wenzelm@9536: (* Title: Pure/term.ML wenzelm@9536: Author: Lawrence C Paulson, Cambridge University Computer Laboratory wenzelm@29280: Author: Makarius clasohm@1364: wenzelm@4444: Simply typed lambda-calculus: types, terms, and basic operations. clasohm@0: *) clasohm@0: wenzelm@29257: infix 9 $; clasohm@1364: infixr 5 -->; wenzelm@4444: infixr --->; wenzelm@4444: infix aconv; clasohm@1364: wenzelm@4444: signature BASIC_TERM = wenzelm@4444: sig wenzelm@22572: eqtype indexname wenzelm@22572: eqtype class wenzelm@22572: eqtype sort wenzelm@22572: eqtype arity wenzelm@4444: datatype typ = wenzelm@4444: Type of string * typ list | wenzelm@4444: TFree of string * sort | wenzelm@4444: TVar of indexname * sort wenzelm@16537: datatype term = wenzelm@16537: Const of string * typ | wenzelm@16537: Free of string * typ | wenzelm@16537: Var of indexname * typ | wenzelm@16537: Bound of int | wenzelm@16537: Abs of string * typ * term | wenzelm@17756: $ of term * term wenzelm@16537: exception TYPE of string * typ list * term list wenzelm@16537: exception TERM of string * term list wenzelm@21353: val dummyS: sort wenzelm@16710: val dummyT: typ wenzelm@16710: val no_dummyT: typ -> typ wenzelm@4444: val --> : typ * typ -> typ wenzelm@4444: val ---> : typ list * typ -> typ wenzelm@16710: val dest_Type: typ -> string * typ list wenzelm@16710: val dest_TVar: typ -> indexname * sort wenzelm@16710: val dest_TFree: typ -> string * sort wenzelm@16710: val is_Bound: term -> bool wenzelm@16710: val is_Const: term -> bool wenzelm@16710: val is_Free: term -> bool wenzelm@16710: val is_Var: term -> bool wenzelm@4444: val is_TVar: typ -> bool wenzelm@16710: val dest_Const: term -> string * typ wenzelm@16710: val dest_Free: term -> string * typ wenzelm@16710: val dest_Var: term -> indexname * typ wenzelm@4444: val domain_type: typ -> typ wenzelm@4480: val range_type: typ -> typ wenzelm@4444: val binder_types: typ -> typ list wenzelm@4444: val body_type: typ -> typ wenzelm@4444: val strip_type: typ -> typ list * typ wenzelm@16710: val type_of1: typ list * term -> typ wenzelm@4444: val type_of: term -> typ wenzelm@16710: val fastype_of1: typ list * term -> typ wenzelm@4444: val fastype_of: term -> typ wenzelm@10806: val list_abs: (string * typ) list * term -> term haftmann@18927: val strip_abs: term -> (string * typ) list * term wenzelm@4444: val strip_abs_body: term -> term wenzelm@4444: val strip_abs_vars: term -> (string * typ) list wenzelm@4444: val strip_qnt_body: string -> term -> term wenzelm@4444: val strip_qnt_vars: string -> term -> (string * typ) list wenzelm@4444: val list_comb: term * term list -> term wenzelm@4444: val strip_comb: term -> term * term list wenzelm@4444: val head_of: term -> term wenzelm@4444: val size_of_term: term -> int kleing@29882: val size_of_typ: typ -> int haftmann@18847: val map_atyps: (typ -> typ) -> typ -> typ haftmann@18847: val map_aterms: (term -> term) -> term -> term wenzelm@4444: val map_type_tvar: (indexname * sort -> typ) -> typ -> typ wenzelm@4444: val map_type_tfree: (string * sort -> typ) -> typ -> typ wenzelm@20548: val map_types: (typ -> typ) -> term -> term wenzelm@16943: val fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a wenzelm@16943: val fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a wenzelm@16943: val fold_term_types: (term -> typ -> 'a -> 'a) -> term -> 'a -> 'a wenzelm@16943: val fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a wenzelm@24483: val burrow_types: (typ list -> typ list) -> term list -> term list wenzelm@16710: val aconv: term * term -> bool wenzelm@4444: val propT: typ wenzelm@4444: val strip_all_body: term -> term wenzelm@4444: val strip_all_vars: term -> (string * typ) list wenzelm@4444: val incr_bv: int * int * term -> term wenzelm@4444: val incr_boundvars: int -> term -> term wenzelm@4444: val add_loose_bnos: term * int * int list -> int list wenzelm@4444: val loose_bnos: term -> int list wenzelm@4444: val loose_bvar: term * int -> bool wenzelm@4444: val loose_bvar1: term * int -> bool wenzelm@4444: val subst_bounds: term list * term -> term wenzelm@4444: val subst_bound: term * term -> term wenzelm@4444: val betapply: term * term -> term wenzelm@18183: val betapplys: term * term list -> term wenzelm@4444: val subst_free: (term * term) list -> term -> term wenzelm@4444: val abstract_over: term * term -> term wenzelm@11922: val lambda: term -> term -> term wenzelm@4444: val absfree: string * typ * term -> term wenzelm@17786: val absdummy: typ * term -> term wenzelm@4444: val list_abs_free: (string * typ) list * term -> term wenzelm@4444: val list_all_free: (string * typ) list * term -> term wenzelm@4444: val list_all: (string * typ) list * term -> term wenzelm@16710: val subst_atomic: (term * term) list -> term -> term wenzelm@16710: val typ_subst_atomic: (typ * typ) list -> typ -> typ wenzelm@16710: val subst_atomic_types: (typ * typ) list -> term -> term wenzelm@16710: val typ_subst_TVars: (indexname * typ) list -> typ -> typ wenzelm@16710: val subst_TVars: (indexname * typ) list -> term -> term wenzelm@16710: val subst_Vars: (indexname * term) list -> term -> term wenzelm@16710: