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Roadmap

Ongoing work

• Coq/Yalla export
• LaTeX export
• call to an automated prover (this includes some proof import)
• add cut rule (issue #12)
• cyclic linear logic (exchange restricted to circular shifts)
• explicit exchange rule (with colored backgrounds to follow instances of formulas) (issue #11)
• formula naming through (possibly recursive) equations (with click on name to unfold a definition inside a proof)

  𝔹 ::= (A ⊗ A) ⊸ (A ⊗ A)
  ℕ ::= !(A ⊸ A) ⊸ !(A ⊸ A)
  o ::= !o ⊸ o
  

Other directions

• two-sided sequent calculus
• intuitionistic linear logic
• quantifiers (issue #16)
• contexts as first-class objects (issue #13)
• additional tool for proof transformations (cut elimination, axiom expansion, reversing, focusing, etc.) (issue #12)
• back edges for regular proofs
• fixed-point connectives in formulas
• mix rules

Examples

• A⊗B ⊢ B⊗A
• (A⊗B)⊗C ⊢ A⊗(B⊗C)
• A⊗(B⊸C) ⊢ B⊸(A⊗C)
• A⊗(B⊕C) ⊢ (A⊗B)⊕(A⊗C)
• !(A&B) ⊢ !A⊗!B
• !A⊗!B ⊢ !(A&B)
• !A⊗!B ⊢ !(A⊗B)
• A⊗(A⊸A) ⊢ A⊗!(A⊸A)
• !(!A⊸B), !(!B⊸C) ⊢ !A⊸C
• !(A⊸A)⊸!(A⊸A)
• ((A⊸R)⊸R)⊗((B⊸R)⊸R) ⊢ ((A⊗B)⊸R)⊸R
• ((A⊸R)⊸R)⊕((B⊸R)⊸R) ⊢ ((A⊕B)⊸R)⊸R
• ((A⊸?B)⊸A)⊸?A
• !(A⅋B)⊸(?!?A⅋?!?B)
• ⊢ ?A, ?(B⅋B), ?(A^⅋B^), ?(⊥⊗⊥)
• ((((0⊸1)⊸1)⊸0)⊸0)⊸1
• (((A⊗⊤)&(B⊗⊤))⊸0)⊸((A⊸A')⊕(B⊸B'))