Type information storage functionality (assume_type, assume_types keywords) done! Inference and pretty-printing for function composition done.

3 files changed, 237 insertions, 64 deletions

diff --git a/HoTT_Base.thy b/HoTT_Base.thy
index e74ef31..ed8c18b 100644
--- a/HoTT_Base.thy
+++ b/HoTT_Base.thy
@@ -1,11 +1,11 @@
 (********
 Isabelle/HoTT: Foundational definitions and notation
-Jan 2019
+Feb 2019
 
 This file is the starting point of the Isabelle/HoTT object logic, and contains the basic setup and definitions.
 Among other things, it:
 
-* Sets up object-level type inference functionality (via typing.ML).
+* Calls the setup of object-level type inference functionality.
 * Defines the universe hierarchy and its governing rules.
 * Defines named theorems for later use by proof methods.
 
@@ -13,19 +13,49 @@ Among other things, it:
 
 theory HoTT_Base
 imports Pure
+keywords "assume_type" "assume_types" :: thy_decl
 
 begin
 
 section \<open>Terms and typing\<close>
 
-declare[[eta_contract=false]]
-
 typedecl t \<comment> \<open>Type of object-logic terms (which includes the types)\<close>
 
 judgment has_type :: "[t, t] \<Rightarrow> prop"  ("(3_:/ _)")
 
+section \<open>Setup non-core logic functionality\<close>
+
+declare[[eta_contract=false]] \<comment> \<open>Do not eta-contract\<close>
+
+text \<open>The following file sets up type assumption and inference functionality.\<close>
+
 ML_file "typing.ML"
 
+ML \<open>
+val _ =
+  let
+    fun store_typing ctxt = Typing.put_declared_typing o (Syntax.read_prop ctxt)
+  in
+    Outer_Syntax.local_theory
+      @{command_keyword "assume_type"}
+      "Declare typing assumptions"
+      (Parse.prop >>
+        (fn prop => fn lthy => Local_Theory.background_theory (store_typing lthy prop) lthy))
+  end
+
+val _ =
+  let
+    val parser = Parse.and_list (Parse.prop)
+    fun store_typings ctxt = fold (Typing.put_declared_typing o (Syntax.read_prop ctxt))
+  in
+    Outer_Syntax.local_theory
+      @{command_keyword "assume_types"}
+      "Declare typing assumptions"
+      (parser >>
+        (fn props => fn lthy => Local_Theory.background_theory (store_typings lthy props) lthy))
+  end
+\<close>
+                                                                                  
 section \<open>Universes\<close>
 
 typedecl ord \<comment> \<open>Type of meta-numerals\<close>
diff --git a/Prod.thy b/Prod.thy
index 0de7d89..ce785d6 100644
--- a/Prod.thy
+++ b/Prod.thy
@@ -1,6 +1,6 @@
 (********
 Isabelle/HoTT: Dependent product (dependent function)
-Jan 2019
+Feb 2019
 
 ********)
 
@@ -20,13 +20,13 @@ axiomatization
 syntax
   "_Prod"  :: "[idt, t, t] \<Rightarrow> t"  ("(3TT '(_: _')./ _)" 30)
   "_Prod'" :: "[idt, t, t] \<Rightarrow> t"  ("(3TT _: _./ _)" 30)
-  "_lam"   :: "[idt, t, t] \<Rightarrow> t"  ("(3,\\ '(_: _')./ _)" 30)
-  "_lam'"  :: "[idt, t, t] \<Rightarrow> t"  ("(3,\\ _: _./ _)" 30)
+  "_lam"   :: "[idt, t, t] \<Rightarrow> t"  ("(3\<lambda>'(_: _')./ _)" 30)
+  "_lam'"  :: "[idt, t, t] \<Rightarrow> t"  ("(3\<lambda>_: _./ _)" 30)
 translations
-  "TT(x: A). B"  \<rightleftharpoons> "(CONST Prod) A (\<lambda>x. B)"
-  "TT x: A. B"   \<rightleftharpoons> "(CONST Prod) A (\<lambda>x. B)"
-  ",\\(x: A). b" \<rightleftharpoons> "(CONST lam) A (\<lambda>x. b)"
-  ",\\x: A. b"   \<rightleftharpoons> "(CONST lam) A (\<lambda>x. b)"
+  "TT(x: A). B" \<rightleftharpoons> "(CONST Prod) A (\<lambda>x. B)"
+  "TT x: A. B" \<rightleftharpoons> "(CONST Prod) A (\<lambda>x. B)"
+  "\<lambda>(x: A). b" \<rightleftharpoons> "(CONST lam) A (\<lambda>x. b)"
+  "\<lambda>x: A. b" \<rightleftharpoons> "(CONST lam) A (\<lambda>x. b)"
 
