Comments (3)
The number calls following the recursive definition may seems more likely to this one:
contraction₀ : ℕ → Prop → Prop
contraction₀ (suc n) φ with contra-view φ
... | impl φ₁ φ₂ φ₃ = contraction₀ n ((φ₁ ∧ φ₂) ⇒ φ₃)
... | other _ = φ
contraction₀ zero φ = φ
steps-contraction : Prop → ℕ
steps-contraction φ with contra-view φ
steps-contraction .(φ₁ ⇒ (φ₂ ⇒ φ₃)) | impl φ₁ φ₂ φ₃ with impl-view φ₃
steps-contraction .(φ₁ ⇒ (φ₂ ⇒ (φ ⇒ ψ))) | impl φ₁ φ₂ .(φ ⇒ ψ) | (impl φ ψ) =
2 + steps-contraction (φ ⇒ ψ)
steps-contraction .(φ₁ ⇒ (φ₂ ⇒ φ₃)) | impl φ₁ φ₂ φ₃ | (other .φ₃) = 2
steps-contraction φ | other .φ = 1
Something like counting the number of chains implications.
from agda-metis.
I renamed the steps-contraction to ♯contractions and simplify the counting.
♯contractions : Prop → ℕ
♯contractions φ with contra-view φ
♯contractions .(φ₁ ⇒ (φ₂ ⇒ φ₃)) | impl φ₁ φ₂ φ₃ = 2 + ♯contractions φ₃
♯contractions φ | other .φ = 1
from agda-metis.
- In http://www.cl.cam.ac.uk/~jrh13/atp/OCaml/lcfprop.ml, there is the unshunt method like contractions here.
p ==> (q ==> r)
-------------
p /\ q ==> r
- Consider this case
p ==> (q /\ r)
-------------
p ==> q and p ==> r
from agda-metis.
Related Issues (15)
- atp-resolve exhibits a pattern HOT 1
- canonicalize
- thm-reorder-v omits cases HOT 1
- mix of a reordering ∧ and ∨.
- atp-conjunct HOT 1
- Theorems to simplify expressions HOT 2
- Improve the proof for build-∨ HOT 1
- Missing proofs for auxiliar theorem in Resolve module HOT 1
- clausify evidence
- canonicalize evidence HOT 4
- Normalized Formula data type HOT 1
- Deduce $false in this case
- Missing case in atp-conjunct, fails projecting.
- Splitting goals: proving atp-split HOT 5
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from agda-metis.