64 lines
2 KiB
OCaml
64 lines
2 KiB
OCaml
type label =
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| Axiom
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| AndI
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| AndE
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| OrI
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| OrE
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| ArrI
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| ArrE
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| NegI
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| NegE
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| RAA
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| IffI
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| IffE
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| EqI
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| EqE
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| ForallI
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| ForallE
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| ExistsI
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| ExistsE
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type pref = Linenum of int | Named of string
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type t = { children : pref list; label : label; formula : Formula.t }
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let rec valid res a { children; label; formula } =
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let children = List.map res children in
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match (children, label, formula) with
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| [], Axiom, phi -> List.mem phi a
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| [ left; right ], AndI, Conj (phi, psi) ->
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left.formula = phi && right.formula = psi && valid res a left
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&& valid res a right
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| [ ({ formula = Conj (phi, psi); _ } as kid) ], AndE, chi ->
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(chi = phi || chi = psi) && valid res a kid
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| [ kid ], OrI, Disj (phi, psi) ->
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(kid.formula = phi || kid.formula = psi) && valid res a kid
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| [ ({ formula = Disj (phi, psi); _ } as left); middle; right ], OrE, chi ->
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middle.formula = chi && right.formula = chi && valid res a left
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&& valid res (phi :: a) middle
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&& valid res (psi :: a) right
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| [ kid ], ArrI, Impl (phi, psi) ->
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kid.formula = psi && valid res (phi :: a) kid
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| [ left; right ], ArrE, psi ->
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left.formula = Impl (right.formula, psi)
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&& valid res a left && valid res a right
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| [ kid ], NegI, Neg phi -> kid.formula = Bottom && valid res (phi :: a) kid
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| [ left; right ], NegE, Bottom ->
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left.formula = Neg right.formula && valid res a left && valid res a right
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| [ kid ], RAA, phi -> kid.formula = Bottom && valid res (Neg phi :: a) kid
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| [ left; right ], IffI, Iff (phi, psi) ->
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left.formula = Impl (phi, psi)
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&& right.formula = Impl (psi, phi)
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&& valid res a left && valid res a right
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| [ left; right ], IffE, phi ->
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(left.formula = Iff (right.formula, phi)
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|| left.formula = Iff (phi, right.formula))
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&& valid res a left && valid res a right
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| [], EqI, Equal (x, y) -> x = y
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(* TODO:
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- EqE
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- ForallI
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- ForallE
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- ExistsI
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- ExistsE
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*)
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