 text \<open>
 The syntax translations above bind the variable @{term x} in the expressions @{term B} and @{term b}.
@@ -40,22 +40,22 @@ where "A \<rightarrow> B \<equiv> TT(_: A). B"
 axiomatization where
 \<comment> \<open>Type rules\<close>
 
-  Prod_form: "\<lbrakk>A: U i; \<And>x. x: A \<Longrightarrow> B x: U i\<rbrakk> \<Longrightarrow> TT x: A. B x: U i" and
+  Prod_form: "\<lbrakk>A: U i; B: A \<leadsto> U i\<rbrakk> \<Longrightarrow> TT x: A. B x: U i" and
 
-  Prod_intro: "\<lbrakk>A: U i; \<And>x. x: A \<Longrightarrow> b x: B x\<rbrakk> \<Longrightarrow> ,\\x: A. b x: TT x: A. B x" and
+  Prod_intro: "\<lbrakk>A: U i; \<And>x. x: A \<Longrightarrow> b x: B x\<rbrakk> \<Longrightarrow> \<lambda>x: A. b x: TT x: A. B x" and
 
   Prod_elim: "\<lbrakk>f: TT x: A. B x; a: A\<rbrakk> \<Longrightarrow> f`a: B a" and
 
-  Prod_cmp: "\<lbrakk>\<And>x. x: A \<Longrightarrow> b x: B x; a: A\<rbrakk> \<Longrightarrow> (,\\x: A. b x)`a \<equiv> b a" and
+  Prod_cmp: "\<lbrakk>\<And>x. x: A \<Longrightarrow> b x: B x; a: A\<rbrakk> \<Longrightarrow> (\<lambda>x: A. b x)`a \<equiv> b a" and
 
-  Prod_uniq: "f: TT x: A. B x \<Longrightarrow> ,\\x: A. f`x \<equiv> f" and
+  Prod_uniq: "f: TT x: A. B x \<Longrightarrow> \<lambda>x: A. f`x \<equiv> f" and
 
 \<comment> \<open>Congruence rules\<close>
 
   Prod_form_eq: "\<lbrakk>A: U i; B: A \<leadsto> U i; C: A \<leadsto> U i; \<And>x. x: A \<Longrightarrow> B x \<equiv> C x\<rbrakk>
     \<Longrightarrow> TT x: A. B x \<equiv> TT x: A. C x" and
 
-  Prod_intro_eq: "\<lbrakk>\<And>x. x: A \<Longrightarrow> b x \<equiv> c x; A: U i\<rbrakk> \<Longrightarrow> ,\\x: A. b x \<equiv> ,\\x: A. c x"
+  Prod_intro_eq: "\<lbrakk>\<And>x. x: A \<Longrightarrow> b x \<equiv> c x; A: U i\<rbrakk> \<Longrightarrow> \<lambda>x: A. b x \<equiv> \<lambda>x: A. c x"
 
 text \<open>
 The Pure rules for \<open>\<equiv>\<close> only let us judge strict syntactic equality of object lambda expressions.
@@ -71,23 +71,23 @@ lemmas Prod_cong [cong] = Prod_form_eq Prod_intro_eq
 section \<open>Function composition\<close>
 
 definition compose :: "[t, t, t] \<Rightarrow> t"
-where "compose A g f \<equiv> ,\\x: A. g`(f`x)"
+where "compose A g f \<equiv> \<lambda>x: A. g`(f`x)"
 
 declare compose_def [comp]
 
