61 lines
1.6 KiB
Coq
61 lines
1.6 KiB
Coq
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(* Boolean formula *)
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Inductive boolf: Type :=
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| Atom: bool -> boolf
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| Neg: boolf -> boolf
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| And: boolf -> boolf -> boolf
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| Or: boolf -> boolf -> boolf
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| Impl: boolf -> boolf -> boolf.
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Notation "⊤" := (Atom true) (at level 10).
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Notation "⊥" := (Atom false) (at level 10).
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Notation "'¬' b" := (Neg b) (at level 10).
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Infix "∧" := And (at level 15).
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Infix "∨" := Or (at level 20).
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Infix "→" := Impl (at level 25).
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Example f1 := ((⊤ ∨ ⊥) ∧ ⊥) → (¬ ⊥).
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Inductive kont {V:Type}: Type :=
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| Letk: kont -> kont -> kont.
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Arguments kont: clear implicits.
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Inductive kont {V:Type}: Type :=
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| KAtom: bool -> kont
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| KNeg: kont -> kont
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| KAnd: (V -> kont) -> (V -> kont) -> kont
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| KOr: (V -> kont) -> (V -> kont) -> kont
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| KImpl: (V -> kont) -> (V -> kont) -> kont.
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Arguments kont: clear implicits.
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Fixpoint compile {V:Type} (f:boolf): kont V :=
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match f with
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| Atom b => KAtom b
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| Neg f => KNeg (compile f)
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| And f1 f2 => KAnd (fun k => compile f1) (fun k => compile f2)
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| Or f1 f2 => KOr (fun k => compile f1) (fun k => compile f2)
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| Impl f1 f2 => KImpl (fun k => compile f1) (fun k => compile f2)
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end.
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Check compile (V:=unit) f1.
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Compute compile (V:=unit) f1.
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(* https://en.wikipedia.org/wiki/Tseytin_transformation *)
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Inductive cnf: Type :=
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| CTru | CFls: cnf
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| CNeg: cnf -> cnf
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| CCons: cnf -> cnf -> cnf.
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Fixpoint cnfy (f:boolf): cnf :=
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match f with
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| Tru => CTru
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| Fls => CFls
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| Neg b => CNeg (cnfy b)
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| And Fls _ => CFls
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| And _ Fls => CFls
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| And Tru f2 => cnfy f2
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| And f1 Tru => cnfy f1
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| And f1 f2 =>
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| Or f1 f2 =>
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| Impl f1 f2 => CCons (CNeg (cnfy f1)) (cnfy f2)
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end.
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