Theory Main

section ‹Main HOL›

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

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

subsection ‹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


subsection ‹Syntax cleanup›

no_notation
  ordLeq2 (infix ‹<=o› 50) and
  ordLeq3 (infix ‹≤o› 50) and
  ordLess2 (infix ‹<o› 50) and
  ordIso2 (infix ‹=o› 50) and
  card_of (‹(‹open_block notation=‹mixfix 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 (‹(‹indent=1 notation=‹mixfix 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 (‹(‹open_block notation=‹mixfix 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


subsection ‹Lattice syntax›

bundle lattice_syntax
begin

notation
  bot  (‹⊥›) and
  top  (‹⊤›) and
  inf  (infixl ‹⊓› 70) and
  sup  (infixl ‹⊔› 65) and
  Inf  (‹(‹open_block notation=‹prefix ⨅››⨅ _)› [900] 900) and
  Sup  (‹(‹open_block notation=‹prefix ⨆››⨆ _)› [900] 900)

syntax
  "_INF1"     :: "pttrns ⇒ 'b ⇒ 'b"           (‹(‹indent=3 notation=‹binder ⨅››⨅_./ _)› [0, 10] 10)
  "_INF"      :: "pttrn ⇒ 'a set ⇒ 'b ⇒ 'b"  (‹(‹indent=3 notation=‹binder ⨅››⨅_∈_./ _)› [0, 0, 10] 10)
  "_SUP1"     :: "pttrns ⇒ 'b ⇒ 'b"           (‹(‹indent=3 notation=‹binder ⨆››⨆_./ _)› [0, 10] 10)
  "_SUP"      :: "pttrn ⇒ 'a set ⇒ 'b ⇒ 'b"  (‹(‹indent=3 notation=‹binder ⨆››⨆_∈_./ _)› [0, 0, 10] 10)

end

unbundle no lattice_syntax

end