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src/ZF/listfn.thy

author | clasohm |

Thu, 16 Sep 1993 12:20:38 +0200 | |

changeset 0 | a5a9c433f639 |

child 14 | 1c0926788772 |

permissions | -rw-r--r-- |

Initial revision

(* Title: ZF/list-fn ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1993 University of Cambridge Functions for Lists in Zermelo-Fraenkel Set Theory map is a binding operator -- it applies to meta-level functions, not object-level functions. This simplifies the final form of term_rec_conv, although complicating its derivation. *) ListFn = List + consts "@" :: "[i,i]=>i" (infixr 60) list_rec :: "[i, i, [i,i,i]=>i] => i" map :: "[i=>i, i] => i" length,rev :: "i=>i" flat :: "i=>i" list_add :: "i=>i" (* List Enumeration *) "[]" :: "i" ("[]") "@List" :: "args => i" ("[(_)]") translations "[x, xs]" == "Cons(x, [xs])" "[x]" == "Cons(x, [])" "[]" == "Nil" rules list_rec_def "list_rec(l,c,h) == Vrec(l, %l g.list_case(c, %x xs. h(x, xs, g`xs), l))" map_def "map(f,l) == list_rec(l, Nil, %x xs r. Cons(f(x), r))" length_def "length(l) == list_rec(l, 0, %x xs r. succ(r))" app_def "xs@ys == list_rec(xs, ys, %x xs r. Cons(x,r))" rev_def "rev(l) == list_rec(l, Nil, %x xs r. r @ [x])" flat_def "flat(ls) == list_rec(ls, Nil, %l ls r. l @ r)" list_add_def "list_add(l) == list_rec(l, 0, %x xs r. x#+r)" end