 syntax "_compose" :: "[t, t] \<Rightarrow> t"  (infixr "o" 110)
-
 parse_translation \<open>
-let fun compose_tr ctxt tms =
+let fun compose_tr ctxt [g, f] =
   let
-    val g :: f :: _ = tms |> map (Typing.tm_of_ptm ctxt)
+    val [g, f] = [g, f] |> map (Typing.prep_term @{context})
     val dom =
       case f of
         Const ("Prod.lam", _) $ T $ _ => T
-      | _ => (case Typing.get_typing f (Typing.typing_assms ctxt) of
+      | Const ("Prod.compose", _) $ T $ _ $ _ => T
+      | _ => (case Typing.get_typing ctxt f of
                SOME (Const ("Prod.Prod", _) $ T $ _) => T
-             | SOME _ => Exn.error "Can't compose with a non-function"
-             | NONE => Exn.error "Cannot infer domain of composition: please state this explicitly")
+             | SOME t => (@{print} t; Exn.error "Can't compose with a non-function")
+             | NONE => Exn.error "Cannot infer domain of composition; please state this explicitly")
   in
     @{const compose} $ dom $ g $ f
   end
@@ -96,16 +96,30 @@ in
 end
 \<close>
 
+text \<open>Pretty-printing switch for composition; hides domain type information.\<close>
+
+ML \<open>val pretty_compose = Attrib.setup_config_bool @{binding "pretty_compose"} (K true)\<close>
+
+print_translation \<open>
+let fun compose_tr' ctxt [A, g, f] =
+  if Config.get ctxt pretty_compose
+  then Syntax.const @{syntax_const "_compose"} $ g $ f
+  else Const ("compose", Syntax.read_typ ctxt "t \<Rightarrow> t \<Rightarrow> t") $ A $ g $ f
+in
+  [(@{const_syntax compose}, compose_tr')]
+end
+\<close>
+
 lemma compose_assoc:
-  assumes "A: U i" "f: A \<rightarrow> B" "g: B \<rightarrow> C" "h: TT x: C. D x"
+  assumes "A: U i" and "f: A \<rightarrow> B" and "g: B \<rightarrow> C" and "h: TT x: C. D x"
   shows "compose A (compose B h g) f \<equiv> compose A h (compose A g f)"
 by (derive lems: assms cong)
 
 lemma compose_comp:
   assumes "A: U i" and "\<And>x. x: A \<Longrightarrow> b x: B" and "\<And>x. x: B \<Longrightarrow> c x: C x"
-  shows "(,\\x: B. c x) o (,\\x: A. b x) \<equiv> ,\\x: A. c (b x)"
+  shows "(\<lambda>x: B. c x) o (\<lambda>x: A. b x) \<equiv> \<lambda>x: A. c (b x)"
 by (derive lems: assms cong)
 
-abbreviation id :: "t \<Rightarrow> t" where "id A \<equiv> ,\\x: A. x"
+abbreviation id :: "t \<Rightarrow> t" where "id A \<equiv> \<lambda>x: A. x"
 
 end
diff --git a/typing.ML b/typing.ML
index bfe8409..4bcb633 100644
--- a/typing.ML
+++ b/typing.ML
@@ -6,15 +6,96 @@ Functionality for object-level type inference.
 
