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Extra resources for Computation and automata
Rewriting” is more honest than “simplification” because the terms do not necessarily become simpler in the process. 28 3. More Functional Programming The simplifier proves arithmetic goals as described in Sect. 1 above. Arithmetic expressions are simplified using built-in procedures that go beyond mere rewrite rules. New simplification procedures can be coded and installed, but they are definitely not a matter for this tutorial. 2 Simplification Rules To facilitate simplification, the attribute [simp] declares theorems to be simplification rules, which the simplifier will use automatically.
9 Automatic Case Splits Goals containing if -expressions are usually proved by case distinction on the boolean condition. Here is an example: lemma " ∀ xs. if xs =  then rev xs =  else rev xs = " The goal can be split by a special method, split : apply(split split_if) 32 3. More Functional Programming 1. ∀ xs. (xs =  −→ rev xs = ) ∧ (xs =  −→ rev xs = ) where split_if is a theorem that expresses splitting of if s. Because splitting the if s is usually the right proof strategy, the simplifier does it automatically.
Because splitting the if s is usually the right proof strategy, the simplifier does it automatically. Try apply(simp) on the initial goal above. This splitting idea generalizes from if to case . split) 1. (xs =  −→ zs = xs @ zs) ∧ ( ∀ a list. xs = a # list −→ a # list @ zs = xs @ zs) The simplifier does not split case -expressions, as it does if -expressions, because with recursive datatypes it could lead to nontermination. Instead, the simplifier has a modifier split for adding splitting rules explicitly.