[isabelle] Higher-order matching against schematic variables



Hi all,

I have a question with higher-order matching against schematic variables. I can't figure out why the pattern trm1 can't be matched against lem if lem was "A x y --> x y = 0". However, if the RHS contains constants instead, e.g., "A x y --> g a = 0", a matcher is found. Since x and y have the same types of g and a respectively, how come there isn't a matcher in the former case? A difference is that x and y are schematic variables, but why can't schematic variables be matched against?

Here's the code:

locale A =
  fixes f :: "nat => nat"
  and a :: nat
  assumes ax: "f a = 0"

consts
  g :: "nat => nat"
  a :: nat

lemma lem: "A x y --> x y = 0"
sorry


ML {*

val trm1 = term_of @{cpat "?P --> (?f::((?'a=>?'b)=>?'c)) ?stuff = ?v"};
val trm2 = Thm.prop_of @{thm lem};

val mtch_seq = let
  val init = Envir.empty 0
  val ctxt = @{context}
val (Const ("Trueprop",_) $ trm2) = Thm.prop_of (ProofContext.get_thm ctxt "lem")
in
  Unify.matchers @{theory} [(trm1,trm2)]
end;

val seq as SOME (mtch,_) = nthseq 0 mtch_seq;
pretty_env @{context} (Envir.term_env mtch);
*}

Thanks
Michael

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