matita/matita/contribs/lambdadelta/basic_2/grammar/test.ma

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  14
  15 universe constraint Type[0] < Type[1].
  16
  17 (* notations ****************************************************************)
  18
  19 notation "hvbox(a break \to b)"
  20   right associative with precedence 20
  21 for @{ \forall $_:$a.$b }.
  22
  23 notation "hvbox( T . break ⓑ { term 46 I } break term 48 T1 )"
  24  non associative with precedence 47
  25  for @{ 'DxBind2 $T $I $T1 }.
  26
  27 (* definitions **************************************************************)
  28
  29 inductive lenv: Type[0] ≝
  30 | LAtom: lenv
  31 | LPair: lenv → lenv → lenv → lenv
  32 .
  33
  34 inductive genv: Type[0] ≝
  35 | GAtom: genv
  36 | GPair: genv → genv → genv → genv
  37 .
  38
  39 axiom fw: genv → lenv → Prop.
  40
  41 (* interpretations **********************************************************)
  42
  43 interpretation "environment binding construction (binary)"
  44    'DxBind2 L I T = (LPair L I T).
  45
  46 interpretation "environment binding construction (binary)"
  47    'DxBind2 G I T = (GPair G I T).
  48
  49 (* statements ***************************************************************)
  50
  51 axiom fw_shift: ∀I,G,K,V. fw G (K.ⓑ{I}V).