open IsSymmetric2 ⦃ … ⦄
>>
>> postulate
>>   B : Set
>>   G : B → B → B
>>   R : B → B → Set
>>   instance I-IsSymmetric1 : IsSymmetric1 {B} G R
>>   instance I-IsRelation : IsRelation R
>>   instance I-IsSymmetric2 : IsSymmetric2 {B} G R
>>
>> test1 : ∀ {x y} → R (G x y) (G y x)
>> test1 = symmetry1 -- yellow unless {F = G} or {Q = R} is specified
>> {-
>> _A_39 : Set  [ at ….agda:29,9-18 ]
>> _F_40 : _A_39 {.x} {.y} → _A_39 {.x} {.y} → _A_39 {.x} {.y}  [ at 
>> ….agda:29,9-18 ]
>> _Q_41 : _A_39 {.x} {.y} → _A_39 {.x} {.y} → Set  [ at ….agda:29,9-18 ]
>> _r_42 : IsSymmetric1 {_A_39 {.x} {.y}} (_F_40 {.x} {.y}) (_Q_41 {.x} 
>> {.y})  [ at ….agda:29,9-18 ]
>> _x_43 : _A_39 {.x} {.y}  [ at ….agda:29,9-18 ]
>> _y_44 : _A_39 {.x} {.y}  [ at ….agda:29,9-18 ]
>> _45 : R (G .x .y) (G .y .x)  [ at ….agda:29,9-18 ]
>> _46 : R (G .x .y) (G .y .x)  [ at ….agda:29,9-18 ]
>>
>> ———— Errors ————————————————————————————————————————————————
>> Failed to solve the following constraints:
>>   Resolve instance argument
>>     _42 :
>>       {.x .y : B} →
>>       IsSymmetric1 {_A_39 {.x} {.y}} (_F_40 {.x} {.y}) (_Q_41 {.x} {.y})
>>   Candidates I-IsSymmetric1 : IsSymmetric1 {B} G R
>>   [55] _Q_41 {.x} {.y}
>>        (_F_40 {.x} {.y} (_x_43 {.x} {.y}) (_y_44 {.x} {.y}))
>>        (_F_40 {.x} {.y} (_y_44 {.x} {.y}) (_x_43 {.x} {.y}))
>>        =< R (G .x .y) (G .y .x)
>>          : Set
>>   _45 :=
>>     λ {.x} {.y} →
>>       IsSymmetric1.symmetry1 (_r_42 {.x} {.y}) {_x_43 {.x} {.y}}
>>       {_y_44 {.x} {.y}}
>>     [blocked on problem 55]
>> -}
>>
>> test2 : ∀ {x y} → R (G x y) (G y x)
>> test2 = symmetry2
>>
>

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