Compilation of an extended lambda-calculus to minimal stack style virtual machine.

Things to be done in order to a have a complete POC:

• Function application (not partial one)
• Sum data covering Inl, Inr and Case
• Product data covering Pair, First and Second
• Code Optimisation
• Recursive function
• Partial evaluation

pure source 
    >>= transpile
    <&> expand 
    >>= optimise 
    <&> simplify 
    <&> normalise 

The transpilation takes a lambda-calculus with recursion, sum and product data and produces the corresponding Michelson code.

Expansion is a de-normalisation operation building a source code based on a tree from a one which is a DAG.

For instance, a code like:

IF_LEFT A B ; C

becomes

IF_LEFT { A ; C } { B ; C }

This stage provides an optimised version of the initial Michelson source code. This optimisation is done thanks to a symbolic evaluation.

For instance, a code like:

LEFT; IF_LEFT B C

becomes

B

The simplification is the process which detects patterns and apply rewriting rules.

For instance, a code like:

SWAP; SWAP; C

becomes

C

This last stages revert the expansion process turning a tree based source code to a DAG in order to reduce the size of the source code finally.

For instance, a code like:

IF_LEFT { A ; C } { B ; C }

becomes

IF_LEFT A B ; C

Note: types are not given in the Michelson sample (for the moment).

(fun x -> case (inl x) (fun x -> x) (fun _ -> 3))

is transpiled to

LAMBDA { DUP 0; LEFT; IF_LEFT { DUP 0; DROP 1 } { PUSH (INT 3); DROP 1 }; DROP 1 }

optimised to

LAMBDA { DUP 0; DROP 1 }

and finally simplified to

LAMBDA { }

(fun p -> (snd p) (fst p))

is transpiled to

LAMBDA { DUP 0; CDR; DUP 1; CAR; EXEC; DROP 1 }

and finally simplified to

LAMBDA { UNPAIR; EXEC }

rec(f).(fun x -> f x)

is transpiled to

LAMBDA_REC { DUP 1; DUP 1; EXEC; DROP 1; DROP 1 }

then simplified to

LAMBDA_REC { EXEC }

Note: This is a tail recursive function - which never terminates of course!

• Michelson: the language of Smart Contracts in Tezos
• DaiLambda, Inc. Michelson optimizer

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