src/HOL/IMP/Def_Init_Exp.thy
author paulson <lp15@cam.ac.uk>
Mon May 23 15:33:24 2016 +0100 (2016-05-23)
changeset 63114 27afe7af7379
parent 53015 a1119cf551e8
permissions -rw-r--r--
Lots of new material for multivariate analysis
     1 (* Author: Tobias Nipkow *)
     2 
     3 theory Def_Init_Exp
     4 imports Vars
     5 begin
     6 
     7 subsection "Initialization-Sensitive Expressions Evaluation"
     8 
     9 type_synonym state = "vname \<Rightarrow> val option"
    10 
    11 
    12 fun aval :: "aexp \<Rightarrow> state \<Rightarrow> val option" where
    13 "aval (N i) s = Some i" |
    14 "aval (V x) s = s x" |
    15 "aval (Plus a\<^sub>1 a\<^sub>2) s =
    16   (case (aval a\<^sub>1 s, aval a\<^sub>2 s) of
    17      (Some i\<^sub>1,Some i\<^sub>2) \<Rightarrow> Some(i\<^sub>1+i\<^sub>2) | _ \<Rightarrow> None)"
    18 
    19 
    20 fun bval :: "bexp \<Rightarrow> state \<Rightarrow> bool option" where
    21 "bval (Bc v) s = Some v" |
    22 "bval (Not b) s = (case bval b s of None \<Rightarrow> None | Some bv \<Rightarrow> Some(\<not> bv))" |
    23 "bval (And b\<^sub>1 b\<^sub>2) s = (case (bval b\<^sub>1 s, bval b\<^sub>2 s) of
    24   (Some bv\<^sub>1, Some bv\<^sub>2) \<Rightarrow> Some(bv\<^sub>1 & bv\<^sub>2) | _ \<Rightarrow> None)" |
    25 "bval (Less a\<^sub>1 a\<^sub>2) s = (case (aval a\<^sub>1 s, aval a\<^sub>2 s) of
    26  (Some i\<^sub>1, Some i\<^sub>2) \<Rightarrow> Some(i\<^sub>1 < i\<^sub>2) | _ \<Rightarrow> None)"
    27 
    28 
    29 lemma aval_Some: "vars a \<subseteq> dom s \<Longrightarrow> \<exists> i. aval a s = Some i"
    30 by (induct a) auto
    31 
    32 lemma bval_Some: "vars b \<subseteq> dom s \<Longrightarrow> \<exists> bv. bval b s = Some bv"
    33 by (induct b) (auto dest!: aval_Some)
    34 
    35 end