(* Title: Pure/morphism.ML
Author: Makarius
Abstract morphisms on formal entities.
*)
infix 1 $>
signature BASIC_MORPHISM =
sig
type morphism
type declaration = morphism -> Context.generic -> Context.generic
val $> : morphism * morphism -> morphism
end
signature MORPHISM =
sig
include BASIC_MORPHISM
exception MORPHISM of string * exn
val pretty: morphism -> Pretty.T
val binding: morphism -> binding -> binding
val typ: morphism -> typ -> typ
val term: morphism -> term -> term
val fact: morphism -> thm list -> thm list
val thm: morphism -> thm -> thm
val cterm: morphism -> cterm -> cterm
val morphism: string ->
{binding: (binding -> binding) list,
typ: (typ -> typ) list,
term: (term -> term) list,
fact: (thm list -> thm list) list} -> morphism
val binding_morphism: string -> (binding -> binding) -> morphism
val typ_morphism: string -> (typ -> typ) -> morphism
val term_morphism: string -> (term -> term) -> morphism
val fact_morphism: string -> (thm list -> thm list) -> morphism
val thm_morphism: string -> (thm -> thm) -> morphism
val transfer_morphism: theory -> morphism
val trim_context_morphism: morphism
val identity: morphism
val compose: morphism -> morphism -> morphism
val transform: morphism -> (morphism -> 'a) -> morphism -> 'a
val form: (morphism -> 'a) -> 'a
end;
structure Morphism: MORPHISM =
struct
(* named functions *)
type 'a funs = (string * ('a -> 'a)) list;
exception MORPHISM of string * exn;
fun app (name, f) x = f x
handle exn =>
if Exn.is_interrupt exn then Exn.reraise exn else raise MORPHISM (name, exn);
fun apply fs = fold_rev app fs;
(* type morphism *)
datatype morphism = Morphism of
{names: string list,
binding: binding funs,
typ: typ funs,
term: term funs,
fact: thm list funs};
type declaration = morphism -> Context.generic -> Context.generic;
fun pretty (Morphism {names, ...}) = Pretty.enum ";" "{" "}" (map Pretty.str (rev names));
val _ = PolyML.addPrettyPrinter (fn _ => fn _ => Pretty.to_polyml o pretty);
fun binding (Morphism {binding, ...}) = apply binding;
fun typ (Morphism {typ, ...}) = apply typ;
fun term (Morphism {term, ...}) = apply term;
fun fact (Morphism {fact, ...}) = apply fact;
val thm = singleton o fact;
val cterm = Drule.cterm_rule o thm;
fun morphism a {binding, typ, term, fact} =
Morphism {
names = if a = "" then [] else [a],
binding = map (pair a) binding,
typ = map (pair a) typ,
term = map (pair a) term,
fact = map (pair a) fact};
fun binding_morphism a binding = morphism a {binding = [binding], typ = [], term = [], fact = []};
fun typ_morphism a typ = morphism a {binding = [], typ = [typ], term = [], fact = []};
fun term_morphism a term = morphism a {binding = [], typ = [], term = [term], fact = []};
fun fact_morphism a fact = morphism a {binding = [], typ = [], term = [], fact = [fact]};
fun thm_morphism a thm = morphism a {binding = [], typ = [], term = [], fact = [map thm]};
val transfer_morphism = thm_morphism "transfer" o Thm.transfer;
val trim_context_morphism = thm_morphism "trim_context" Thm.trim_context;
val identity = morphism "" {binding = [], typ = [], term = [], fact = []};
(* morphism combinators *)
fun compose
(Morphism {names = names1, binding = binding1, typ = typ1, term = term1, fact = fact1})
(Morphism {names = names2, binding = binding2, typ = typ2, term = term2, fact = fact2}) =
Morphism {
names = names1 @ names2,
binding = binding1 @ binding2,
typ = typ1 @ typ2,
term = term1 @ term2,
fact = fact1 @ fact2};
fun phi1 $> phi2 = compose phi2 phi1;
fun transform phi f = fn psi => f (phi $> psi);
fun form f = f identity;
end;
structure Basic_Morphism: BASIC_MORPHISM = Morphism;
open Basic_Morphism;