HERMIT has some code for building dictionaries for a given predicate type (by invoking the typechecker functions that do this): https://github.com/ku-fpg/hermit/blob/master/src/HERMIT/Dictionary/GHC.hs#L2... The functions to run TcM computations inside CoreM are here: https://github.com/ku-fpg/hermit/blob/master/src/HERMIT/Monad.hs#L242 and https://github.com/ku-fpg/hermit/blob/master/src/HERMIT/GHC/Typechecker.hs#L... Perhaps that will help get you started? I would like to push these interfaces back into the GHC API at some point, but just haven't done it yet. HTH Andrew On Mon, Aug 17, 2015 at 4:12 PM, Mike Izbicki wrote:

I'm not sure how either of those two functions can help me. The problem is that given an operator (e.g. `+`), I don't know the name of the dictionary that needs to be passed in as the first argument to the operator. I could probably hard code these names, but then the plugin wouldn't be able to work with alternative preludes.

On Fri, Aug 7, 2015 at 11:20 PM, Edward Z. Yang wrote:

...

Hello Mike,

Give importDecl from LoadIface a try, or maybe tcLookupGlobal if you're in TcM.

Edward

Excerpts from Mike Izbicki's message of 2015-08-07 15:40:30 -0700:

...

I'm trying to write a GHC plugin. The purpose of the plugin is to provide Haskell bindings to Herbie. Herbie (https://github.com/uwplse/herbie) is a program that takes a mathematical statement as input, and gives you a numerically stable formula to compute it as output. The plugin is supposed to automate this process for Haskell programs.

I can convert the core expressions into a format for Herbie just fine. Where I'm having trouble is converting the output from Herbie back into core. Given a string that represents a numeric operator (e.g. "log" or "+"), I can get that converted into a Name that matches the Name of the version of that operator in scope at the location. But in order to create an Expr, I need to convert the Name into a Var. All the functions that I can find for this (e.g. mkGlobalVar) also require the type of the variable. But I can't find a way to figure out the Type given a Name. How can I do this?

---

ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

The `buildDictionary` function takes a Var with a dictionary type, and builds the expression which implements that dictionary. For instance, you might create a new Var: x :: Num Float and pass that to buildDictionary. It will return: (x, [NonRec x $fNumFloat]) which you could blindly turn into: let x = $fNumFloat in x or you could do what buildDictionaryT (a bit further down in the same module), and spot that case and just return $fNumFloat directly. (The list can have more than one element in the case that dictionaries are built in terms of other dictionaries.) Thus, you've built a dictionary expression of type Num Float. As I understand it, you want to pass something 'log' and get back the dictionary argument. You'll need to choose a type (like Float), but once that is done, it should be easy to use buildDictionary to build the dictionary arguments... just take apart the type of 'log @ Float', make a new Var with the argument type, build a dictionary expression, and apply it. On Thu, Aug 20, 2015 at 5:05 PM, Mike Izbicki wrote:

I'm pretty sure the `buildDictionary` function doesn't do what I need. AFAICT, you pass it a `Var` which contains a dictionary, and it tells you what is in that dictionary. What I need is a function with type `Var -> Var` where the first `Var` contains a function, and the output `Var` is the dictionary.

For example, given the expression:

log (a1+a2)

In core, this might look like:

log @ Float $fFloatingFloat (+ @ Float $fNumFloat a1 a2)

I want to mechanically construct the core code above. When doing so, each function within a type class has an extra argument, which is the dictionary for that type class. `log` no longer takes one parameter; in core, it takes two. I'm having trouble figuring out how to get the appropriate dictionary to pass as the "dictionary parameter" to these functions.

On Mon, Aug 17, 2015 at 4:21 PM, Andrew Farmer wrote:

...

HERMIT has some code for building dictionaries for a given predicate type (by invoking the typechecker functions that do this):

https://github.com/ku-fpg/hermit/blob/master/src/HERMIT/Dictionary/GHC.hs#L2...

The functions to run TcM computations inside CoreM are here:

https://github.com/ku-fpg/hermit/blob/master/src/HERMIT/Monad.hs#L242 and https://github.com/ku-fpg/hermit/blob/master/src/HERMIT/GHC/Typechecker.hs#L...

Perhaps that will help get you started?

I would like to push these interfaces back into the GHC API at some point, but just haven't done it yet.

HTH Andrew

On Mon, Aug 17, 2015 at 4:12 PM, Mike Izbicki wrote:

...

I'm not sure how either of those two functions can help me. The problem is that given an operator (e.g. `+`), I don't know the name of the dictionary that needs to be passed in as the first argument to the operator. I could probably hard code these names, but then the plugin wouldn't be able to work with alternative preludes.

On Fri, Aug 7, 2015 at 11:20 PM, Edward Z. Yang wrote:

...

Hello Mike,

Give importDecl from LoadIface a try, or maybe tcLookupGlobal if you're in TcM.

Edward

Excerpts from Mike Izbicki's message of 2015-08-07 15:40:30 -0700:

...

I'm trying to write a GHC plugin. The purpose of the plugin is to provide Haskell bindings to Herbie. Herbie (https://github.com/uwplse/herbie) is a program that takes a mathematical statement as input, and gives you a numerically stable formula to compute it as output. The plugin is supposed to automate this process for Haskell programs.