val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term wenzelm@16710: val is_first_order: string list -> term -> bool wenzelm@4444: val maxidx_of_typ: typ -> int wenzelm@4444: val maxidx_of_typs: typ list -> int wenzelm@4444: val maxidx_of_term: term -> int wenzelm@19909: val exists_subtype: (typ -> bool) -> typ -> bool wenzelm@20531: val exists_type: (typ -> bool) -> term -> bool wenzelm@16943: val exists_subterm: (term -> bool) -> term -> bool wenzelm@16710: val exists_Const: (string * typ -> bool) -> term -> bool wenzelm@15986: val show_question_marks: bool ref wenzelm@4444: end; clasohm@0: wenzelm@4444: signature TERM = wenzelm@4444: sig wenzelm@4444: include BASIC_TERM wenzelm@19394: val aT: sort -> typ wenzelm@19394: val itselfT: typ -> typ wenzelm@19394: val a_itselfT: typ wenzelm@27335: val all: typ -> term wenzelm@22908: val argument_type_of: term -> int -> typ wenzelm@29257: val add_tvar_namesT: typ -> indexname list -> indexname list wenzelm@29257: val add_tvar_names: term -> indexname list -> indexname list wenzelm@16943: val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list wenzelm@16943: val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list wenzelm@29257: val add_var_names: term -> indexname list -> indexname list wenzelm@16943: val add_vars: term -> (indexname * typ) list -> (indexname * typ) list wenzelm@29257: val add_tfree_namesT: typ -> string list -> string list wenzelm@29257: val add_tfree_names: term -> string list -> string list wenzelm@16943: val add_tfreesT: typ -> (string * sort) list -> (string * sort) list wenzelm@16943: val add_tfrees: term -> (string * sort) list -> (string * sort) list wenzelm@29257: val add_free_names: term -> string list -> string list wenzelm@16943: val add_frees: term -> (string * typ) list -> (string * typ) list wenzelm@29286: val add_const_names: term -> string list -> string list wenzelm@29286: val add_consts: term -> (string * typ) list -> (string * typ) list wenzelm@25050: val hidden_polymorphism: term -> (indexname * sort) list wenzelm@29278: val declare_typ_names: typ -> Name.context -> Name.context wenzelm@29278: val declare_term_names: term -> Name.context -> Name.context wenzelm@29278: val declare_term_frees: term -> Name.context -> Name.context wenzelm@29278: val variant_frees: term -> (string * 'a) list -> (string * 'a) list wenzelm@29278: val rename_wrt_term: term -> (string * 'a) list -> (string * 'a) list wenzelm@29269: val eq_ix: indexname * indexname -> bool wenzelm@29269: val eq_tvar: (indexname * sort) * (indexname * sort) -> bool wenzelm@29269: val eq_var: (indexname * typ) * (indexname * typ) -> bool wenzelm@29269: val could_unify: term * term -> bool haftmann@20109: val strip_abs_eta: int -> term -> (string * typ) list * term wenzelm@12981: val match_bvars: (term * term) * (string * string) list -> (string * string) list haftmann@22031: val map_abs_vars: (string -> string) -> term -> term wenzelm@12981: val rename_abs: term -> term -> term -> term option wenzelm@25050: val close_schematic_term: term -> term wenzelm@16710: val maxidx_typ: typ -> int -> int wenzelm@16710: val maxidx_typs: typ list -> int -> int wenzelm@16710: val maxidx_term: term -> int -> int wenzelm@24671: val has_abs: term -> bool wenzelm@20239: val dest_abs: string * typ * term -> string * term wenzelm@9536: val dummy_patternN: string wenzelm@18253: val dummy_pattern: typ -> term wenzelm@22723: val is_dummy_pattern: term -> bool wenzelm@24733: val free_dummy_patterns: term -> Name.context -> term * Name.context wenzelm@9536: val no_dummy_patterns: term -> term wenzelm@24762: val replace_dummy_patterns: term -> int -> term * int wenzelm@10552: val is_replaced_dummy_pattern: indexname -> bool wenzelm@16035: val show_dummy_patterns: term -> term wenzelm@14786: val string_of_vname: indexname -> string wenzelm@14786: val string_of_vname': indexname -> string wenzelm@4444: end; wenzelm@4444: wenzelm@4444: structure Term: TERM = clasohm@1364: struct clasohm@0: clasohm@0: (*Indexnames can be quickly renamed by adding an offset to the integer part, clasohm@0: for resolution.*) wenzelm@16537: type indexname = string * int; clasohm@0: wenzelm@4626: (* Types are classified by sorts. *) clasohm@0: type class = string; clasohm@0: type sort = class list; wenzelm@14829: type arity = string * sort list * sort; clasohm@0: clasohm@0: (* The sorts attached to TFrees and TVars specify the sort of that variable *) clasohm@0: datatype typ = Type of string * typ list clasohm@0: | TFree of string * sort wenzelm@9536: | TVar of indexname * sort; clasohm@0: paulson@6033: (*Terms. Bound variables are indicated by depth number. clasohm@0: Free variables, (scheme) variables and constants have names. wenzelm@4626: An term is "closed" if every bound variable of level "lev" wenzelm@13000: is enclosed by at least "lev" abstractions. clasohm@0: clasohm@0: It is possible to create meaningless terms containing loose bound vars clasohm@0: or type mismatches. But such terms are not allowed in rules. *) clasohm@0: wenzelm@13000: datatype term = clasohm@0: Const of string * typ wenzelm@13000: | Free of string * typ clasohm@0: | Var of indexname * typ clasohm@0: | Bound of int clasohm@0: | Abs of string*typ*term wenzelm@3965: | op $ of term*term; clasohm@0: wenzelm@16537: (*Errors involving type mismatches*) clasohm@0: exception TYPE of string * typ list * term list; clasohm@0: wenzelm@16537: (*Errors errors involving terms*) clasohm@0: exception TERM of string * term list; clasohm@0: clasohm@0: (*Note variable naming conventions! clasohm@0: a,b,c: string clasohm@0: f,g,h: functions (including terms of function type) clasohm@0: i,j,m,n: int clasohm@0: t,u: term clasohm@0: v,w: indexnames clasohm@0: x,y: any clasohm@0: A,B,C: term (denoting formulae) clasohm@0: T,U: typ clasohm@0: *) clasohm@0: clasohm@0: paulson@6033: (** Types **) paulson@6033: wenzelm@21353: (*dummies for type-inference etc.