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(* Title: GroupDefs.thy
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ID: $Id$
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Author: Markus Wenzel, TU Muenchen
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*)
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GroupDefs = MonoidGroupInsts + Prod + Fun +
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(* bool *)
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instance
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bool :: {times, inv, one}
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defs
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times_bool_def "x * y == (x ~= y)"
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inv_bool_def "inv x == (x::bool)"
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one_bool_def "1 == False"
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(* cartesian products *)
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instance
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"*" :: (term, term) {times, inv, one}
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defs
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times_prod_def "p * q == (fst p * fst q, snd p * snd q)"
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inv_prod_def "inv p == (inv (fst p), inv (snd p))"
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one_prod_def "1 == (1, 1)"
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(* function spaces *)
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instance
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fun :: (term, term) {times, inv, one}
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defs
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times_fun_def "f * g == (%x. f x * g x)"
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inv_fun_def "inv f == (%x. inv (f x))"
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one_fun_def "1 == (%x. 1)"
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end
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