src/Pure/morphism.ML
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(*  Title:      Pure/morphism.ML
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    Author:     Makarius
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Abstract morphisms on formal entities.
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*)
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infix 1 $>
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signature BASIC_MORPHISM =
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sig
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  type morphism
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  type declaration = morphism -> Context.generic -> Context.generic
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  val $> : morphism * morphism -> morphism
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end
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signature MORPHISM =
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sig
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  include BASIC_MORPHISM
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  exception MORPHISM of string * exn
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  val morphism: string ->
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   {binding: (binding -> binding) list,
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    typ: (typ -> typ) list,
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    term: (term -> term) list,
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    fact: (thm list -> thm list) list} -> morphism
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  val pretty: morphism -> Pretty.T
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  val binding: morphism -> binding -> binding
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  val binding_prefix: morphism -> (string * bool) list
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  val typ: morphism -> typ -> typ
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  val term: morphism -> term -> term
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  val fact: morphism -> thm list -> thm list
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  val thm: morphism -> thm -> thm
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  val cterm: morphism -> cterm -> cterm
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  val identity: morphism
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  val compose: morphism -> morphism -> morphism
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  val transform: morphism -> (morphism -> 'a) -> morphism -> 'a
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  val form: (morphism -> 'a) -> 'a
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  val binding_morphism: string -> (binding -> binding) -> morphism
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  val typ_morphism: string -> (typ -> typ) -> morphism
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  val term_morphism: string -> (term -> term) -> morphism
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  val fact_morphism: string -> (thm list -> thm list) -> morphism
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  val thm_morphism: string -> (thm -> thm) -> morphism
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  val transfer_morphism: theory -> morphism
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  val transfer_morphism': Proof.context -> morphism
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  val transfer_morphism'': Context.generic -> morphism
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  val trim_context_morphism: morphism
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  val instantiate_frees_morphism:
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    ((string * sort) * ctyp) list * ((string * typ) * cterm) list -> morphism
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  val instantiate_morphism:
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    ((indexname * sort) * ctyp) list * ((indexname * typ) * cterm) list -> morphism
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end;
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structure Morphism: MORPHISM =
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struct
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(* named functions *)
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type 'a funs = (string * ('a -> 'a)) list;
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exception MORPHISM of string * exn;
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fun app (name, f) x = f x
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  handle exn =>
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    if Exn.is_interrupt exn then Exn.reraise exn else raise MORPHISM (name, exn);
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fun apply fs = fold_rev app fs;
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(* type morphism *)
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datatype morphism = Morphism of
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 {names: string list,
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  binding: binding funs,
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  typ: typ funs,
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  term: term funs,
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  fact: thm list funs};
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type declaration = morphism -> Context.generic -> Context.generic;
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fun morphism a {binding, typ, term, fact} =
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  Morphism {
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    names = if a = "" then [] else [a],
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    binding = map (pair a) binding,
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    typ = map (pair a) typ,
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    term = map (pair a) term,
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    fact = map (pair a) fact};
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fun pretty (Morphism {names, ...}) = Pretty.enum ";" "{" "}" (map Pretty.str (rev names));
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val _ = ML_system_pp (fn _ => fn _ => Pretty.to_polyml o pretty);
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fun binding (Morphism {binding, ...}) = apply binding;
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fun binding_prefix morph = Binding.name "x" |> binding morph |> Binding.prefix_of;
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fun typ (Morphism {typ, ...}) = apply typ;
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fun term (Morphism {term, ...}) = apply term;
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fun fact (Morphism {fact, ...}) = apply fact;
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val thm = singleton o fact;
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val cterm = Drule.cterm_rule o thm;
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(* morphism combinators *)
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val identity = morphism "" {binding = [], typ = [], term = [], fact = []};
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fun compose
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    (Morphism {names = names1, binding = binding1, typ = typ1, term = term1, fact = fact1})
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    (Morphism {names = names2, binding = binding2, typ = typ2, term = term2, fact = fact2}) =
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  Morphism {
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    names = names1 @ names2,
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    binding = binding1 @ binding2,
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    typ = typ1 @ typ2,
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    term = term1 @ term2,
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    fact = fact1 @ fact2};
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fun phi1 $> phi2 = compose phi2 phi1;
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fun transform phi f = fn psi => f (phi $> psi);
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fun form f = f identity;
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(* concrete morphisms *)
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fun binding_morphism a binding = morphism a {binding = [binding], typ = [], term = [], fact = []};
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fun typ_morphism a typ = morphism a {binding = [], typ = [typ], term = [], fact = []};
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fun term_morphism a term = morphism a {binding = [], typ = [], term = [term], fact = []};
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fun fact_morphism a fact = morphism a {binding = [], typ = [], term = [], fact = [fact]};
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fun thm_morphism a thm = morphism a {binding = [], typ = [], term = [], fact = [map thm]};
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val transfer_morphism = thm_morphism "transfer" o Thm.join_transfer;
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val transfer_morphism' = transfer_morphism o Proof_Context.theory_of;
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val transfer_morphism'' = transfer_morphism o Context.theory_of;
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val trim_context_morphism = thm_morphism "trim_context" Thm.trim_context;
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(* instantiate *)
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fun instantiate_frees_morphism ([], []) = identity
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  | instantiate_frees_morphism (cinstT, cinst) =
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      let
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        val instT = map (apsnd Thm.typ_of) cinstT;
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        val inst = map (apsnd Thm.term_of) cinst;
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      in
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        morphism "instantiate_frees"
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          {binding = [],
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           typ = if null instT then [] else [Term_Subst.instantiateT_frees instT],
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           term = [Term_Subst.instantiate_frees (instT, inst)],
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           fact = [map (Thm.instantiate_frees (cinstT, cinst))]}
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      end;
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fun instantiate_morphism ([], []) = identity
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  | instantiate_morphism (cinstT, cinst) =
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      let
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        val instT = map (apsnd Thm.typ_of) cinstT;
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        val inst = map (apsnd Thm.term_of) cinst;
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      in
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        morphism "instantiate"
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          {binding = [],
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           typ = if null instT then [] else [Term_Subst.instantiateT instT],
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           term = [Term_Subst.instantiate (instT, inst)],
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           fact = [map (Thm.instantiate (cinstT, cinst))]}
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      end;
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end;
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structure Basic_Morphism: BASIC_MORPHISM = Morphism;
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open Basic_Morphism;