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Mitch

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

Compilation stage

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

Compilation Stages

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

Transpilation

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

Expansion

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 }

Optimisation

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

Simplification

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

For instance, a code like:

SWAP; SWAP; C

becomes

C

Normalisation

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

Some examples ...

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

Basic sum manipulation

(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 { }

Basic product manipulation

(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 }

Recursive function

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!

Tezos related projects

License

MIT License

Copyright (c) 2023-2024 Didier Plaindoux

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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