*) wenzelm@21353: val dummyS = [""]; wenzelm@16537: val dummyT = Type ("dummy", []); wenzelm@16537: wenzelm@16537: fun no_dummyT typ = wenzelm@16537: let wenzelm@16537: fun check (T as Type ("dummy", _)) = wenzelm@16537: raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) wenzelm@16537: | check (Type (_, Ts)) = List.app check Ts wenzelm@16537: | check _ = (); wenzelm@16537: in check typ; typ end; wenzelm@16537: paulson@6033: fun S --> T = Type("fun",[S,T]); paulson@6033: paulson@6033: (*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) skalberg@15570: val op ---> = Library.foldr (op -->); paulson@6033: paulson@6033: fun dest_Type (Type x) = x paulson@6033: | dest_Type T = raise TYPE ("dest_Type", [T], []); dixon@15914: fun dest_TVar (TVar x) = x dixon@15914: | dest_TVar T = raise TYPE ("dest_TVar", [T], []); dixon@15914: fun dest_TFree (TFree x) = x dixon@15914: | dest_TFree T = raise TYPE ("dest_TFree", [T], []); paulson@6033: wenzelm@16537: clasohm@0: (** Discriminators **) clasohm@0: nipkow@7318: fun is_Bound (Bound _) = true nipkow@7318: | is_Bound _ = false; nipkow@7318: clasohm@0: fun is_Const (Const _) = true clasohm@0: | is_Const _ = false; clasohm@0: clasohm@0: fun is_Free (Free _) = true clasohm@0: | is_Free _ = false; clasohm@0: clasohm@0: fun is_Var (Var _) = true clasohm@0: | is_Var _ = false; clasohm@0: clasohm@0: fun is_TVar (TVar _) = true clasohm@0: | is_TVar _ = false; clasohm@0: wenzelm@16537: clasohm@0: (** Destructors **) clasohm@0: clasohm@0: fun dest_Const (Const x) = x clasohm@0: | dest_Const t = raise TERM("dest_Const", [t]); clasohm@0: clasohm@0: fun dest_Free (Free x) = x clasohm@0: | dest_Free t = raise TERM("dest_Free", [t]); clasohm@0: clasohm@0: fun dest_Var (Var x) = x clasohm@0: | dest_Var t = raise TERM("dest_Var", [t]); clasohm@0: clasohm@0: paulson@4464: fun domain_type (Type("fun", [T,_])) = T paulson@4464: and range_type (Type("fun", [_,T])) = T; paulson@4064: clasohm@0: (* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*) clasohm@0: fun binder_types (Type("fun",[S,T])) = S :: binder_types T clasohm@0: | binder_types _ = []; clasohm@0: clasohm@0: (* maps [T1,...,Tn]--->T to T*) clasohm@0: fun body_type (Type("fun",[S,T])) = body_type T clasohm@0: | body_type T = T; clasohm@0: clasohm@0: (* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *) clasohm@0: fun strip_type T : typ list * typ = clasohm@0: (binder_types T, body_type T); clasohm@0: clasohm@0: clasohm@0: (*Compute the type of the term, checking that combinations are well-typed clasohm@0: Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) clasohm@0: fun type_of1 (Ts, Const (_,T)) = T clasohm@0: | type_of1 (Ts, Free (_,T)) = T wenzelm@30146: | type_of1 (Ts, Bound i) = (nth Ts i skalberg@15570: handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i])) clasohm@0: | type_of1 (Ts, Var (_,T)) = T clasohm@0: | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body) wenzelm@13000: | type_of1 (Ts, f$u) = clasohm@0: let val U = type_of1(Ts,u) clasohm@0: and T = type_of1(Ts,f) clasohm@0: in case T of wenzelm@9536: Type("fun",[T1,T2]) => wenzelm@9536: if T1=U then T2 else raise TYPE wenzelm@9536: ("type_of: type mismatch in application", [T1,U], [f$u]) wenzelm@13000: | _ => raise TYPE wenzelm@9536: ("type_of: function type is expected in application", wenzelm@9536: [T,U], [f$u]) clasohm@0: end; clasohm@0: clasohm@0: fun type_of t : typ = type_of1 ([],t); clasohm@0: clasohm@0: (*Determines the type of a term, with minimal checking*) wenzelm@13000: fun fastype_of1 (Ts, f$u) = lcp@61: (case fastype_of1 (Ts,f) of wenzelm@9536: Type("fun",[_,T]) => T wenzelm@9536: | _ => raise TERM("fastype_of: expected function type", [f$u])) lcp@61: | fastype_of1 (_, Const (_,T)) = T lcp@61: | fastype_of1 (_, Free (_,T)) = T wenzelm@30146: | fastype_of1 (Ts, Bound i) = (nth Ts i skalberg@15570: handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) wenzelm@13000: | fastype_of1 (_, Var (_,T)) = T lcp@61: | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); lcp@61: lcp@61: fun fastype_of t : typ = fastype_of1 ([],t); clasohm@0: wenzelm@16678: (*Determine the argument type of a function*) wenzelm@22908: fun argument_type_of tm k = wenzelm@16678: let wenzelm@16678: fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U wenzelm@16678: | argT _ T = raise TYPE ("argument_type_of", [T], []); wenzelm@16678: wenzelm@16678: