| author | blanchet |
| Thu, 22 Oct 2009 16:34:49 +0200 | |
| changeset 33194 | 13450310a776 |
| parent 23510 | 4521fead5609 |
| child 39353 | 7f11d833d65b |
| permissions | -rw-r--r-- |
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The Metis prover (slightly modified version from Larry);
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(* ========================================================================= *) |
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(* A LOGICAL KERNEL FOR FIRST ORDER CLAUSES *) |
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(* Copyright (c) 2001-2004 Joe Hurd, distributed under the BSD License *) |
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(* ========================================================================= *) |
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signature Thm = |
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The Metis prover (slightly modified version from Larry);
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sig |
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The Metis prover (slightly modified version from Larry);
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(* ------------------------------------------------------------------------- *) |
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(* An abstract type of first order logic theorems. *) |
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(* ------------------------------------------------------------------------- *) |
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type clause = LiteralSet.set |
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datatype inferenceType = |
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Axiom |
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The Metis prover (slightly modified version from Larry);
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| Assume |
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| Subst |
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| Factor |
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| Resolve |
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| Refl |
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| Equality |
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type thm |
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type inference = inferenceType * thm list |
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(* ------------------------------------------------------------------------- *) |
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(* Theorem destructors. *) |
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(* ------------------------------------------------------------------------- *) |
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val clause : thm -> clause |
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val inference : thm -> inference |
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(* Tautologies *) |
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val isTautology : thm -> bool |
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(* Contradictions *) |
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val isContradiction : thm -> bool |
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(* Unit theorems *) |
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val destUnit : thm -> Literal.literal |
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The Metis prover (slightly modified version from Larry);
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val isUnit : thm -> bool |
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The Metis prover (slightly modified version from Larry);
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The Metis prover (slightly modified version from Larry);
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(* Unit equality theorems *) |
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val destUnitEq : thm -> Term.term * Term.term |
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The Metis prover (slightly modified version from Larry);
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val isUnitEq : thm -> bool |
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The Metis prover (slightly modified version from Larry);
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The Metis prover (slightly modified version from Larry);
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(* Literals *) |
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val member : Literal.literal -> thm -> bool |
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val negateMember : Literal.literal -> thm -> bool |
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(* ------------------------------------------------------------------------- *) |
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(* A total order. *) |
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(* ------------------------------------------------------------------------- *) |
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val compare : thm * thm -> order |
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val equal : thm -> thm -> bool |
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(* ------------------------------------------------------------------------- *) |
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(* Free variables. *) |
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(* ------------------------------------------------------------------------- *) |
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val freeIn : Term.var -> thm -> bool |
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val freeVars : thm -> NameSet.set |
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(* ------------------------------------------------------------------------- *) |
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The Metis prover (slightly modified version from Larry);
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(* Pretty-printing. *) |
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(* ------------------------------------------------------------------------- *) |
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val ppInferenceType : inferenceType Parser.pp |
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val inferenceTypeToString : inferenceType -> string |
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val pp : thm Parser.pp |
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val toString : thm -> string |
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(* ------------------------------------------------------------------------- *) |
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(* Primitive rules of inference. *) |
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(* ------------------------------------------------------------------------- *) |
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(* ------------------------------------------------------------------------- *) |
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The Metis prover (slightly modified version from Larry);
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(* *) |
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(* ----- axiom C *) |
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(* C *) |
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(* ------------------------------------------------------------------------- *) |
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val axiom : clause -> thm |
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(* ------------------------------------------------------------------------- *) |
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(* *) |
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(* ----------- assume L *) |
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(* L \/ ~L *) |
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(* ------------------------------------------------------------------------- *) |
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val assume : Literal.literal -> thm |
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(* ------------------------------------------------------------------------- *) |
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(* C *) |
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(* -------- subst s *) |
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The Metis prover (slightly modified version from Larry);
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(* C[s] *) |
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(* ------------------------------------------------------------------------- *) |
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val subst : Subst.subst -> thm -> thm |
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(* ------------------------------------------------------------------------- *) |
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(* L \/ C ~L \/ D *) |
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(* --------------------- resolve L *) |
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(* C \/ D *) |
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(* *) |
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(* The literal L must occur in the first theorem, and the literal ~L must *) |
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(* occur in the second theorem. *) |
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The Metis prover (slightly modified version from Larry);
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(* ------------------------------------------------------------------------- *) |
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val resolve : Literal.literal -> thm -> thm -> thm |
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(* ------------------------------------------------------------------------- *) |
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(* *) |
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(* --------- refl t *) |
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(* t = t *) |
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The Metis prover (slightly modified version from Larry);
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(* ------------------------------------------------------------------------- *) |
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The Metis prover (slightly modified version from Larry);
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The Metis prover (slightly modified version from Larry);
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val refl : Term.term -> thm |
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The Metis prover (slightly modified version from Larry);
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The Metis prover (slightly modified version from Larry);
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(* ------------------------------------------------------------------------- *) |
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(* *) |
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139 |
(* ------------------------ equality L p t *) |
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140 |
(* ~(s = t) \/ ~L \/ L' *) |
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141 |
(* *) |
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142 |
(* where s is the subterm of L at path p, and L' is L with the subterm at *) |
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143 |
(* path p being replaced by t. *) |
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144 |
(* ------------------------------------------------------------------------- *) |
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145 |
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val equality : Literal.literal -> Term.path -> Term.term -> thm |
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147 |
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148 |
end |