Quelle Recur.thy

Sprache: Isabelle

theory Recur imports Main begin

text‹
{thm[display] mono_def[no_vars]}
rulename{mono_def}

{thm[display] monoI[no_vars]}
rulename{monoI}

{thm[display] monoD[no_vars]}
rulename{monoD}

{thm[display] lfp_unfold[no_vars]}
rulename{lfp_unfold}

{thm[display] lfp_induct[no_vars]}
rulename{lfp_induct}

{thm[display] gfp_unfold[no_vars]}
rulename{gfp_unfold}

{thm[display] coinduct[no_vars]}
rulename{coinduct}
›

text‹\noindent
relation $<$ is
java.lang.NullPointerException: Cannot invoke "String.equals(Object)" because "macro" is null
@2 < a@1 < a@0$. Clearly, a function definition is total iff the set
all pairs $(r,l)$, where $l$ is the argument on the left-hand side
an equation and $r$ the argument of some recursive call on the
right-hand side, induces a wellfounded relation.

HOL library formalizes
of the theory of wellfounded relations. For example
prop‹wf r›\index{*wf|bold} means that relation @{term[show_types]"r::('a*'a)set"} is
.
we should mention that HOL already provides the mother of all
, \textbf{wellfounded
}\indexbold{induction!wellfounded}\index{wellfounded
|see{induction, wellfounded}} (@{thm[source]wf_induct}):
{thm[display]wf_induct[no_vars]}
term‹wf r› means that the relation term‹r› is wellfounded

›

text‹

{thm[display] wf_induct[no_vars]}
rulename{wf_induct}

{thm[display] less_than_iff[no_vars]}
rulename{less_than_iff}

{thm[display] inv_image_def[no_vars]}
rulename{inv_image_def}

{thm[display] measure_def[no_vars]}
rulename{measure_def}

{thm[display] wf_less_than[no_vars]}
rulename{wf_less_than}

{thm[display] wf_inv_image[no_vars]}
rulename{wf_inv_image}

{thm[display] wf_measure[no_vars]}
rulename{wf_measure}

{thm[display] lex_prod_def[no_vars]}
rulename{lex_prod_def}

{thm[display] wf_lex_prod[no_vars]}
rulename{wf_lex_prod}

›

end

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