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(* basic examples *)
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Test = HOHH +
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types nat
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arities nat :: term
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types 'a list
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arities list :: (term) term
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consts Nil :: 'a list ("[]")
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Cons :: 'a => 'a list => 'a list (infixr "#" 65)
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syntax
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(* list Enumeration *)
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"@list" :: args => 'a list ("[(_)]")
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translations
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"[x, xs]" == "x#[xs]"
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"[x]" == "x#[]"
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types person
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arities person :: term
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consts
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append :: ['a list, 'a list, 'a list] => bool
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reverse :: ['a list, 'a list] => bool
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mappred :: [('a => 'b => bool), 'a list, 'b list] => bool
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mapfun :: [('a => 'b), 'a list, 'b list] => bool
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bob :: person
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sue :: person
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ned :: person
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"23" :: nat ("23")
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"24" :: nat ("24")
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"25" :: nat ("25")
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age :: [person, nat] => bool
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eq :: ['a, 'a] => bool
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empty :: ['b] => bool
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add :: ['a, 'b, 'b] => bool
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remove :: ['a, 'b, 'b] => bool
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bag_appl:: ['a, 'a, 'a, 'a] => bool
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rules append "append [] xs xs ..
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append (x#xs) ys (x#zs) :- append xs ys zs"
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reverse "reverse L1 L2 :- (!rev_aux.
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(!L. rev_aux [] L L )..
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(!X L1 L2 L3. rev_aux (X#L1) L2 L3 :- rev_aux L1 L2 (X#L3))
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=> rev_aux L1 L2 [])"
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mappred "mappred P [] [] ..
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mappred P (x#xs) (y#ys) :- P x y & mappred P xs ys"
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mapfun "mapfun f [] [] ..
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mapfun f (x#xs) (f x#ys) :- mapfun f xs ys"
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age "age bob 24 ..
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age sue 23 ..
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age ned 23"
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eq "eq x x"
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(* actual definitions of empty and add is hidden -> yields abstract data type *)
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bag_appl"bag_appl A B X Y:- (? S1 S2 S3 S4 S5.
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empty S1 &
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add A S1 S2 &
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add B S2 S3 &
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remove X S3 S4 &
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remove Y S4 S5 &
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empty S5)"
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end
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