section \<open>Main HOL\<close>
text \<open>
Classical Higher-order Logic -- only ``Main'', excluding real and
complex numbers etc.
\<close>
theory Main
imports
Predicate_Compile
Quickcheck_Narrowing
Extraction
Nunchaku
BNF_Greatest_Fixpoint
Filter
Conditionally_Complete_Lattices
Binomial
GCD
begin
text \<open>Legacy\<close>
context Inf
begin
abbreviation (input) INFIMUM :: "'b set \<Rightarrow> ('b \<Rightarrow> 'a) \<Rightarrow> 'a"
where "INFIMUM A f \<equiv> \<Sqinter>(f ` A)"
end
context Sup
begin
abbreviation (input) SUPREMUM :: "'b set \<Rightarrow> ('b \<Rightarrow> 'a) \<Rightarrow> 'a"
where "SUPREMUM A f \<equiv> \<Squnion>(f ` A)"
end
abbreviation (input) INTER :: "'a set \<Rightarrow> ('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"
where "INTER \<equiv> INFIMUM"
abbreviation (input) UNION :: "'a set \<Rightarrow> ('a \<Rightarrow> 'b set) \<Rightarrow> 'b set"
where "UNION \<equiv> SUPREMUM"
text \<open>Namespace cleanup\<close>
hide_const (open)
czero cinfinite cfinite csum cone ctwo Csum cprod cexp image2 image2p vimage2p Gr Grp collect
fsts snds setl setr convol pick_middlep fstOp sndOp csquare relImage relInvImage Succ Shift
shift proj id_bnf
hide_fact (open) id_bnf_def type_definition_id_bnf_UNIV
text \<open>Syntax cleanup\<close>
no_notation
bot ("\<bottom>") and
top ("\<top>") and
inf (infixl "\<sqinter>" 70) and
sup (infixl "\<squnion>" 65) and
Inf ("\<Sqinter> _" [900] 900) and
Sup ("\<Squnion> _" [900] 900) and
ordLeq2 (infix "<=o" 50) and
ordLeq3 (infix "\<le>o" 50) and
ordLess2 (infix "<o" 50) and
ordIso2 (infix "=o" 50) and
card_of ("|_|") and
BNF_Cardinal_Arithmetic.csum (infixr "+c" 65) and
BNF_Cardinal_Arithmetic.cprod (infixr "*c" 80) and
BNF_Cardinal_Arithmetic.cexp (infixr "^c" 90) and
BNF_Def.convol ("\<langle>(_,/ _)\<rangle>")
no_syntax
"_INF1" :: "pttrns \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Sqinter>_./ _)" [0, 10] 10)
"_INF" :: "pttrn \<Rightarrow> 'a set \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Sqinter>_\<in>_./ _)" [0, 0, 10] 10)
"_SUP1" :: "pttrns \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Squnion>_./ _)" [0, 10] 10)
"_SUP" :: "pttrn \<Rightarrow> 'a set \<Rightarrow> 'b \<Rightarrow> 'b" ("(3\<Squnion>_\<in>_./ _)" [0, 0, 10] 10)
end