 ********)
 
+(* Context attribute for tracing; use declare[[trace=true]] at any point in a theory to turn on *)
+val trace = Attrib.setup_config_bool @{binding "trace"} (K false)
+
+(* ====================================== Helper functions ====================================== *)
+
+signature TYPING_LIB =
+sig
+  (* Lexical functions *)
+  val unmark: string -> string
+  
+  (* General functions *)
+  val get_all_thms: Proof.context -> (string * thm) list
+  val find_thm: Proof.context -> string -> (string * thm) list
+  
+  (* Get specific theorems *)
+  val get_this: Proof.context -> thm list
+  val get_assms: Proof.context -> thm list
+end
+
+structure Typing_Lib: TYPING_LIB =
+struct
+
+fun unmark s =
+  Lexicon.unmark_class s
+  handle Fail "unprefix" =>
+  Lexicon.unmark_type s
+  handle Fail "unprefix" =>
+  Lexicon.unmark_const s
+  handle Fail "unprefix" =>
+  Lexicon.unmark_fixed s
+  handle Fail "unprefix" =>
+  s
+
+fun name_and_thm (fact, thm) =
+  ((case fact of
+    Facts.Named ((name, _), _) => name
+  | Facts.Fact name => name),
+  thm)
+
+fun get_all_thms ctxt =
+  let val (_, ref_thms) = Find_Theorems.find_theorems ctxt NONE NONE true []
+  in ref_thms |> (map name_and_thm)
+  end
+
+(* Search all visible theorems (including local assumptions) containing a given name *)
+fun find_thm ctxt name =
+  let val (_, ref_thms) =
+    Find_Theorems.find_theorems ctxt NONE NONE true [(true, Find_Theorems.Name name)]
+  in
+    ref_thms |> (map name_and_thm)
+  end
+
+(* Get the fact corresponding to the Isar term "this" in the current proof scope *)
+fun get_this ctxt =
+  Proof_Context.get_fact ctxt (Facts.named "local.this")
+  handle ERROR "Undefined fact: \"local.this\"" => (
+    if (Config.get ctxt trace) then warning "\"this\" undefined in the context" else ();
+    []
+  )
+
+(* Get all visible assumptions in the current proof scope.
+   This includes the facts introduced in the statement of the goal using "assumes",
+   as well as all facts introduced using "assume" that are visible in the current block.
+ *)
+val get_assms = Assumption.all_prems_of
+
+end
+
+(* ================================ Type inference functionality ================================ *)
+
 signature TYPING =
 sig
   type jmt = term
+  val is_typing_jmt: term -> bool
   val term_of_jmt: jmt -> term
   val type_of_jmt: jmt -> term
+
+  val typing_this: Proof.context -> jmt list
   val typing_assms: Proof.context -> jmt list
-  val get_typing: term -> jmt list -> term option
-  val get_global_typing: theory -> Proof.context -> term -> term option
-  val tm_of_ptm: Proof.context -> term -> term
+  val typing_all: Proof.context -> jmt list
+
+  val get_typing_in: term -> jmt list -> term option
+  val get_local_typing: Proof.context -> term -> term option
+
+  val get_declared_typing: theory -> term -> term option
+  val put_declared_typing: term -> theory -> theory
+
+  val get_typing: Proof.context -> term -> term option
+
+  val prep_term: Proof.context -> term -> term
 end
 
 structure Typing: TYPING =
@@ -22,6 +103,10 @@ struct
 
 type jmt = term
 
+(* Determine if a term is a typing judgment *)
+fun is_typing_jmt (@{const has_type} $ _ $ _) = true
+  | is_typing_jmt _ = false
+
 (* Functions to extract a and A from propositions "a: A" *)
 fun term_of_jmt (@{const has_type} $ t $ _) = t
   | term_of_jmt _ = Exn.error "Not a typing judgment"
@@ -29,62 +114,106 @@ fun term_of_jmt (@{const has_type} $ t $ _) = t
 fun type_of_jmt (@{const has_type} $ _ $ T) = T
   | type_of_jmt _ = Exn.error "Not a typing judgment"
 
+(* Get typing assumptions in "this" *)
+fun typing_this ctxt = Typing_Lib.get_this ctxt |> map Thm.prop_of |> filter is_typing_jmt
+
 (* Get the typing assumptions in the current context *)
-fun typing_assms ctxt =
-  let
-    fun is_typing_jmt (@{const has_type} $ _ $ _) = true
-      | is_typing_jmt _ = false
-  in
-    Assumption.all_prems_of ctxt |> map Thm.prop_of |> filter is_typing_jmt
-  end
+val typing_assms = Typing_Lib.get_assms #> map Thm.prop_of #> filter is_typing_jmt
 
-(* Search for a term typing in a list of judgments*)
-fun get_typing tm jmts =
+(* Get all visible typing judgments—Quick hack for now; should record them separately *)
+fun typing_all ctxt =
+  Typing_Lib.get_all_thms ctxt |> map (Thm.prop_of o snd) |> filter is_typing_jmt
+
+(* Search for a term typing in a list of judgments, and return the type if found.
+   --
+   The use of aconv_untyped as opposed to aconv is crucial here:
+   meta-level type inference is performed *after* syntax translation, which means that
+   the translation functions see an unannotated term "f" (in contrast to one annotated
+   e.g. "f::t") as having a blank type field.
+   Using aconv would result in no match ever being found for f, because any judgment
+   involving f records it together with its (non-blank) type field, e.g.
+     "Free ("f", "_")"
+   seen by the translation function, vs.
+     "Free ("f", "t")"
+   recorded in the typing judgment.
+*)
+fun get_typing_in tm jmts =
   let val find_type =
         fn jmt => if Term.aconv_untyped (tm, term_of_jmt jmt) then SOME (type_of_jmt jmt) else NONE
   in get_first find_type jmts end
 