I can convert the core expressions into a format for Herbie just fine. Where I'm having trouble is converting the output from Herbie back into core. Given a string that represents a numeric operator (e.g. "log" or "+"), I can get that converted into a Name that matches the Name of the version of that operator in scope at the location. But in order to create an Expr, I need to convert the Name into a Var. All the functions that I can find for this (e.g. mkGlobalVar) also require the type of the variable. But I can't find a way to figure out the Type given a Name. How can I do this?

---

ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

I have a new question: I'm working on supporting literals now. I'm having trouble creating something that looks like `(App (Var F#) (Lit 1.0))` because I don't know how to create a variable that corresponds to the `F#` constructor. The mkWiredInName function looks promising, but overly complicated. Is this the correct function? If so, what do I pass in for the Module, Unique, TyThing, and BuiltInSyntax parameters?

mkConApp intDataCon [mkIntLit dynFlags PUT_YOUR_INTEGER HERE] mkConApp floatDataCon [mkFloatLit dynFlags PUT_YOUR_FLOAT_HERE] Similarly for other literals...

I'm not positive, but I believe each dictionary has a field for its superclass dictionary. So if you have a dictionary for `Floating Float`, one of the fields will be the `Num Float` dictionary. How to get the projector function for the field... I'm not sure. But perhaps you can find it by type? On Mon, Aug 24, 2015 at 2:42 PM, Mike Izbicki wrote:

Thanks! Now one more question :)

The code Andrew Farmer showed me for getting dictionaries works great when I have a concrete type (e.g. Float) I want a dictionary for. But now I'm working on polymorphic code and running into a problem.

Lets say I'm running the plugin on a function with signature `Floating a => a -> a`, then the plugin has access to the `Floating` dictionary for the type. But if I want to add two numbers together, I need the `Num` dictionary. I know I should have access to `Num` since it's a superclass of `Floating`. How can I get access to these superclass dictionaries?

On Sat, Aug 22, 2015 at 7:35 AM, Ömer Sinan Ağacan wrote:

...

...

I have a new question: I'm working on supporting literals now. I'm having trouble creating something that looks like `(App (Var F#) (Lit 1.0))` because I don't know how to create a variable that corresponds to the `F#` constructor. The mkWiredInName function looks promising, but overly complicated. Is this the correct function? If so, what do I pass in for the Module, Unique, TyThing, and BuiltInSyntax parameters?

mkConApp intDataCon [mkIntLit dynFlags PUT_YOUR_INTEGER HERE] mkConApp floatDataCon [mkFloatLit dynFlags PUT_YOUR_FLOAT_HERE]

Similarly for other literals...

---

ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs

Mike, here's a piece of code that may be helpful to you: https://github.com/osa1/sc-plugin/blob/master/src/Supercompilation/Show.hs Copy this module to your plugin, it doesn't have any dependencies other than ghc itself. When your plugin is initialized, update `dynFlags_ref` with your DynFlags as first thing to do. Then use Show instance to print AST directly. Horrible hack, but very useful for learning purposes. In fact, I don't know how else we can learn what Core is generated for a given code, and reverse-engineer to figure out details. Hope it helps. 2015-08-24 21:59 GMT-04:00 Ömer Sinan Ağacan :

...

Lets say I'm running the plugin on a function with signature `Floating a => a -> a`, then the plugin has access to the `Floating` dictionary for the type. But if I want to add two numbers together, I need the `Num` dictionary. I know I should have access to `Num` since it's a superclass of `Floating`. How can I get access to these superclass dictionaries?

I don't have a working code for this but this should get you started:

let ord_dictionary :: Id = ... ord_class :: Class = ... in mkApps (Var (head (classSCSels ord_class))) [Var ord_dictionary]

I don't know how to get Class for Ord. I do `head` here because in the case of Ord we only have one superclass so `classSCSels` should have one Id. Then I apply ord_dictionary to this selector and it should return dictionary for Eq.

I assumed you already have ord_dictionary, it should be passed to your function already if you had `(Ord a) => ` in your function.

Now I realized you asked for getting Num from Floating. I think you should follow a similar path except you need two applications, first to get Fractional from Floating and second to get Num from Fractional:

mkApps (Var (head (classSCSels fractional_class))) [mkApps (Var (head (classSCSels floating_class))) [Var floating_dictionary]]

Return value should be a Num dictionary.

It seems like in your App syntax you're having a non-function in function position. You can see this by looking at what failing function (splitFunTy_maybe) is doing: splitFunTy_maybe :: Type -> Maybe (Type, Type) -- ^ Attempts to extract the argument and result types from a type ... (definition is not important) ... Then it's used like this at the error site: (arg_ty, res_ty) = expectJust "cpeBody:collect_args" $ splitFunTy_maybe fun_ty In your case this function is returning Nothing and then exceptJust is signalling the panic. Your code looked correct to me, I don't see any problems with that. Maybe you're using something wrong as selectors. Could you paste CoreExpr representation of your program? It may also be the case that the panic is caused by something else, maybe your syntax is invalidating some assumptions/invariants in GHC but it's not immediately checked etc. Working at the Core level is frustrating at times. Can I ask what kind of plugin are you working on? (Btw, how did you generate this representation of AST? Did you write it manually? If you have a pretty-printer, would you mind sharing it?) 2015-08-25 18:50 GMT-04:00 Mike Izbicki :

Thanks Ömer!

