Theory Meta_Pure

(******************************************************************************
 * A Meta-Model for the Isabelle API
 *
 * Copyright (c) 2011-2018 Université Paris-Saclay, Univ. Paris-Sud, France
 *               2013-2017 IRT SystemX, France
 *               2011-2015 Achim D. Brucker, Germany
 *               2016-2018 The University of Sheffield, UK
 *               2016-2017 Nanyang Technological University, Singapore
 *               2017-2018 Virginia Tech, USA
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section‹(Pure) Term Meta-Model aka. AST definition of (Pure) Term›

theory  Meta_Pure
imports "../Init"
begin

subsection‹Type Definition›

type_synonym indexname = "string × nat"
type_synonym "class" = string
type_synonym sort = "class list"
datatype "typ" =
  Type string "typ list" |
  TFree string sort |
  TVar indexname sort
datatype "term" =
  Const string "typ" |
  Free string "typ" |
  Var indexname "typ" |
  Bound nat |
  Abs string "typ" "term" |
  App "term" "term" (infixl "$" 200)

subsection‹Operations of Fold, Map, ..., on the Meta-Model›

fun map_Const where
   "map_Const f expr = (λ Const s ty ⇒ Const (f s ty) ty
                        | Free s ty ⇒ Free s ty
                        | Var i ty ⇒ Var i ty
                        | Bound n ⇒ Bound n
                        | Abs s ty term ⇒ Abs s ty (map_Const f term)
                        | App term1 term2 ⇒ App (map_Const f term1)
                                                         (map_Const f term2))
                        expr"

fun fold_Const where
   "fold_Const f accu expr = (λ Const s _ ⇒ f accu s 
                              | Abs _ _ term ⇒ fold_Const f accu term
                              | App term1 term2 ⇒ fold_Const f (fold_Const f accu term1) term2
                              | _ ⇒ accu)
                               expr"

fun fold_Free where
   "fold_Free f accu expr = (λ Free s _ ⇒ f accu s 
                             | Abs _ _ term ⇒ fold_Free f accu term
                             | App term1 term2 ⇒ fold_Free f (fold_Free f accu term1) term2
                             | _ ⇒ accu)
                              expr"

end