fun arg 0 _ (Abs (_, T, _)) = T wenzelm@16678: | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t wenzelm@16678: | arg i Ts (t $ _) = arg (i + 1) Ts t wenzelm@16678: | arg i Ts a = argT i (fastype_of1 (Ts, a)); wenzelm@22908: in arg k [] tm end; wenzelm@16678: clasohm@0: wenzelm@19473: val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t))); wenzelm@10806: haftmann@18927: fun strip_abs (Abs (a, T, t)) = haftmann@18927: let val (a', t') = strip_abs t haftmann@18927: in ((a, T) :: a', t') end haftmann@18927: | strip_abs t = ([], t); haftmann@18927: clasohm@0: (* maps (x1,...,xn)t to t *) wenzelm@13000: fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t clasohm@0: | strip_abs_body u = u; clasohm@0: clasohm@0: (* maps (x1,...,xn)t to [x1, ..., xn] *) wenzelm@13000: fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t clasohm@0: | strip_abs_vars u = [] : (string*typ) list; clasohm@0: clasohm@0: clasohm@0: fun strip_qnt_body qnt = clasohm@0: let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm clasohm@0: | strip t = t clasohm@0: in strip end; clasohm@0: clasohm@0: fun strip_qnt_vars qnt = clasohm@0: let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] clasohm@0: | strip t = [] : (string*typ) list clasohm@0: in strip end; clasohm@0: clasohm@0: clasohm@0: (* maps (f, [t1,...,tn]) to f(t1,...,tn) *) skalberg@15570: val list_comb : term * term list -> term = Library.foldl (op $); clasohm@0: clasohm@0: clasohm@0: (* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) wenzelm@13000: fun strip_comb u : term * term list = clasohm@0: let fun stripc (f$t, ts) = stripc (f, t::ts) wenzelm@13000: | stripc x = x clasohm@0: in stripc(u,[]) end; clasohm@0: clasohm@0: clasohm@0: (* maps f(t1,...,tn) to f , which is never a combination *) clasohm@0: fun head_of (f$t) = head_of f clasohm@0: | head_of u = u; clasohm@0: wenzelm@16599: (*number of atoms and abstractions in a term*) wenzelm@16599: fun size_of_term tm = wenzelm@16599: let wenzelm@30144: fun add_size (t $ u) n = add_size t (add_size u n) wenzelm@30144: | add_size (Abs (_ ,_, t)) n = add_size t (n + 1) wenzelm@30144: | add_size _ n = n + 1; wenzelm@30144: in add_size tm 0 end; clasohm@0: wenzelm@30144: (*number of atoms and constructors in a type*) kleing@29882: fun size_of_typ ty = kleing@29882: let wenzelm@30144: fun add_size (Type (_, tys)) n = fold add_size tys (n + 1) wenzelm@30144: | add_size _ n = n + 1; wenzelm@30144: in add_size ty 0 end; kleing@29882: haftmann@18847: fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts) haftmann@18976: | map_atyps f T = f T; haftmann@18847: haftmann@18847: fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u haftmann@18847: | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t) haftmann@18847: | map_aterms f t = f t; haftmann@18847: wenzelm@18981: fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T); wenzelm@18981: fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T); nipkow@949: wenzelm@20548: fun map_types f = wenzelm@16678: let wenzelm@16678: fun map_aux (Const (a, T)) = Const (a, f T) wenzelm@16678: | map_aux (Free (a, T)) = Free (a, f T) wenzelm@16678: | map_aux (Var (v, T)) = Var (v, f T) wenzelm@16678: | map_aux (t as Bound _) = t wenzelm@16678: | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t) wenzelm@16678: | map_aux (t $ u) = map_aux t $ map_aux u; wenzelm@16678: in map_aux end; clasohm@0: clasohm@0: wenzelm@16943: (* fold types and terms *) wenzelm@16943: wenzelm@16943: fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts wenzelm@16943: | fold_atyps f T = f T; wenzelm@16943: wenzelm@16943: fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u wenzelm@16943: | fold_aterms f (Abs (_, _, t)) = fold_aterms f t wenzelm@16943: | fold_aterms f a = f a; wenzelm@16943: wenzelm@16943: fun fold_term_types f (t as Const (_, T)) = f t T wenzelm@16943: | fold_term_types f (t as Free (_, T)) = f t T wenzelm@16943: | fold_term_types f (t as Var (_, T)) = f t T wenzelm@16943: | fold_term_types f (Bound _) = I wenzelm@16943: | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b wenzelm@16943: | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u; wenzelm@16943: wenzelm@16943: fun fold_types f = fold_term_types (K f); wenzelm@16943: wenzelm@24483: fun replace_types (Const (c, _)) (T :: Ts) = (Const (c, T), Ts) wenzelm@24483: | replace_types (Free (x, _)) (T :: Ts) = (Free (x, T), Ts) wenzelm@24483: | replace_types (Var (xi, _)) (T :: Ts) = (Var (xi, T), Ts) wenzelm@24483: | replace_types (Bound i) Ts = (Bound i, Ts) wenzelm@24483: | replace_types (Abs (x, _, b)) (T :: Ts) = wenzelm@24483: let val (b', Ts') = replace_types b Ts wenzelm@24483: in (Abs (x, T, b'), Ts') end wenzelm@24483: | replace_types (t $ u) Ts = wenzelm@24483: let wenzelm@24483: val (t', Ts') = replace_types t Ts; wenzelm@24483: val (u', Ts'') = replace_types u Ts'; wenzelm@24483: in (t' $ u', Ts'') end; wenzelm@24483: wenzelm@24483: fun burrow_types f ts = wenzelm@24483: let wenzelm@24483: val Ts = rev (fold (fold_types cons) ts []); wenzelm@24483: val Ts' = f Ts; wenzelm@24483: val (ts', []) = fold_map replace_types ts Ts'; wenzelm@24483: in