I'm able to get dictionaries for the superclasses of a class now, but I get an error whenever I try to get a dictionary for a super-superclass. Here's the Haskell expression I'm working with:

test1 :: Floating a => a -> a test1 x1 = x1+x1

The original core is:

+ @ a $dNum_aJu x1 x1

But my plugin is replacing it with the core:

+ @ a ($p1Fractional ($p1Floating $dFloating_aJq)) x1 x1

The only difference is the way I'm getting the Num dictionary. The corresponding AST (annotated with variable names and types) is:

App (App (App (App (Var +::forall a. Num a => a -> a -> a) (Type a) ) (App (Var $p1Fractional::forall a. Fractional a => Num a) (App (Var $p1Floating::forall a. Floating a => Fractional a) (Var $dFloating_aJq::Floating a) ) ) ) (Var x1::'a') ) (Var x1::'a')

When I insert, GHC gives the following error:

ghc: panic! (the 'impossible' happened) (GHC version 7.10.1 for x86_64-unknown-linux): expectJust cpeBody:collect_args

What am I doing wrong with extracting these super-superclass dictionaries? I've looked up the code for cpeBody in GHC, but I can't figure out what it's trying to do, so I'm not sure why it's failing on my core.

On Mon, Aug 24, 2015 at 7:10 PM, Ömer Sinan Ağacan wrote:

...

Mike, here's a piece of code that may be helpful to you:

https://github.com/osa1/sc-plugin/blob/master/src/Supercompilation/Show.hs

Copy this module to your plugin, it doesn't have any dependencies other than ghc itself. When your plugin is initialized, update `dynFlags_ref` with your DynFlags as first thing to do. Then use Show instance to print AST directly.

Horrible hack, but very useful for learning purposes. In fact, I don't know how else we can learn what Core is generated for a given code, and reverse-engineer to figure out details.

Hope it helps.

2015-08-24 21:59 GMT-04:00 Ömer Sinan Ağacan :

...

...

Lets say I'm running the plugin on a function with signature `Floating a => a -> a`, then the plugin has access to the `Floating` dictionary for the type. But if I want to add two numbers together, I need the `Num` dictionary. I know I should have access to `Num` since it's a superclass of `Floating`. How can I get access to these superclass dictionaries?

I don't have a working code for this but this should get you started:

let ord_dictionary :: Id = ... ord_class :: Class = ... in mkApps (Var (head (classSCSels ord_class))) [Var ord_dictionary]

I don't know how to get Class for Ord. I do `head` here because in the case of Ord we only have one superclass so `classSCSels` should have one Id. Then I apply ord_dictionary to this selector and it should return dictionary for Eq.

I assumed you already have ord_dictionary, it should be passed to your function already if you had `(Ord a) => ` in your function.

Now I realized you asked for getting Num from Floating. I think you should follow a similar path except you need two applications, first to get Fractional from Floating and second to get Num from Fractional:

mkApps (Var (head (classSCSels fractional_class))) [mkApps (Var (head (classSCSels floating_class))) [Var floating_dictionary]]

Return value should be a Num dictionary.

I'm still having trouble creating Core code that can extract superclass dictionaries from a given dictionary. I suspect the problem is that I don't actually understand what the Core code to do this is supposed to look like. I keep getting the errors mentioned above when I try what I think should work. Can anyone help me figure this out? Is there any chance this is a bug in how GHC parses Core? On Tue, Aug 25, 2015 at 9:24 PM, Mike Izbicki wrote:

The purpose of the plugin is to automatically improve the numerical stability of Haskell code. It is supposed to identify numeric expressions, then use Herbie (https://github.com/uwplse/herbie) to generate a numerically stable version, then rewrite the numerically stable version back into the code. The first two steps were really easy. It's the last step of inserting back into the code that I'm having tons of trouble with. Core is a lot more complicated than I thought :)

I'm not sure what you mean by the CoreExpr representation? Here's the output of the pretty printer you gave: App (App (App (App (Var Id{+,r2T,ForAllTy TyVar{a} (FunTy (TyConApp Num [TyVarTy TyVar{a}]) (FunTy (TyVarTy TyVar{a}) (FunTy (TyVarTy TyVar{a}) (TyVarTy TyVar{a})))),VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (Type (TyVarTy TyVar{a}))) (App (Var Id{$p1Fractional,rh3,ForAllTy TyVar{a} (FunTy (TyConApp Fractional [TyVarTy TyVar{a}]) (TyConApp Num [TyVarTy TyVar{a}])),ClassOpId <Class>,Info{1,SpecInfo [BuiltinRule {ru_name = "Class op $p1Fractional", ru_fn = $p1Fractional, ru_nargs = 2, ru_try = <RuleFun>}] <UniqFM>,NoUnfolding,NoCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [JD {strd = Str (SProd [Str HeadStr,Lazy,Lazy,Lazy]), absd = Use Many (UProd [Use Many Used,Abs,Abs,Abs])}] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (App (Var Id{$p1Floating,rh2,ForAllTy TyVar{a} (FunTy (TyConApp Floating [TyVarTy TyVar{a}]) (TyConApp Fractional [TyVarTy TyVar{a}])),ClassOpId <Class>,Info{1,SpecInfo [BuiltinRule {ru_name = "Class op $p1Floating", ru_fn = $p1Floating, ru_nargs = 2, ru_try = <RuleFun>}] <UniqFM>,NoUnfolding,NoCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [JD {strd = Str (SProd [Str HeadStr,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy]), absd = Use Many (UProd [Use Many Used,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs])}] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (Var Id{$dFloating,aBM,TyConApp Floating [TyVarTy TyVar{a}],VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})))) (Var Id{x1,anU,TyVarTy TyVar{a},VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})) (Var Id{x1,anU,TyVarTy TyVar{a},VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})

You can find my pretty printer (and all the other code for the plugin) at: https://github.com/mikeizbicki/herbie-haskell/blob/master/src/Herbie.hs#L627

The function getDictMap (https://github.com/mikeizbicki/herbie-haskell/blob/master/src/Herbie.hs#L171) is where I'm constructing the dictionaries that are getting inserted back into the Core.

