Mini ML

This theory defines the type inference rules and the type inference algorithm W for MiniML (simply-typed lambda terms with let) due to Milner. It proves the soundness and completeness of W w.r.t. the rules. A report describing the theory is found in [1] and [2]. 1 Universal error monad theory Maybe imports Main begin definition option_bind :: "[’a option, ’a => ’b option] => ’b option" where "option_bind m f = (case m of None => None | Some r => f r)" syntax "_option_bind" :: "[pttrns,’a option,’b] => ’c" ("(_ := _;//_)" 0) translations "P := E; F" == "CONST option_bind E (%P. F)" — constructor laws for option_bind lemma option_bind_Some: "option_bind (Some s) f = (f s)" by (simp add: option_bind_def) lemma option_bind_None: "option_bind None f = None" by (simp add: option_bind_def) declare option_bind_Some [simp] option_bind_None [simp] — expansion of option_bind lemma split_option_bind: "P(option_bind res f) = ((res = None --> P None) & (!s. res = Some s --> P(f s)))" unfolding option_bind_def by (rule option.split) lemma option_bind_eq_None [simp]: "((option_bind m f) = None) = ((m=None) | (? p. m = Some p & f p = None))"