-(* Private storage space for global typing data *)
-structure Typing_Data = Theory_Data
+(* Search for typing in the local proof context (no global data).
+   We search the facts bound to "this" before searching the assumptions.
+   --
+   A previous version of this function passed the argument
+    (typing_this ctxt @ typing_assms ctxt)
+   to get_typing_in.
+   --
+   This version only evaluates successive lists if the search on the previous list was unsuccessful.
+*)
+fun get_local_typing ctxt tm =
+  case get_typing_in tm (typing_this ctxt) of
+    NONE => get_typing_in tm (typing_assms ctxt)
+  | res => res
+
+(* Storage space for declared typings *)
+structure Declared_Typings = Theory_Data
 (
   type T = term Symtab.table
   val empty = Symtab.empty
   val extend = I
-
-  fun merge (tbl, tbl') =
-    let
-      val key_vals = map (Symtab.lookup_key tbl') (Symtab.keys tbl')
-      val updates = map (fn SOME kv => Symtab.update kv) key_vals
-      fun f u t = u t
-    in fold f updates tbl end
+  val merge = K Symtab.empty
 )
-
 (* Accessor for the above data *)
-fun get_global_typing thy ctxt tm = Symtab.lookup (Typing_Data.get thy) (Syntax.string_of_term ctxt tm)
+fun get_declared_typing thy tm =
+  case tm of
+    (Free (v, _)) => Symtab.lookup (Declared_Typings.get thy) v
+  | _ => NONE
+
+(* Store new typing information for free variables only
+   (constants should have their types declared at the moment of definition).
+   End users should use the "typing" keyword instead.
+*)
+fun put_declared_typing jmt =
+  case jmt of
+    Const("HoTT_Base.has_type", _) $ term $ typing =>
+      (case term of
+        Free (v, _) => Declared_Typings.map (Symtab.update (v, typing))
+      | _ => Exn.error "Cannot declare typing assumption (not a free variable)")
+  | _ => Exn.error "Not a typing judgment"
+
+(* Get the typing of a term *)
+fun get_typing ctxt tm =
+  case get_local_typing ctxt tm of
+    NONE => get_declared_typing (Proof_Context.theory_of ctxt) tm
+  | res => res
 
-(* Convert a Pure pre-term to an unchecked Pure term *)
-fun tm_of_ptm ctxt ptm =
+(* Prepare a Pure pre-term, converting it partway to a (unchecked) term *)
+fun prep_term ctxt ptm =
   let val ptm = Term_Position.strip_positions ptm
   in
   (case ptm of
-    Const ("_constrain", _) $ Free (t, _) $ (Const ("\<^type>fun", _) $ Const(n1, _) $ Const (n2, _)) =>
+    Const ("_constrain", _) $ Free (t, _) $
+    (Const ("\<^type>fun", _) $ Const(typ1, _) $ Const (typ2, _)) =>
       let
-        val typ1 = unprefix "\<^type>" n1
-        val typ2 = unprefix "\<^type>" n2
+        val typ1 = Lexicon.unmark_type typ1
+        val typ2 = Lexicon.unmark_type typ2
         val typ = typ1 ^ "\<Rightarrow>" ^ typ2 |> Syntax.read_typ ctxt
       in Free (t, typ) end
-  | Const ("_constrain", _) $ Free (t, _) $ Const (T, _) =>
-      Free (t, Syntax.read_typ ctxt (unprefix "\<^type>" T))
+  | Const ("_constrain", _) $ t $ Const (typ, _) =>
+      let 
+        val T = Syntax.read_typ ctxt (Lexicon.unmark_type typ)
+      in
+        case t of
+          Free (s, _) => Free (s, T)
+        | Const (s, _) => Const (Lexicon.unmark_const s, T)
+        | _ => Exn.error "Unimplemented term constraint handler"
+      end
   | ptm1 $ ptm2 =>
-      (tm_of_ptm ctxt ptm1) $ (tm_of_ptm ctxt ptm2)
-  | Const (t, T) =>
-      let val t' =
-        unprefix "\<^const>" t handle Fail "unprefix" =>
-        unprefix "\<^type>" t handle Fail "unprefix" =>
-        t
-      in Const (t', T) end
+      (prep_term ctxt ptm1) $ (prep_term ctxt ptm2)
   | Abs (t, T, ptm') =>
-      Abs (t, T, tm_of_ptm ctxt ptm')
+      Abs (t, T, prep_term ctxt ptm')
+  | Const (t, T) => Const (Typing_Lib.unmark t, T)
   | t => t)
   end