On Tue, Aug 25, 2015 at 7:17 PM, Ömer Sinan Ağacan wrote:

...

It seems like in your App syntax you're having a non-function in function position. You can see this by looking at what failing function (splitFunTy_maybe) is doing:

splitFunTy_maybe :: Type -> Maybe (Type, Type) -- ^ Attempts to extract the argument and result types from a type ... (definition is not important) ...

Then it's used like this at the error site:

(arg_ty, res_ty) = expectJust "cpeBody:collect_args" $ splitFunTy_maybe fun_ty

In your case this function is returning Nothing and then exceptJust is signalling the panic.

Your code looked correct to me, I don't see any problems with that. Maybe you're using something wrong as selectors. Could you paste CoreExpr representation of your program?

It may also be the case that the panic is caused by something else, maybe your syntax is invalidating some assumptions/invariants in GHC but it's not immediately checked etc. Working at the Core level is frustrating at times.

Can I ask what kind of plugin are you working on?

(Btw, how did you generate this representation of AST? Did you write it manually? If you have a pretty-printer, would you mind sharing it?)

2015-08-25 18:50 GMT-04:00 Mike Izbicki :

...

Thanks Ömer!

I'm able to get dictionaries for the superclasses of a class now, but I get an error whenever I try to get a dictionary for a super-superclass. Here's the Haskell expression I'm working with:

test1 :: Floating a => a -> a test1 x1 = x1+x1

The original core is:

+ @ a $dNum_aJu x1 x1

But my plugin is replacing it with the core:

+ @ a ($p1Fractional ($p1Floating $dFloating_aJq)) x1 x1

The only difference is the way I'm getting the Num dictionary. The corresponding AST (annotated with variable names and types) is:

App (App (App (App (Var +::forall a. Num a => a -> a -> a) (Type a) ) (App (Var $p1Fractional::forall a. Fractional a => Num a) (App (Var $p1Floating::forall a. Floating a => Fractional a) (Var $dFloating_aJq::Floating a) ) ) ) (Var x1::'a') ) (Var x1::'a')

When I insert, GHC gives the following error:

ghc: panic! (the 'impossible' happened) (GHC version 7.10.1 for x86_64-unknown-linux): expectJust cpeBody:collect_args

What am I doing wrong with extracting these super-superclass dictionaries? I've looked up the code for cpeBody in GHC, but I can't figure out what it's trying to do, so I'm not sure why it's failing on my core.

On Mon, Aug 24, 2015 at 7:10 PM, Ömer Sinan Ağacan wrote:

...

Mike, here's a piece of code that may be helpful to you:

https://github.com/osa1/sc-plugin/blob/master/src/Supercompilation/Show.hs

Copy this module to your plugin, it doesn't have any dependencies other than ghc itself. When your plugin is initialized, update `dynFlags_ref` with your DynFlags as first thing to do. Then use Show instance to print AST directly.

Horrible hack, but very useful for learning purposes. In fact, I don't know how else we can learn what Core is generated for a given code, and reverse-engineer to figure out details.

Hope it helps.

2015-08-24 21:59 GMT-04:00 Ömer Sinan Ağacan :

...

...

Lets say I'm running the plugin on a function with signature `Floating a => a -> a`, then the plugin has access to the `Floating` dictionary for the type. But if I want to add two numbers together, I need the `Num` dictionary. I know I should have access to `Num` since it's a superclass of `Floating`. How can I get access to these superclass dictionaries?

I don't have a working code for this but this should get you started:

let ord_dictionary :: Id = ... ord_class :: Class = ... in mkApps (Var (head (classSCSels ord_class))) [Var ord_dictionary]

I don't know how to get Class for Ord. I do `head` here because in the case of Ord we only have one superclass so `classSCSels` should have one Id. Then I apply ord_dictionary to this selector and it should return dictionary for Eq.

I assumed you already have ord_dictionary, it should be passed to your function already if you had `(Ord a) => ` in your function.

Now I realized you asked for getting Num from Floating. I think you should follow a similar path except you need two applications, first to get Fractional from Floating and second to get Num from Fractional:

mkApps (Var (head (classSCSels fractional_class))) [mkApps (Var (head (classSCSels floating_class))) [Var floating_dictionary]]

Return value should be a Num dictionary.

Typo: "You're parsing your code" I mean "You're passing your code" 2015-09-05 0:16 GMT-04:00 Ömer Sinan Ağacan :

Hi Mike,

I'll try to hack an example for you some time tomorrow(I'm returning from ICFP and have some long flights ahead of me).

But in the meantime, here's a working Core code, generated by GHC:

f_rjH :: forall a_alz. Ord a_alz => a_alz -> Bool f_rjH = \ (@ a_aCH) ($dOrd_aCI :: Ord a_aCH) (eta_B1 :: a_aCH) -> == @ a_aCH (GHC.Classes.$p1Ord @ a_aCH $dOrd_aCI) eta_B1 eta_B1

You can clearly see here how Eq dictionary is selected from Ord dicitonary($dOrd_aCI in the example), it's just an application of selector to type and dictionary, that's all.

