Untyped Plutus Core

Plutus smart contracts are written in Haskell, and are ultimately ¹ compiled to a language known as Untyped Plutus Core (UPLC). Unlike Haskell, UPLC is a low-level and untyped language. It supports only a handful of builtin types and functions, that are then strung together in lambda applications (see lambda calculus).

Here is a simple example of a UPLC program that is equivalent to the Haskell id function:

Program
  ()
  (Version () 1 0 0)
  (LamAbs
     ()
     (DeBruijn {dbnIndex = 0})
     (Var () (DeBruijn {dbnIndex = 1})))

(See further below for an explanation of this syntax.)

Pluto

As you might have noticed it is not practical to write UPLC by hand. Pluto is a simple programming language that assembles directly to UPLC; that is to say, it ‘maps’ directly (more or less) to the AST of UPLC. Understanding Pluto facilitates an understanding of UPLC. Here’s the equivalent Pluto program for the above UPLC example:

(\x -> x)

Pluto retains the structure of UPLC, and enables you to write UPLC “by hand” (as it were) but in a more ergonomic way.

UPLC Representation

Plutus represents a UPLC program using the following Haskell type:

data Program name uni fun ann = 
  Program ann (TPLC.Version ann) (Term name uni fun ann)

The part we are interested in is Term name uni fun ann. A UPLC program is just a Term defined recursively in terms of itself, similar to languages like Lisp. The Term type is defined as follows:

data Term name uni fun ann
    = Var !ann !name
    | LamAbs !ann !name !(Term name uni fun ann)
    | Apply !ann !(Term name uni fun ann) !(Term name uni fun ann)
    | Force !ann !(Term name uni fun ann)
    | Delay !ann !(Term name uni fun ann)
    | Constant !ann !(Some (ValueOf uni))
    | Builtin !ann !fun
    | Error !ann

Term is parametrized over two type variables of particular interest to us.

• fun is the list of builtin functions supported by Term or Program (see UPLC builtins below), and
• uni is the kind of value types supported by Term or Program.

They are normally instantiated to DefaultFun and DefaultUni respectively, and Pluto uses exactly these.

UPLC builtins

The builtin functions supported by UPLC are specified by the DefaultFun type. The Plutus evaluator (which all cardano nodes in the blockchain use to execute script validators) provides the implementation for them, and they are available in the same module (PlutusCore.Default.Builtins). Here is a subset of those builtins:

data DefaultFun
    = AddInteger
    | SubtractInteger
    ...
    | AppendByteString
    | ConsByteString    
    ...
    | Sha2_256
    | VerifySignature
    ...
    | IfThenElse
    ...

Bear in mind that UPLC is untyped, therefore these builtin functions will fail to evaluate if their types don’t match what they expect.

See builtin-functions for full list of builtins.

UPLC values

The values supported by UPLC are specified by the DefaultUni type.

data DefaultUni a where
    DefaultUniInteger    :: DefaultUni (Esc Integer)
    DefaultUniByteString :: DefaultUni (Esc BS.ByteString)
    DefaultUniString     :: DefaultUni (Esc Text.Text)
    DefaultUniUnit       :: DefaultUni (Esc ())
    DefaultUniBool       :: DefaultUni (Esc Bool)
    DefaultUniProtoList  :: DefaultUni (Esc [])
    DefaultUniProtoPair  :: DefaultUni (Esc (,))
    DefaultUniApply      :: !(DefaultUni (Esc f)) -> !(DefaultUni (Esc a)) -> DefaultUni (Esc (f a))
    DefaultUniData       :: DefaultUni (Esc Data)

A primitive value is one of integer, bytestring, string, unit (()), boolean, or a pair ² of values. Or they can be a list ² of values. Lambdas are first-class values, and therefore a lambda application is represented as a value as well.

Finally, Plutus provides a special value called Data - which acts as an intermediate representation for Haskell values, allowing easy encoding and decoding of them. To access and build values of type Data you would be using Plutus-provided builtins.

Working with Plutus Data

Data is defined simply as:

data Data =
      Constr Integer [Data]
    | Map [(Data, Data)]
    | List [Data]
    | I Integer
    | B BS.ByteString

See builtin-data for further details.

List of Data

To begin with understanding how to operate on a Plutus Data value, let’s look at the builtin functions operating on lists. The specific functions from DefaultFun we need are:

• MkCons – constructs a list from a head and tail
• HeadList – returns the head of a list
• TailList – returns the tail of a list

But first, how do we know that a given Data is a List [Data]? There is ChooseData for this, but for now - let’s assume that it is indeed a list. The following builtin then provides the [Data] argument of the List constructor:

UnListData :: Data -> [Data]

Here’s an example in Pluto that uses some of the above builtins:

let 
  x = data [1, 2, 3]
in 
  ! HeadList (UnListData x)

Running this program will produce 1 as the result:

$ pluto run lists.pluto
Constant () (Some (ValueOf data (I 1)))

What you just saw here is the Show value of Term. Specifically its Constant constructor (see section UPLC Representation above). Inside of it we have a Data value that was built using the I constructor, corresponding to the integer 1. If you want to pull out that integer, you would be using UnIData builtin.

let 
  x = data [1, 2, 3]
in 
  UnIData (! HeadList (UnListData x))

(Note: Pluto’s ! maps to UPLC’s Force builtin, which eliminates polymorphic types; more on this in a section below.)

Running:

$ pluto run lists.pluto
Constant () (Some (ValueOf integer 1))

This value, an “integer”, maps to the DefaultUniInteger type above. Incidentally, the above Pluto program compiles to the following UPLC program:

Program
  ()
  (Version () 1 0 0)
  (Apply
     ()
     (LamAbs
        ()
        (DeBruijn {dbnIndex = 0})
        (Apply
           ()
           (Builtin () UnIData)
           (Apply
              ()
              (Force () (Builtin () HeadList))
              (Apply
                 ()
                 (Builtin () UnListData)
                 (Var () (DeBruijn {dbnIndex = 1}))))))
     (Constant
        () (Some (ValueOf data (List [I 1, I 2, I 3])))))

For further details, see builtin-lists, as well as builtin-pairs.

Interlude: Untyped Lambda Calculus

UPLC is based on Untyped Lambda Calculus. In the UPLC example above, the “term” in (Program () (Version ..) term) is a lambda term, which can be one ³ of the following:

Essentially, any program can be reduced to a lambda term. The UPLC above can be interpreted in a rather straightforward manner if you understand what DeBruijn indices here stand for (a DeBruijn representation eliminates named variables like x). Specifically (Var () (DeBruijn {dbnIndex = n})) refers to the bound variable in the nth ancestor lambda. See this blog post for an informal introduction to these concepts.

Script Validator

A smart contract Script is a Program that evalutes to a lambda that taking three arguments – datum, redeemer, scriptcontext, and returns () or fails.