src/Pure/morphism.ML
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(*  Title:      Pure/morphism.ML
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    ID:         $Id$
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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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  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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  val var: morphism -> string * mixfix -> string * mixfix
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  val name: morphism -> string -> string
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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 morphism:
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   {name: string -> string,
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    var: string * mixfix -> string * mixfix,
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    typ: typ -> typ,
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    term: term -> term,
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    fact: thm list -> thm list} -> morphism
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  val name_morphism: (string -> string) -> morphism
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  val var_morphism: (string * mixfix -> string * mixfix) -> morphism
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  val typ_morphism: (typ -> typ) -> morphism
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  val term_morphism: (term -> term) -> morphism
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  val fact_morphism: (thm list -> thm list) -> morphism
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  val thm_morphism: (thm -> thm) -> morphism
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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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end;
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structure Morphism: MORPHISM =
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struct
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datatype morphism = Morphism of
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 {name: string -> string,
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  var: string * mixfix -> string * mixfix,
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  typ: typ -> typ,
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  term: term -> term,
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  fact: thm list -> thm list};
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fun name (Morphism {name, ...}) = name;
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fun var (Morphism {var, ...}) = var;
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fun typ (Morphism {typ, ...}) = typ;
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fun term (Morphism {term, ...}) = term;
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fun fact (Morphism {fact, ...}) = 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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val morphism = Morphism;
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fun name_morphism name = morphism {name = name, var = I, typ = I, term = I, fact = I};
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fun var_morphism var = morphism {name = I, var = var, typ = I, term = I, fact = I};
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fun typ_morphism typ = morphism {name = I, var = I, typ = typ, term = I, fact = I};
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fun term_morphism term = morphism {name = I, var = I, typ = I, term = term, fact = I};
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fun fact_morphism fact = morphism {name = I, var = I, typ = I, term = I, fact = fact};
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fun thm_morphism thm = morphism {name = I, var = I, typ = I, term = I, fact = map thm};
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val identity = morphism {name = I, var = I, typ = I, term = I, fact = I};
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fun compose
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    (Morphism {name = name1, var = var1, typ = typ1, term = term1, fact = fact1})
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    (Morphism {name = name2, var = var2, typ = typ2, term = term2, fact = fact2}) =
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  morphism {name = name1 o name2, var = var1 o var2,
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    typ = typ1 o typ2, term = term1 o term2, fact = fact1 o 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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end;
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structure BasicMorphism: BASIC_MORPHISM = Morphism;
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open BasicMorphism;