This is generated from this code:

{-# NOINLINE f #-} f :: Ord a => a -> Bool f x = x == x

Compile it with this:

ghc --make -fforce-recomp -O0 -ddump-simpl -ddump-to-file Main.hs -dsuppress-idinfo

...

Can anyone help me figure this out? Is there any chance this is a bug in how GHC parses Core?

This seems unlikely, because GHC doesn't have a Core parser and there's no Core parsing going on here, you're parsing your Code in the form of AST(CoreExpr, CoreProgram etc. defined in CoreSyn.hs). Did you mean something else and am I misunderstanding?

2015-09-04 19:39 GMT-04:00 Mike Izbicki :

...

I'm still having trouble creating Core code that can extract superclass dictionaries from a given dictionary. I suspect the problem is that I don't actually understand what the Core code to do this is supposed to look like. I keep getting the errors mentioned above when I try what I think should work.

Can anyone help me figure this out? Is there any chance this is a bug in how GHC parses Core?

On Tue, Aug 25, 2015 at 9:24 PM, Mike Izbicki wrote:

...

The purpose of the plugin is to automatically improve the numerical stability of Haskell code. It is supposed to identify numeric expressions, then use Herbie (https://github.com/uwplse/herbie) to generate a numerically stable version, then rewrite the numerically stable version back into the code. The first two steps were really easy. It's the last step of inserting back into the code that I'm having tons of trouble with. Core is a lot more complicated than I thought :)

I'm not sure what you mean by the CoreExpr representation? Here's the output of the pretty printer you gave: App (App (App (App (Var Id{+,r2T,ForAllTy TyVar{a} (FunTy (TyConApp Num [TyVarTy TyVar{a}]) (FunTy (TyVarTy TyVar{a}) (FunTy (TyVarTy TyVar{a}) (TyVarTy TyVar{a})))),VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (Type (TyVarTy TyVar{a}))) (App (Var Id{$p1Fractional,rh3,ForAllTy TyVar{a} (FunTy (TyConApp Fractional [TyVarTy TyVar{a}]) (TyConApp Num [TyVarTy TyVar{a}])),ClassOpId <Class>,Info{1,SpecInfo [BuiltinRule {ru_name = "Class op $p1Fractional", ru_fn = $p1Fractional, ru_nargs = 2, ru_try = <RuleFun>}] <UniqFM>,NoUnfolding,NoCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [JD {strd = Str (SProd [Str HeadStr,Lazy,Lazy,Lazy]), absd = Use Many (UProd [Use Many Used,Abs,Abs,Abs])}] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (App (Var Id{$p1Floating,rh2,ForAllTy TyVar{a} (FunTy (TyConApp Floating [TyVarTy TyVar{a}]) (TyConApp Fractional [TyVarTy TyVar{a}])),ClassOpId <Class>,Info{1,SpecInfo [BuiltinRule {ru_name = "Class op $p1Floating", ru_fn = $p1Floating, ru_nargs = 2, ru_try = <RuleFun>}] <UniqFM>,NoUnfolding,NoCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [JD {strd = Str (SProd [Str HeadStr,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy]), absd = Use Many (UProd [Use Many Used,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs])}] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (Var Id{$dFloating,aBM,TyConApp Floating [TyVarTy TyVar{a}],VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})))) (Var Id{x1,anU,TyVarTy TyVar{a},VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})) (Var Id{x1,anU,TyVarTy TyVar{a},VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})

You can find my pretty printer (and all the other code for the plugin) at: https://github.com/mikeizbicki/herbie-haskell/blob/master/src/Herbie.hs#L627

The function getDictMap (https://github.com/mikeizbicki/herbie-haskell/blob/master/src/Herbie.hs#L171) is where I'm constructing the dictionaries that are getting inserted back into the Core.

On Tue, Aug 25, 2015 at 7:17 PM, Ömer Sinan Ağacan wrote:

...

It seems like in your App syntax you're having a non-function in function position. You can see this by looking at what failing function (splitFunTy_maybe) is doing:

splitFunTy_maybe :: Type -> Maybe (Type, Type) -- ^ Attempts to extract the argument and result types from a type ... (definition is not important) ...

Then it's used like this at the error site:

(arg_ty, res_ty) = expectJust "cpeBody:collect_args" $ splitFunTy_maybe fun_ty

In your case this function is returning Nothing and then exceptJust is signalling the panic.

Your code looked correct to me, I don't see any problems with that. Maybe you're using something wrong as selectors. Could you paste CoreExpr representation of your program?

It may also be the case that the panic is caused by something else, maybe your syntax is invalidating some assumptions/invariants in GHC but it's not immediately checked etc. Working at the Core level is frustrating at times.

Can I ask what kind of plugin are you working on?

(Btw, how did you generate this representation of AST? Did you write it manually? If you have a pretty-printer, would you mind sharing it?)

2015-08-25 18:50 GMT-04:00 Mike Izbicki :

...

Thanks Ömer!

