Follow-Lang/set.mm.json

Metamath to Follow

Transform metamath database to follow language.

• Github link: https://github.com/follow-lang/metamath-to-follow
• Huggingface link: https://huggingface.co/datasets/Follow-Lang/set.mm.json

How to use it?

1. Generate the database:

python -m metamath_to_follow.translator -s ./set.mm/set.mm -o ./follow/set.mm/

This command will cost about 3 hours. It will generate these:

• follow/set.mm/code(329M): the data in follow language format.
• follow/set.mm/json(9.6G): the data in json format.
• follow/set.mm/words.txt: words used in train folder. It includes some special token.
• follow/set.mm/types.txt: stores all name of types.
• follow/set.mm/terms.txt: stores all term content, which can be used to build tokenizer.
• follow/set.mm/axioms.txt: stores all name of axioms.
• follow/set.mm/thms.txt: stores all name of thms.
• follow/set.mm/blocks.txt: stores all name of blocks.

2. Upload to huggingface:

python -m metamath_to_follow.upload -s ./follow/set.mm -d Follow-Lang/set.mm

This command will create "*.zip" file and upload it to huggingface.

Code Folder Introduction

• content.follow.json: stores file list of all follow files.
• [name].fol: stores the code of [name] block.

Follow Folder Introduction

• content.follow.json: store file list of all json files.
• [name].json: stores the imformation of [name] block, which can be used for training.

Block type

{
    "type": "type",
    "label": <LABEL>
}

Block term

{
    "type": "term",
    "label": <LABEL>,
    "type": <TYPE>,
    "args": ["<TYPE> <NAME>", "<TYPE> <NAME>", ...],
    "stmt": <STMT SEQUENCE>
}

Block axiom

{
    "type": "axiom",
    "label": <LABEL>,
    "args": [[<TYPE>, <NAME>], [<TYPE>, <NAME>], ...],
    "targets": [<STMT SEQUENCE>],
    "conditions": [<STMT SEQUENCE>, <STMT SEQUENCE>, ...],
    "dvs": [(<V1>, <V2>), (<V3>, <V4>), ...],
    "cost": 1
}

Block thm

{
    "type": "thm",
    "label": <LABEL>,
    "args": [[<TYPE>, <NAME>], [<TYPE>, <NAME>], ...],
    "targets": [<STMT SEQUENCE>],
    "conditions": [<STMT SEQUENCE>, <STMT SEQUENCE>, ...],
    "dvs": [(<V>, <V>), (<V>, <V>), ...],
    "states": [<STATE>, <STATE>, ...],
    "actions": [ <ACTION>, <ACTION>, ...],
    "operators": [ <OP>, <OP>, ...],
    "cost": <COST>,
    "state_costs": [<COST>, <COST>, ...],
    "action_costs": [<COST>, <COST>, ...],
}

• <STATE> is combined with target statements.
• <ACTION> is combined with target statements, assumptions and diff statements.
• <OP> is a function call of axiom or theorem, <OP> = [<LABEL>, [<ARG>, <ARG>, ...]].
• <COST> is the max number of proof ops: Cost(s) = max(Cost(a), Cost(s')+1).