ts' end; wenzelm@24483: wenzelm@16943: (*collect variables*) wenzelm@29257: val add_tvar_namesT = fold_atyps (fn TVar (xi, _) => insert (op =) xi | _ => I); wenzelm@29257: val add_tvar_names = fold_types add_tvar_namesT; wenzelm@16943: val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I); wenzelm@16943: val add_tvars = fold_types add_tvarsT; wenzelm@29257: val add_var_names = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I); wenzelm@16943: val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I); wenzelm@29257: val add_tfree_namesT = fold_atyps (fn TFree (xi, _) => insert (op =) xi | _ => I); wenzelm@29257: val add_tfree_names = fold_types add_tfree_namesT; wenzelm@16943: val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I); wenzelm@16943: val add_tfrees = fold_types add_tfreesT; wenzelm@29257: val add_free_names = fold_aterms (fn Free (x, _) => insert (op =) x | _ => I); wenzelm@16943: val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I); wenzelm@29286: val add_const_names = fold_aterms (fn Const (c, _) => insert (op =) c | _ => I); wenzelm@29286: val add_consts = fold_aterms (fn Const c => insert (op =) c | _ => I); wenzelm@16943: wenzelm@25050: (*extra type variables in a term, not covered by its type*) wenzelm@25050: fun hidden_polymorphism t = wenzelm@21682: let wenzelm@25050: val T = fastype_of t; wenzelm@21682: val tvarsT = add_tvarsT T []; wenzelm@21682: val extra_tvars = fold_types (fold_atyps wenzelm@21682: (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t []; wenzelm@21682: in extra_tvars end; wenzelm@21682: wenzelm@16943: wenzelm@29278: (* renaming variables *) wenzelm@29278: wenzelm@29278: val declare_typ_names = fold_atyps (fn TFree (a, _) => Name.declare a | _ => I); wenzelm@29278: wenzelm@29278: fun declare_term_names tm = wenzelm@29278: fold_aterms wenzelm@29278: (fn Const (a, _) => Name.declare (NameSpace.base a) wenzelm@29278: | Free (a, _) => Name.declare a wenzelm@29278: | _ => I) tm #> wenzelm@29278: fold_types declare_typ_names tm; wenzelm@29278: wenzelm@29278: val declare_term_frees = fold_aterms (fn Free (x, _) => Name.declare x | _ => I); wenzelm@29278: wenzelm@29278: fun variant_frees t frees = wenzelm@29278: fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees; wenzelm@29278: wenzelm@29278: fun rename_wrt_term t frees = rev (variant_frees t frees); (*reversed result!*) wenzelm@29278: wenzelm@29278: wenzelm@25050: wenzelm@29269: (** Comparing terms **) wenzelm@29269: wenzelm@29269: (* variables *) wenzelm@29269: wenzelm@29269: fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y; wenzelm@16537: wenzelm@29269: fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S'; wenzelm@29269: fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T'; wenzelm@29269: wenzelm@29269: wenzelm@29269: (* alpha equivalence *) wenzelm@20511: wenzelm@20511: fun tm1 aconv tm2 = wenzelm@20511: pointer_eq (tm1, tm2) orelse wenzelm@20511: (case (tm1, tm2) of wenzelm@20511: (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2 wenzelm@20511: | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2 wenzelm@20511: | (a1, a2) => a1 = a2); wenzelm@20511: wenzelm@20511: wenzelm@29269: (*A fast unification filter: true unless the two terms cannot be unified. wenzelm@29269: Terms must be NORMAL. Treats all Vars as distinct. *) wenzelm@29269: fun could_unify (t, u) = wenzelm@29269: let wenzelm@29269: fun matchrands (f $ t) (g $ u) = could_unify (t, u) andalso matchrands f g wenzelm@29269: | matchrands _ _ = true; wenzelm@29269: in wenzelm@29269: case (head_of t, head_of u) of wenzelm@29269: (_, Var _) => true wenzelm@29269: | (Var _, _) => true wenzelm@29269: | (Const (a, _), Const (b, _)) => a = b andalso matchrands t u wenzelm@29269: | (Free (a, _), Free (b, _)) => a = b andalso matchrands t u wenzelm@29269: | (Bound i, Bound j) => i = j andalso matchrands t u wenzelm@29269: | (Abs _, _) => true (*because of possible eta equality*) wenzelm@29269: | (_, Abs _) => true wenzelm@29269: | _ => false wenzelm@29269: end; wenzelm@16678: nipkow@16570: wenzelm@16537: clasohm@0: (** Connectives of higher order logic **) clasohm@0: wenzelm@24850: fun aT S = TFree (Name.aT, S); wenzelm@19394: wenzelm@375: fun itselfT ty = Type ("itself", [ty]); wenzelm@24850: val a_itselfT = itselfT (TFree (Name.aT, [])); wenzelm@375: clasohm@0: val propT : typ = Type("prop",[]); clasohm@0: clasohm@0: fun all T = Const("all", (T-->propT)-->propT); clasohm@0: clasohm@0: (* maps !!x1...xn. t to t *) wenzelm@13000: fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t clasohm@0: | strip_all_body t = t; clasohm@0: clasohm@0: (* maps !!x1...xn. t to [x1, ..., xn] *) clasohm@0: fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = wenzelm@13000: (a,T) :: strip_all_vars t clasohm@0: | strip_all_vars t = [] : (string*typ) list; clasohm@0: clasohm@0: (*increments a term's non-local bound variables clasohm@0: required when moving a term within abstractions clasohm@0: inc is increment for bound variables clasohm@0: lev is level at which a bound variable is considered 'loose'*) wenzelm@13000: fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u clasohm@0: | incr_bv (inc, lev, Abs(a,T,body)) = wenzelm@9536: Abs(a, T, incr_bv(inc,lev+1,body)) wenzelm@13000: | incr_bv (inc, lev, f$t) = clasohm@0: incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) clasohm@0: | incr_bv (inc, lev, u) = u; clasohm@0: clasohm@0: fun incr_boundvars 0 t = t clasohm@0: | incr_boundvars inc t = incr_bv(inc,0,t); clasohm@0: wenzelm@12981: (*Scan a pair of terms; while they are similar, wenzelm@12981: accumulate corresponding bound vars in "al"*) wenzelm@12981: fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = wenzelm@12981: match_bvs(s, t, if x="" orelse y="" then al wenzelm@12981: else (x,y)::al) wenzelm@12981: | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) wenzelm@12981: | match_bvs(_,_,al) = al; wenzelm@12981: wenzelm@12981: (* strip abstractions created by parameters *) wenzelm@12981: fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); wenzelm@12981: haftmann@22031: fun map_abs_vars f (t $ u) = map_abs_vars f t $ map_abs_vars f u haftmann@22031: | map_abs_vars f (Abs (a, T, t)) = Abs (f a, T, map_abs_vars f t) haftmann@22031: | map_abs_vars f t = t; haftmann@22031: wenzelm@12981: fun rename_abs pat obj t = wenzelm@12981: let wenzelm@12981: val ren = match_bvs (pat, obj, []); wenzelm@12981: fun ren_abs (Abs (x, T, b)) = wenzelm@18942: Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b) wenzelm@12981: | ren_abs (f $ t) = ren_abs f $ ren_abs t wenzelm@12981: | ren_abs t = t skalberg@15531: in if null ren then NONE else SOME (ren_abs t) end; clasohm@0: clasohm@0: (*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. clasohm@0: (Bound 0) is loose at level 0 *) wenzelm@13000: fun add_loose_bnos (Bound i, lev, js) = haftmann@20854: if i= k clasohm@0: | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) clasohm@0: | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) clasohm@0: | loose_bvar _ = false; clasohm@0: nipkow@2792: fun loose_bvar1(Bound i,k) = i = k nipkow@2792: | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) nipkow@2792: | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) nipkow@2792: | loose_bvar1 _ = false; clasohm@0: clasohm@0: (*Substitute arguments for loose bound variables. clasohm@0: Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi). wenzelm@4626: Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0 wenzelm@9536: and the appropriate call is subst_bounds([b,a], c) . clasohm@0: Loose bound variables >=n are reduced by "n" to clasohm@0: compensate for the disappearance of lambdas. clasohm@0: *) wenzelm@13000: fun subst_bounds (args: term list, t) : term = wenzelm@19065: let wenzelm@19065: exception SAME; wenzelm@19065: val n = length args; wenzelm@19065: fun subst (t as Bound i, lev) = wenzelm@19065: (if i < lev then raise SAME (*var is locally bound*) wenzelm@30146: else incr_boundvars lev (nth args (i - lev)) wenzelm@19065: handle Subscript => Bound (i - n)) (*loose: change it*) wenzelm@19065: | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1)) wenzelm@19065: | subst (f $ t, lev) = wenzelm@19065: (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev)) wenzelm@19065: | subst _ = raise SAME; wenzelm@19065: in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end; clasohm@0: paulson@2192: (*Special case: one argument*) wenzelm@13000: fun subst_bound (arg, t) : term = wenzelm@19065: let wenzelm@19065: exception SAME; wenzelm@19065: fun subst (Bound i, lev) = wenzelm@19065: if i < lev then raise SAME (*var is locally bound*) wenzelm@19065: else if i = lev then incr_boundvars lev arg wenzelm@19065: else Bound (i - 1) (*loose: change it*) wenzelm@19065: | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1)) wenzelm@19065: | subst (f $ t, lev) = wenzelm@19065: (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev)) wenzelm@19065: | subst _ = raise SAME; wenzelm@19065: in subst (t, 0) handle SAME => t end; paulson@2192: clasohm@0: (*beta-reduce if possible, else form application*) paulson@2192: fun betapply (Abs(_,_,t), u) = subst_bound (u,t) clasohm@0: | betapply (f,u) = f$u; clasohm@0: wenzelm@18183: val betapplys = Library.foldl betapply; wenzelm@18183: wenzelm@14786: haftmann@20109: (*unfolding abstractions with substitution haftmann@20109: of bound variables and implicit eta-expansion*) haftmann@20109: fun strip_abs_eta k t = haftmann@20109: let wenzelm@29278: val used = fold_aterms declare_term_frees t Name.context; haftmann@20109: fun strip_abs t (0, used) = (([], t), (0, used)) haftmann@20109: | strip_abs (Abs (v, T, t)) (k, used) = haftmann@20109: let wenzelm@20122: val ([v'], used') = Name.variants [v] used; haftmann@21013: val t' = subst_bound (Free (v', T), t); wenzelm@20122: val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used'); wenzelm@20122: in (((v', T) :: vs, t''), (k', used'')) end haftmann@20109: | strip_abs t (k, used) = (([], t), (k, used)); haftmann@20109: fun expand_eta [] t _ = ([], t) haftmann@20109: | expand_eta (T::Ts) t used = haftmann@20109: let wenzelm@20122: val ([v], used') = Name.variants [""] used; wenzelm@20122: val (vs, t') = expand_eta Ts (t $ Free (v, T)) used'; haftmann@20109: in ((v, T) :: vs, t') end; haftmann@20109: val ((vs1, t'), (k', used')) = strip_abs t (k, used); haftmann@20109: val Ts = (fst o chop k' o fst o strip_type o fastype_of) t'; haftmann@20109: val (vs2, t'') = expand_eta Ts t' used'; haftmann@20109: in (vs1 @ vs2, t'') end; haftmann@20109: haftmann@20109: clasohm@0: (*Substitute new for free occurrences of old in a term*) wenzelm@29256: fun subst_free [] = I clasohm@0: | subst_free pairs = wenzelm@13000: let fun substf u = haftmann@17314: case AList.lookup (op aconv) pairs u of skalberg@15531: SOME u' => u' skalberg@15531: | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t) wenzelm@9536: | t$u' => substf t $ substf u' wenzelm@9536: | _ => u) clasohm@0: in substf end; clasohm@0: wenzelm@13000: (*Abstraction of the term "body" over its occurrences of v, clasohm@0: which must contain no loose bound variables. clasohm@0: The resulting term is ready to become the body of an Abs.*) wenzelm@16882: fun abstract_over (v, body) = wenzelm@16882: let wenzelm@16990: exception SAME; wenzelm@16990: fun abs lev tm = wenzelm@16990: if v aconv tm then Bound lev wenzelm@16882: else wenzelm@16990: (case tm of wenzelm@16990: Abs (a, T, t) => Abs (a, T, abs (lev + 1) t) wenzelm@16990: | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u) wenzelm@16990: | _ => raise SAME); wenzelm@16990: in abs 0 body handle SAME => body end; clasohm@0: wenzelm@21975: fun lambda v t = wenzelm@21975: let val x = wenzelm@21975: (case v of wenzelm@21975: Const (x, _) => NameSpace.base x wenzelm@21975: | Free (x, _) => x wenzelm@21975: | Var ((x, _), _) => x wenzelm@24850: | _ => Name.uu) wenzelm@21975: in Abs (x, fastype_of v, abstract_over (v, t)) end; clasohm@0: clasohm@0: (*Form an abstraction over a free variable.*) wenzelm@21975: fun absfree (a,T,body) = Abs (a, T, abstract_over (Free (a, T), body)); wenzelm@24850: fun absdummy (T, body) = Abs (Name.internal Name.uu, T, body); clasohm@0: clasohm@0: (*Abstraction over a list of free variables*) clasohm@0: fun list_abs_free ([ ] , t) = t wenzelm@13000: | list_abs_free ((a,T)::vars, t) = clasohm@0: absfree(a, T, list_abs_free(vars,t)); clasohm@0: clasohm@0: (*Quantification over a list of free variables*) clasohm@0: fun list_all_free ([], t: term) = t wenzelm@13000: | list_all_free ((a,T)::vars, t) = clasohm@0: (all T) $ (absfree(a, T, list_all_free(vars,t))); clasohm@0: clasohm@0: (*Quantification over a list of variables (already bound in body) *) clasohm@0: fun list_all ([], t) = t wenzelm@13000: | list_all ((a,T)::vars, t) = clasohm@0: (all T) $ (Abs(a, T, list_all(vars,t))); clasohm@0: wenzelm@16678: (*Replace the ATOMIC term ti by ui; inst = [(t1,u1), ..., (tn,un)]. clasohm@0: A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) wenzelm@16678: fun subst_atomic [] tm = tm wenzelm@16678: | subst_atomic inst tm = wenzelm@16678: let wenzelm@16678: fun subst (Abs (a, T, body)) = Abs (a, T, subst body) wenzelm@16678: | subst (t $ u) = subst t $ subst u wenzelm@18942: | subst t = the_default t (AList.lookup (op aconv) inst t); wenzelm@16678: in subst tm end; clasohm@0: wenzelm@16678: (*Replace the ATOMIC type Ti by Ui; inst = [(T1,U1), ..., (Tn,Un)].*) wenzelm@16678: fun typ_subst_atomic [] ty = ty wenzelm@16678: | typ_subst_atomic inst ty = wenzelm@16678: let wenzelm@16678: fun subst (Type (a, Ts)) = Type (a, map subst Ts) wenzelm@18942: | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T); wenzelm@16678: in subst ty end; berghofe@15797: wenzelm@16678: fun subst_atomic_types [] tm = tm wenzelm@20548: | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm; wenzelm@16678: wenzelm@16678: fun typ_subst_TVars [] ty = ty wenzelm@16678: | typ_subst_TVars inst ty = wenzelm@16678: let wenzelm@16678: fun subst (Type (a, Ts)) = Type (a, map subst Ts) wenzelm@18942: | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi) wenzelm@16678: | subst T = T; wenzelm@16678: in subst ty end; clasohm@0: wenzelm@16678: fun subst_TVars [] tm = tm wenzelm@20548: | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm; clasohm@0: wenzelm@16678: fun subst_Vars [] tm = tm wenzelm@16678: | subst_Vars inst tm = wenzelm@16678: let wenzelm@18942: fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi) wenzelm@16678: | subst (Abs (a, T, t)) = Abs (a, T, subst t) wenzelm@16678: | subst (t $ u) = subst t $ subst u wenzelm@16678: | subst t = t; wenzelm@16678: in subst tm end; clasohm@0: wenzelm@16678: fun subst_vars ([], []) tm = tm wenzelm@16678: | subst_vars ([], inst) tm = subst_Vars inst tm wenzelm@16678: | subst_vars (instT, inst) tm = wenzelm@16678: let wenzelm@16678: fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T) wenzelm@16678: | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T) wenzelm@16678: | subst (t as Var (xi, T)) = haftmann@17271: (case AList.lookup (op =) inst xi of wenzelm@16678: NONE => Var (xi, typ_subst_TVars instT T) wenzelm@16678: | SOME t => t) wenzelm@16678: | subst (t as Bound _) = t wenzelm@16678: | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t) wenzelm@16678: | subst (t $ u) = subst t $ subst u; wenzelm@16678: in subst tm end; clasohm@0: wenzelm@25050: fun close_schematic_term t = wenzelm@25050: let wenzelm@25050: val