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Types

As we saw in Concepts plu-ts is an eDSL embedded in Typescript, as such we have two type systems; the Typescript one and the plu-ts one

Typescript Types​

  • Term is a Typescript type defined in plu-ts.
  • Every value in plu-ts is a Term. In Typescript, we say each value extends Term (in the same way that "Dog" extends "Mammal").
  • A Term also keeps track of the type of the value it holds.

The possible types a Term can keep track of are defined in PTypes, and listed here:

  • PUnit a unique value that has no real meaning; you can see it as plu-ts version of undefined or null in Typescript
  • PInt a signed integer that can be as big as you want
  • PBool a boolean value
  • PByteString equivalent of a Buffer or a Uint8Array
  • PString equivalent of the Typescript string
  • PData equivalent of the object type in Typescript (it is the low level representation of PStructs that we'll cover in a moment, so you usually won't use PData)
  • PList<PType> equivalent of an Array in Typescript; note that all the elements in the list must be of the same PType
  • PPair<PType1, PType2> equivalent of a Typescript tuple ([ type1 , type2 ])
  • PDelayed<PType> a delayed computation that returns a value of type PType; the computation can be run by passing the delayed value to the pforce function
  • PLam<PInput, POutput> a function that takes one single argument of type PInput and returns something of type POutput
  • PFn<[ PInput_0 , ...PType[] ],POutput> a function that takes multiple arguments (at least one) and returns something of type POutput
  • PAlias<PType> just an alias of the provided type; it behaves exactly like the Types of its argument, so PAlias<PInt> is equivalent to a PInt. This is useful for keeping track of a different meaning the type might have.
  • PStruct<{...}> an abstraction over PData, useful to construct more complex data structures.

plu-ts Types​

plu-ts would not be a strongly typed language if limited to Typescript types, because the types of Typescript are only useful during compilation to javascript; and then everything is untyped!

info

Typescript can be compiled to Javascript. When this happens, the resulting Javascript is untyped!

For this reason plu-ts implements its own type through some constants and functions that can be imported.

In the same order of above, the plu-ts equivalents are:

  • PUnit -> unit
  • PInt -> int
  • PBool -> bool
  • PByteString -> bs
  • PString -> str
  • PData -> data
  • PList -> list( type )
  • PPair -> pair( type1, type2 )
  • PDelayed -> delayed( type )
  • PLam -> lam( from, to )
  • PFn -> fn([ ...inputs ], output )
  • aliases types and structs types will be retreived by the type static property of the classes (explained in the dedicated section for aliases and structs)

plu-ts generics​

As we know, Typescript gives us the possibility to define polymorphic types trough generics.

In a way you could see generics as functions that take a type as input and returns another type.

Fortunately for us, plu-ts types are just values when seen from the Typescript world, so we can have some sort of generic in plu-ts too!

To see how, let's try to define the previous polymorphic types using the generic method:

const anyPlutsFunction = ( a: TermType, b: TermType ) => lam( a, b );

const identityFunctionType = ( a: TermType ) => lam( a, a );

const mkPairType = ( a: TermType, b: TermType ) => fn([ a, b ], pair( a, b ) )

Polymorphic types defined as functions also have the advantage of being fully defined once the type arguments are passed.

This works great, but there's still a problem though... Typescript isn't able to infer these types!

This is because TermType is the generic type for all plu-ts types, so when Typescript tries to infer the type of the term, it sees the most generic type of all, and once again thinks we want to use the anonymous PType.

To finally solve this problem we need to make the functions generic too:

function anyFunction<A extends TermType, B extends TermType>( a: A, b: B )
{ 
    return lam( a, b ) 
};

function identityFunctionType<A extends TermType>( a: A )
{ 
    return lam( a, a ) 
};

function mkPairType<A extends TermType, B extends TermType>( a: A, b: B )
{ 
    return fn([ a, b ], pair( a, b ) ) 
};

This way Typescript first infers the specific TermType we are passing, and with that is able to determine the exact type of the Term.

Generics will turn useful especially in the case where the type requires a type variable as return type, a notable example is pif which is of type bool -> a -> a -> a.