I'm able to get dictionaries for the superclasses of a class now, but I get an error whenever I try to get a dictionary for a super-superclass. Here's the Haskell expression I'm working with:

test1 :: Floating a => a -> a test1 x1 = x1+x1

The original core is:

+ @ a $dNum_aJu x1 x1

But my plugin is replacing it with the core:

+ @ a ($p1Fractional ($p1Floating $dFloating_aJq)) x1 x1

The only difference is the way I'm getting the Num dictionary. The corresponding AST (annotated with variable names and types) is:

App (App (App (App (Var +::forall a. Num a => a -> a -> a) (Type a) ) (App (Var $p1Fractional::forall a. Fractional a => Num a) (App (Var $p1Floating::forall a. Floating a => Fractional a) (Var $dFloating_aJq::Floating a) ) ) ) (Var x1::'a') ) (Var x1::'a')

When I insert, GHC gives the following error:

ghc: panic! (the 'impossible' happened) (GHC version 7.10.1 for x86_64-unknown-linux): expectJust cpeBody:collect_args

What am I doing wrong with extracting these super-superclass dictionaries? I've looked up the code for cpeBody in GHC, but I can't figure out what it's trying to do, so I'm not sure why it's failing on my core.

On Mon, Aug 24, 2015 at 7:10 PM, Ömer Sinan Ağacan wrote:

...

Mike, here's a piece of code that may be helpful to you:

https://github.com/osa1/sc-plugin/blob/master/src/Supercompilation/Show.hs

Copy this module to your plugin, it doesn't have any dependencies other than ghc itself. When your plugin is initialized, update `dynFlags_ref` with your DynFlags as first thing to do. Then use Show instance to print AST directly.

Horrible hack, but very useful for learning purposes. In fact, I don't know how else we can learn what Core is generated for a given code, and reverse-engineer to figure out details.

Hope it helps.

2015-08-24 21:59 GMT-04:00 Ömer Sinan Ağacan : >> Lets say I'm running the plugin on a function with signature `Floating a => a >> -> a`, then the plugin has access to the `Floating` dictionary for the type. >> But if I want to add two numbers together, I need the `Num` dictionary. I >> know I should have access to `Num` since it's a superclass of `Floating`. >> How can I get access to these superclass dictionaries? > > I don't have a working code for this but this should get you started: > > let ord_dictionary :: Id = ... > ord_class :: Class = ... > in > mkApps (Var (head (classSCSels ord_class))) [Var ord_dictionary] > > I don't know how to get Class for Ord. I do `head` here because in the case of > Ord we only have one superclass so `classSCSels` should have one Id. Then I > apply ord_dictionary to this selector and it should return dictionary for Eq. > > I assumed you already have ord_dictionary, it should be passed to your function > already if you had `(Ord a) => ` in your function. > > > Now I realized you asked for getting Num from Floating. I think you should > follow a similar path except you need two applications, first to get Fractional > from Floating and second to get Num from Fractional: > > mkApps (Var (head (classSCSels fractional_class))) > [mkApps (Var (head (classSCSels floating_class))) > [Var floating_dictionary]] > > Return value should be a Num dictionary.

---

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Thanks to everyone who helped me on this project! I've released the final result on github at https://github.com/mikeizbicki/HerbiePlugin#herbie-ghc-plugin On Mon, Sep 7, 2015 at 1:26 PM, Mike Izbicki wrote:

I have another question :) This one relates to Andrew Farmer's answer a while back on how to build dictionaries given a Concrete type. Everything I have works when I use my own numeric hierarchy, but when I use the Prelude's numeric hierarchy, GHC can't find the `Num Float` instance (or any other builtin instance).

I created the following function (based on HERMIT's buildDictionary function) to build my dictionaries (for GHC 7.10.1):

-- | Given a function name and concrete type, get the needed dictionary. getDictConcrete :: ModGuts -> String -> Type -> CoreM (Maybe (Expr CoreBndr)) getDictConcrete guts opstr t = trace ("getDictConcrete "++opstr) $ do hscenv <- getHscEnv dflags <- getDynFlags eps <- liftIO $ hscEPS hscenv let (opname,ParentIs classname) = getNameParent guts opstr classType = mkTyConTy $ case lookupNameEnv (eps_PTE eps) classname of Just (ATyCon t) -> t Just (AnId _) -> error "loopupNameEnv AnId" Just (AConLike _) -> error "loopupNameEnv AConLike" Just (ACoAxiom _) -> error "loopupNameEnv ACoAxiom" Nothing -> error "getNameParent gutsEnv Nothing"

dictType = mkAppTy classType t dictVar = mkGlobalVar VanillaId (mkSystemName (mkUnique 'z' 1337) (mkVarOcc $ "magicDictionaryName")) dictType vanillaIdInfo

bnds <- runTcM guts $ do loc <- getCtLoc $ GivenOrigin UnkSkol let nonC = mkNonCanonical $ CtWanted { ctev_pred = dictType , ctev_evar = dictVar , ctev_loc = loc } wCs = mkSimpleWC [nonC] (x, evBinds) <- solveWantedsTcM wCs bnds <- initDsTc $ dsEvBinds evBinds

liftIO $ do putStrLn $ "dictType="++showSDoc dflags (ppr dictType) putStrLn $ "dictVar="++showSDoc dflags (ppr dictVar)

putStrLn $ "nonC="++showSDoc dflags (ppr nonC) putStrLn $ "wCs="++showSDoc dflags (ppr wCs) putStrLn $ "bnds="++showSDoc dflags (ppr bnds) putStrLn $ "x="++showSDoc dflags (ppr x)

return bnds

case bnds of [NonRec _ dict] -> return $ Just dict otherwise -> return Nothing

When I use my own numeric class hierarchy, this works great! But when I use the Prelude numeric hierarchy, this doesn't work for some reason. In particular, if I pass `+` as the operation I want a dictionary for on the type `Float`, then the function returns `Nothing` with the following output:

getDictConcrete + dictType=Num Float dictVar=magicDictionaryName_zlz nonC=[W] magicDictionaryName_zlz :: Num Float (CNonCanonical) wCs=WC {wc_simple = [W] magicDictionaryName_zlz :: Num Float (CNonCanonical)} bnds=[] x=WC {wc_simple = [W] magicDictionaryName_zlz :: Num Float (CNonCanonical)}

