Theory Lem

(*========================================================================*)
(*                        Lem                                             *)
(*                                                                        *)
(*          Dominic Mulligan, University of Cambridge                     *)
(*          Francesco Zappa Nardelli, INRIA Paris-Rocquencourt            *)
(*          Gabriel Kerneis, University of Cambridge                      *)
(*          Kathy Gray, University of Cambridge                           *)
(*          Peter Boehm, University of Cambridge (while working on Lem)   *)
(*          Peter Sewell, University of Cambridge                         *)
(*          Scott Owens, University of Kent                               *)
(*          Thomas Tuerk, University of Cambridge                         *)
(*          Brian Campbell, University of Edinburgh                       *)
(*          Shaked Flur, University of Cambridge                          *)
(*          Thomas Bauereiss, University of Cambridge                     *)
(*          Stephen Kell, University of Cambridge                         *)
(*          Thomas Williams                                               *)
(*          Lars Hupel                                                    *)
(*          Basile Clement                                                *)
(*                                                                        *)
(*  The Lem sources are copyright 2010-2018                               *)
(*  by the authors above and Institut National de Recherche en            *)
(*  Informatique et en Automatique (INRIA).                               *)
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chapter‹Mappings of Syntax needed by Lem›

theory "Lem"

imports
         LemExtraDefs
         "HOL-Library.Word"
         "Word_Lib.Reversed_Bit_Lists"
begin

type_synonym numeral = nat

subsection ‹Finite Maps›

abbreviation (input) "map_find k m ≡ the (m k)"
abbreviation (input) "map_update k v m ≡ m (k ↦ v)"
abbreviation (input) "map_remove k m ≡ m |` (- {k})"
abbreviation (input) "map_any P m ≡ ∃ (k, v) ∈ map_to_set m. P k v"
abbreviation (input) "map_all P m ≡ ∀ (k, v) ∈ map_to_set m. P k v"

subsection ‹Lists›

abbreviation (input) "list_mem e l ≡ (e ∈ set l)"
abbreviation (input) "list_forall P l ≡ (∀e∈set l. P e)"
abbreviation (input) "list_exists P l ≡ (∃e∈set l. P e)"
abbreviation (input) "list_unzip l ≡ (map fst l, map snd l)"

subsection ‹Sets›

abbreviation (input) "set_filter P (s::'a set) ≡ {x ∈ s. P x}"
abbreviation (input) "set_bigunion S ≡ ⋃ S"
abbreviation (input) "set_biginter S ≡ ⋂ S"

subsection ‹Natural numbers›

subsection ‹Integers›


subsection ‹Dummy›

consts
  bitwise_xor :: "nat ⇒ nat ⇒ nat"
  num_asr :: "nat ⇒ nat ⇒ nat"
  num_lsl :: "nat ⇒ nat ⇒ nat"
  bitwise_or :: "nat ⇒ nat ⇒ nat"
  bitwise_not :: "nat ⇒ nat"
  bitwise_and :: "nat ⇒ nat ⇒ nat"

subsection ‹Machine words›

definition word_update :: "'a::len word ⇒ nat ⇒ nat ⇒ 'b::len word ⇒ 'a word" where
  "word_update v lo hi w =
    (let sz = size v in
    of_bl (take (sz-hi-1) (to_bl v) @ to_bl w @ drop (sz-lo) (to_bl v)))"

end