Theory Main

theory Main
imports Predicate_Compile Quickcheck_Narrowing Extraction Nunchaku BNF_Greatest_Fixpoint Filter Conditionally_Complete_Lattices Binomial
section ‹Main HOL›

text ‹
  Classical Higher-order Logic -- only ``Main'', excluding real and
  complex numbers etc.
›

theory Main
  imports
    Predicate_Compile
    Quickcheck_Narrowing
    Extraction
    Nunchaku
    BNF_Greatest_Fixpoint
    Filter
    Conditionally_Complete_Lattices
    Binomial
    GCD
begin

text ‹Namespace cleanup›

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 ‹Syntax cleanup›

no_notation
  bot ("⊥") and
  top ("⊤") and
  inf (infixl "⊓" 70) and
  sup (infixl "⊔" 65) and
  Inf ("⨅") and
  Sup ("⨆") and
  ordLeq2 (infix "<=o" 50) and
  ordLeq3 (infix "≤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 ("⟨(_,/ _)⟩")

bundle cardinal_syntax begin
notation
  ordLeq2 (infix "<=o" 50) and
  ordLeq3 (infix "≤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)

alias cinfinite = BNF_Cardinal_Arithmetic.cinfinite
alias czero = BNF_Cardinal_Arithmetic.czero
alias cone = BNF_Cardinal_Arithmetic.cone
alias ctwo = BNF_Cardinal_Arithmetic.ctwo
end

no_syntax
  "_INF1"     :: "pttrns ⇒ 'b ⇒ 'b"           ("(3⨅_./ _)" [0, 10] 10)
  "_INF"      :: "pttrn ⇒ 'a set ⇒ 'b ⇒ 'b"  ("(3⨅_∈_./ _)" [0, 0, 10] 10)
  "_SUP1"     :: "pttrns ⇒ 'b ⇒ 'b"           ("(3⨆_./ _)" [0, 10] 10)
  "_SUP"      :: "pttrn ⇒ 'a set ⇒ 'b ⇒ 'b"  ("(3⨆_∈_./ _)" [0, 0, 10] 10)

end