If I change the `solveWantedTcMs` function to `simplifyInteractive`, then GHC panics with the following message:

Top level: No instance for (GHC.Num.Num GHC.Types.Float) arising from UnkSkol

Why doesn't the TcM monad know about the `Num Float` instance?

On Fri, Sep 4, 2015 at 9:18 PM, Ömer Sinan Ağacan wrote:

...

Typo: "You're parsing your code" I mean "You're passing your code"

2015-09-05 0:16 GMT-04:00 Ömer Sinan Ağacan :

...

Hi Mike,

I'll try to hack an example for you some time tomorrow(I'm returning from ICFP and have some long flights ahead of me).

But in the meantime, here's a working Core code, generated by GHC:

f_rjH :: forall a_alz. Ord a_alz => a_alz -> Bool f_rjH = \ (@ a_aCH) ($dOrd_aCI :: Ord a_aCH) (eta_B1 :: a_aCH) -> == @ a_aCH (GHC.Classes.$p1Ord @ a_aCH $dOrd_aCI) eta_B1 eta_B1

You can clearly see here how Eq dictionary is selected from Ord dicitonary($dOrd_aCI in the example), it's just an application of selector to type and dictionary, that's all.

This is generated from this code:

{-# NOINLINE f #-} f :: Ord a => a -> Bool f x = x == x

Compile it with this:

ghc --make -fforce-recomp -O0 -ddump-simpl -ddump-to-file Main.hs -dsuppress-idinfo

...

Can anyone help me figure this out? Is there any chance this is a bug in how GHC parses Core?

This seems unlikely, because GHC doesn't have a Core parser and there's no Core parsing going on here, you're parsing your Code in the form of AST(CoreExpr, CoreProgram etc. defined in CoreSyn.hs). Did you mean something else and am I misunderstanding?

2015-09-04 19:39 GMT-04:00 Mike Izbicki :

...

I'm still having trouble creating Core code that can extract superclass dictionaries from a given dictionary. I suspect the problem is that I don't actually understand what the Core code to do this is supposed to look like. I keep getting the errors mentioned above when I try what I think should work.

Can anyone help me figure this out? Is there any chance this is a bug in how GHC parses Core?

On Tue, Aug 25, 2015 at 9:24 PM, Mike Izbicki wrote:

...

The purpose of the plugin is to automatically improve the numerical stability of Haskell code. It is supposed to identify numeric expressions, then use Herbie (https://github.com/uwplse/herbie) to generate a numerically stable version, then rewrite the numerically stable version back into the code. The first two steps were really easy. It's the last step of inserting back into the code that I'm having tons of trouble with. Core is a lot more complicated than I thought :)

I'm not sure what you mean by the CoreExpr representation? Here's the output of the pretty printer you gave: App (App (App (App (Var Id{+,r2T,ForAllTy TyVar{a} (FunTy (TyConApp Num [TyVarTy TyVar{a}]) (FunTy (TyVarTy TyVar{a}) (FunTy (TyVarTy TyVar{a}) (TyVarTy TyVar{a})))),VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (Type (TyVarTy TyVar{a}))) (App (Var Id{$p1Fractional,rh3,ForAllTy TyVar{a} (FunTy (TyConApp Fractional [TyVarTy TyVar{a}]) (TyConApp Num [TyVarTy TyVar{a}])),ClassOpId <Class>,Info{1,SpecInfo [BuiltinRule {ru_name = "Class op $p1Fractional", ru_fn = $p1Fractional, ru_nargs = 2, ru_try = <RuleFun>}] <UniqFM>,NoUnfolding,NoCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [JD {strd = Str (SProd [Str HeadStr,Lazy,Lazy,Lazy]), absd = Use Many (UProd [Use Many Used,Abs,Abs,Abs])}] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (App (Var Id{$p1Floating,rh2,ForAllTy TyVar{a} (FunTy (TyConApp Floating [TyVarTy TyVar{a}]) (TyConApp Fractional [TyVarTy TyVar{a}])),ClassOpId <Class>,Info{1,SpecInfo [BuiltinRule {ru_name = "Class op $p1Floating", ru_fn = $p1Floating, ru_nargs = 2, ru_try = <RuleFun>}] <UniqFM>,NoUnfolding,NoCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [JD {strd = Str (SProd [Str HeadStr,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy,Lazy]), absd = Use Many (UProd [Use Many Used,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs,Abs])}] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}}) (Var Id{$dFloating,aBM,TyConApp Floating [TyVarTy TyVar{a}],VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})))) (Var Id{x1,anU,TyVarTy TyVar{a},VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})) (Var Id{x1,anU,TyVarTy TyVar{a},VanillaId,Info{0,SpecInfo [] <UniqFM>,NoUnfolding,MayHaveCafRefs,NoOneShotInfo,InlinePragma {inl_src = "{-# INLINE", inl_inline = EmptyInlineSpec, inl_sat = Nothing, inl_act = AlwaysActive, inl_rule = FunLike},NoOccInfo,StrictSig (DmdType <UniqFM> [] (Dunno NoCPR)),JD {strd = Lazy, absd = Use Many Used},0}})

You can find my pretty printer (and all the other code for the plugin) at: https://github.com/mikeizbicki/herbie-haskell/blob/master/src/Herbie.hs#L627

The function getDictMap (https://github.com/mikeizbicki/herbie-haskell/blob/master/src/Herbie.hs#L171) is where I'm constructing the dictionaries that are getting inserted back into the Core.

