1(*  Title:      Pure/morphism.ML
2    Author:     Makarius
3
4Abstract morphisms on formal entities.
5*)
6
7infix 1 $>
8
9signature BASIC_MORPHISM =
10sig
11  type morphism
12  type declaration = morphism -> Context.generic -> Context.generic
13  val $> : morphism * morphism -> morphism
14end
15
16signature MORPHISM =
17sig
18  include BASIC_MORPHISM
19  exception MORPHISM of string * exn
20  val morphism: string ->
21   {binding: (binding -> binding) list,
22    typ: (typ -> typ) list,
23    term: (term -> term) list,
24    fact: (thm list -> thm list) list} -> morphism
25  val pretty: morphism -> Pretty.T
26  val binding: morphism -> binding -> binding
27  val binding_prefix: morphism -> (string * bool) list
28  val typ: morphism -> typ -> typ
29  val term: morphism -> term -> term
30  val fact: morphism -> thm list -> thm list
31  val thm: morphism -> thm -> thm
32  val cterm: morphism -> cterm -> cterm
33  val identity: morphism
34  val compose: morphism -> morphism -> morphism
35  val transform: morphism -> (morphism -> 'a) -> morphism -> 'a
36  val form: (morphism -> 'a) -> 'a
37  val binding_morphism: string -> (binding -> binding) -> morphism
38  val typ_morphism: string -> (typ -> typ) -> morphism
39  val term_morphism: string -> (term -> term) -> morphism
40  val fact_morphism: string -> (thm list -> thm list) -> morphism
41  val thm_morphism: string -> (thm -> thm) -> morphism
42  val transfer_morphism: theory -> morphism
43  val transfer_morphism': Proof.context -> morphism
44  val transfer_morphism'': Context.generic -> morphism
45  val trim_context_morphism: morphism
46  val instantiate_frees_morphism:
47    ((string * sort) * ctyp) list * ((string * typ) * cterm) list -> morphism
48  val instantiate_morphism:
49    ((indexname * sort) * ctyp) list * ((indexname * typ) * cterm) list -> morphism
50end;
51
52structure Morphism: MORPHISM =
53struct
54
55(* named functions *)
56
57type 'a funs = (string * ('a -> 'a)) list;
58
59exception MORPHISM of string * exn;
60
61fun app (name, f) x = f x
62  handle exn =>
63    if Exn.is_interrupt exn then Exn.reraise exn else raise MORPHISM (name, exn);
64
65fun apply fs = fold_rev app fs;
66
67
68(* type morphism *)
69
70datatype morphism = Morphism of
71 {names: string list,
72  binding: binding funs,
73  typ: typ funs,
74  term: term funs,
75  fact: thm list funs};
76
77type declaration = morphism -> Context.generic -> Context.generic;
78
79fun morphism a {binding, typ, term, fact} =
80  Morphism {
81    names = if a = "" then [] else [a],
82    binding = map (pair a) binding,
83    typ = map (pair a) typ,
84    term = map (pair a) term,
85    fact = map (pair a) fact};
86
87fun pretty (Morphism {names, ...}) = Pretty.enum ";" "{" "}" (map Pretty.str (rev names));
88
89val _ = ML_system_pp (fn _ => fn _ => Pretty.to_polyml o pretty);
90
91fun binding (Morphism {binding, ...}) = apply binding;
92fun binding_prefix morph = Binding.name "x" |> binding morph |> Binding.prefix_of;
93fun typ (Morphism {typ, ...}) = apply typ;
94fun term (Morphism {term, ...}) = apply term;
95fun fact (Morphism {fact, ...}) = apply fact;
96val thm = singleton o fact;
97val cterm = Drule.cterm_rule o thm;
98
99
100(* morphism combinators *)
101
102val identity = morphism "" {binding = [], typ = [], term = [], fact = []};
103
104fun compose
105    (Morphism {names = names1, binding = binding1, typ = typ1, term = term1, fact = fact1})
106    (Morphism {names = names2, binding = binding2, typ = typ2, term = term2, fact = fact2}) =
107  Morphism {
108    names = names1 @ names2,
109    binding = binding1 @ binding2,
110    typ = typ1 @ typ2,
111    term = term1 @ term2,
112    fact = fact1 @ fact2};
113
114fun phi1 $> phi2 = compose phi2 phi1;
115
116fun transform phi f = fn psi => f (phi $> psi);
117fun form f = f identity;
118
119
120(* concrete morphisms *)
121
122fun binding_morphism a binding = morphism a {binding = [binding], typ = [], term = [], fact = []};
123fun typ_morphism a typ = morphism a {binding = [], typ = [typ], term = [], fact = []};
124fun term_morphism a term = morphism a {binding = [], typ = [], term = [term], fact = []};
125fun fact_morphism a fact = morphism a {binding = [], typ = [], term = [], fact = [fact]};
126fun thm_morphism a thm = morphism a {binding = [], typ = [], term = [], fact = [map thm]};
127
128val transfer_morphism = thm_morphism "transfer" o Thm.join_transfer;
129val transfer_morphism' = transfer_morphism o Proof_Context.theory_of;
130val transfer_morphism'' = transfer_morphism o Context.theory_of;
131
132val trim_context_morphism = thm_morphism "trim_context" Thm.trim_context;
133
134
135(* instantiate *)
136
137fun instantiate_frees_morphism ([], []) = identity
138  | instantiate_frees_morphism (cinstT, cinst) =
139      let
140        val instT = map (apsnd Thm.typ_of) cinstT;
141        val inst = map (apsnd Thm.term_of) cinst;
142      in
143        morphism "instantiate_frees"
144          {binding = [],
145           typ = if null instT then [] else [Term_Subst.instantiateT_frees instT],
146           term = [Term_Subst.instantiate_frees (instT, inst)],
147           fact = [map (Thm.instantiate_frees (cinstT, cinst))]}
148      end;
149
150fun instantiate_morphism ([], []) = identity
151  | instantiate_morphism (cinstT, cinst) =
152      let
153        val instT = map (apsnd Thm.typ_of) cinstT;
154        val inst = map (apsnd Thm.term_of) cinst;
155      in
156        morphism "instantiate"
157          {binding = [],
158           typ = if null instT then [] else [Term_Subst.instantiateT instT],
159           term = [Term_Subst.instantiate (instT, inst)],
160           fact = [map (Thm.instantiate (cinstT, cinst))]}
161      end;
162
163end;
164
165structure Basic_Morphism: BASIC_MORPHISM = Morphism;
166open Basic_Morphism;
167