59 lines
998 B
Text
59 lines
998 B
Text
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%--------------------------------------------------------------------------
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% File : NUM-ROZEK : TPTP v8.1.2.
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% Domain : Data Structures
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% Axioms : Lists - Head, Tail, and Length
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%--------------------------------------------------------------------------
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%-- List Basics
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tff(list_t, type, list: $tType).
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tff(list_nil, type, nil : list).
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tff(list_cons, type,
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cons: (
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($int * list) > list
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)
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).
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%-- Head
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tff(head_t, type,
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head: list > $int
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).
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tff(head_cons, axiom,
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![H: $int, T: list]: (
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head(cons(H, T)) = H
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)
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).
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%-- Tail
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tff(tail_t, type,
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tail: list > list
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).
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tff(tail_cons, axiom,
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![H: $int, T: list]: (
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tail(cons(H, T)) = T
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)
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).
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% Note: The existence of head and tail definition shows that
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% cons is injective.
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%-- Length
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tff(length_t, type,
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length: list > $int
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).
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tff(length_nil, axiom, length(nil) = 0).
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tff(length_cons, axiom,
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![H: $int, T: list]: (
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length(cons(H, T)) = $sum(1, length(T))
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)
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).
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