On Tue, Aug 25, 2015 at 7:17 PM, Ömer Sinan Ağacan wrote:

...

It seems like in your App syntax you're having a non-function in function position. You can see this by looking at what failing function (splitFunTy_maybe) is doing:

splitFunTy_maybe :: Type -> Maybe (Type, Type) -- ^ Attempts to extract the argument and result types from a type ... (definition is not important) ...

Then it's used like this at the error site:

(arg_ty, res_ty) = expectJust "cpeBody:collect_args" $ splitFunTy_maybe fun_ty

In your case this function is returning Nothing and then exceptJust is signalling the panic.

Your code looked correct to me, I don't see any problems with that. Maybe you're using something wrong as selectors. Could you paste CoreExpr representation of your program?

It may also be the case that the panic is caused by something else, maybe your syntax is invalidating some assumptions/invariants in GHC but it's not immediately checked etc. Working at the Core level is frustrating at times.

Can I ask what kind of plugin are you working on?

(Btw, how did you generate this representation of AST? Did you write it manually? If you have a pretty-printer, would you mind sharing it?)

2015-08-25 18:50 GMT-04:00 Mike Izbicki : > Thanks Ömer! > > I'm able to get dictionaries for the superclasses of a class now, but > I get an error whenever I try to get a dictionary for a > super-superclass. Here's the Haskell expression I'm working with: > > test1 :: Floating a => a -> a > test1 x1 = x1+x1 > > The original core is: > > + @ a $dNum_aJu x1 x1 > > But my plugin is replacing it with the core: > > + @ a ($p1Fractional ($p1Floating $dFloating_aJq)) x1 x1 > > The only difference is the way I'm getting the Num dictionary. The > corresponding AST (annotated with variable names and types) is: > > App > (App > (App > (App > (Var +::forall a. Num a => a -> a -> a) > (Type a) > ) > (App > (Var $p1Fractional::forall a. Fractional a => Num a) > (App > (Var $p1Floating::forall a. Floating a => Fractional a) > (Var $dFloating_aJq::Floating a) > ) > ) > ) > (Var x1::'a') > ) > (Var x1::'a') > > When I insert, GHC gives the following error: > > ghc: panic! (the 'impossible' happened) > (GHC version 7.10.1 for x86_64-unknown-linux): > expectJust cpeBody:collect_args > > What am I doing wrong with extracting these super-superclass > dictionaries? I've looked up the code for cpeBody in GHC, but I can't > figure out what it's trying to do, so I'm not sure why it's failing on > my core. > > On Mon, Aug 24, 2015 at 7:10 PM, Ömer Sinan Ağacan wrote: >> Mike, here's a piece of code that may be helpful to you: >> >> https://github.com/osa1/sc-plugin/blob/master/src/Supercompilation/Show.hs >> >> Copy this module to your plugin, it doesn't have any dependencies other than >> ghc itself. When your plugin is initialized, update `dynFlags_ref` with your >> DynFlags as first thing to do. Then use Show instance to print AST directly. >> >> Horrible hack, but very useful for learning purposes. In fact, I don't know how >> else we can learn what Core is generated for a given code, and reverse-engineer >> to figure out details. >> >> Hope it helps. >> >> 2015-08-24 21:59 GMT-04:00 Ömer Sinan Ağacan : >>>> Lets say I'm running the plugin on a function with signature `Floating a => a >>>> -> a`, then the plugin has access to the `Floating` dictionary for the type. >>>> But if I want to add two numbers together, I need the `Num` dictionary. I >>>> know I should have access to `Num` since it's a superclass of `Floating`. >>>> How can I get access to these superclass dictionaries? >>> >>> I don't have a working code for this but this should get you started: >>> >>> let ord_dictionary :: Id = ... >>> ord_class :: Class = ... >>> in >>> mkApps (Var (head (classSCSels ord_class))) [Var ord_dictionary] >>> >>> I don't know how to get Class for Ord. I do `head` here because in the case of >>> Ord we only have one superclass so `classSCSels` should have one Id. Then I >>> apply ord_dictionary to this selector and it should return dictionary for Eq. >>> >>> I assumed you already have ord_dictionary, it should be passed to your function >>> already if you had `(Ord a) => ` in your function. >>> >>> >>> Now I realized you asked for getting Num from Floating. I think you should >>> follow a similar path except you need two applications, first to get Fractional >>> from Floating and second to get Num from Fractional: >>> >>> mkApps (Var (head (classSCSels fractional_class))) >>> [mkApps (Var (head (classSCSels floating_class))) >>> [Var floating_dictionary]] >>> >>> Return value should be a Num dictionary.

---

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