extra_types = map (fn v => Const ("TYPE", itselfT (TVar v))) (hidden_polymorphism t); wenzelm@25050: val extra_terms = map Var (rev (add_vars t [])); wenzelm@25050: in fold_rev lambda (extra_types @ extra_terms) t end; wenzelm@25050: wenzelm@25050: clasohm@0: paulson@15573: (** Identifying first-order terms **) paulson@15573: wenzelm@20199: (*Differs from proofterm/is_fun in its treatment of TVar*) wenzelm@29256: fun is_funtype (Type ("fun", [_, _])) = true wenzelm@20199: | is_funtype _ = false; wenzelm@20199: paulson@15573: (*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) wenzelm@29256: fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts, t))); paulson@15573: wenzelm@16537: (*First order means in all terms of the form f(t1,...,tn) no argument has a paulson@16589: function type. The supplied quantifiers are excluded: their argument always paulson@16589: has a function type through a recursive call into its body.*) wenzelm@16667: fun is_first_order quants = paulson@16589: let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body wenzelm@16667: | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) = wenzelm@20664: member (op =) quants q andalso (*it is a known quantifier*) paulson@16589: not (is_funtype T) andalso first_order1 (T::Ts) body wenzelm@16667: | first_order1 Ts t = wenzelm@16667: case strip_comb t of wenzelm@16667: (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts wenzelm@16667: | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts wenzelm@16667: | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts wenzelm@16667: | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts wenzelm@16667: | (Abs _, ts) => false (*not in beta-normal form*) wenzelm@16667: | _ => error "first_order: unexpected case" paulson@16589: in first_order1 [] end; paulson@15573: wenzelm@16710: wenzelm@16990: (* maximum index of typs and terms *) clasohm@0: wenzelm@16710: fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j) wenzelm@16710: | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i wenzelm@16710: | maxidx_typ (TFree _) i = i wenzelm@16710: and maxidx_typs [] i = i wenzelm@16710: | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i); clasohm@0: wenzelm@16710: fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j)) wenzelm@16710: | maxidx_term (Const (_, T)) i = maxidx_typ T i wenzelm@16710: | maxidx_term (Free (_, T)) i = maxidx_typ T i wenzelm@16710: | maxidx_term (Bound _) i = i wenzelm@16710: | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i) wenzelm@16710: | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i); clasohm@0: wenzelm@16710: fun maxidx_of_typ T = maxidx_typ T ~1; wenzelm@16710: fun maxidx_of_typs Ts = maxidx_typs Ts ~1; wenzelm@16710: fun maxidx_of_term t = maxidx_term t ~1; berghofe@13665: clasohm@0: clasohm@0: wenzelm@29270: (** misc syntax operations **) clasohm@0: wenzelm@19909: (* substructure *) wenzelm@4017: wenzelm@19909: fun exists_subtype P = wenzelm@19909: let wenzelm@19909: fun ex ty = P ty orelse wenzelm@19909: (case ty of Type (_, Ts) => exists ex Ts | _ => false); wenzelm@19909: in ex end; nipkow@13646: wenzelm@20531: fun exists_type P = wenzelm@20531: let wenzelm@20531: fun ex (Const (_, T)) = P T wenzelm@20531: | ex (Free (_, T)) = P T wenzelm@20531: | ex (Var (_, T)) = P T wenzelm@20531: | ex (Bound _) = false wenzelm@20531: | ex (Abs (_, T, t)) = P T orelse ex t wenzelm@20531: | ex (t $ u) = ex t orelse ex u; wenzelm@20531: in ex end; wenzelm@20531: wenzelm@16943: fun exists_subterm P = wenzelm@16943: let wenzelm@16943: fun ex tm = P tm orelse wenzelm@16943: (case tm of wenzelm@16943: t $ u => ex t orelse ex u wenzelm@16943: | Abs (_, _, t) => ex t wenzelm@16943: | _ => false); wenzelm@16943: in ex end; obua@16108: wenzelm@29270: fun exists_Const P = exists_subterm (fn Const c => P c | _ => false); wenzelm@29270: wenzelm@24671: fun has_abs (Abs _) = true wenzelm@24671: | has_abs (t $ u) = has_abs t orelse has_abs u wenzelm@24671: | has_abs _ = false; wenzelm@24671: wenzelm@24671: wenzelm@20199: (* dest abstraction *) clasohm@0: wenzelm@16678: fun dest_abs (x, T, body) = wenzelm@16678: let wenzelm@16678: fun name_clash (Free (y, _)) = (x = y) wenzelm@16678: | name_clash (t $ u) = name_clash t orelse name_clash u wenzelm@16678: | name_clash (Abs (_, _, t)) = name_clash t wenzelm@16678: | name_clash _ = false; wenzelm@16678: in wenzelm@27335: if name_clash body then dest_abs (Name.variant [x] x, T, body) (*potentially slow*) wenzelm@16678: else (x, subst_bound (Free (x, T), body)) wenzelm@16678: end; wenzelm@16678: wenzelm@20160: wenzelm@9536: (* dummy patterns *) wenzelm@9536: wenzelm@9536: val dummy_patternN = "dummy_pattern"; wenzelm@9536: wenzelm@18253: fun dummy_pattern T = Const (dummy_patternN, T); wenzelm@18253: wenzelm@9536: fun is_dummy_pattern (Const ("dummy_pattern", _)) = true wenzelm@9536: | is_dummy_pattern _ = false; wenzelm@9536: wenzelm@9536: fun no_dummy_patterns tm = haftmann@16787: if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm wenzelm@9536: else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]); wenzelm@9536: wenzelm@24733: fun free_dummy_patterns (Const ("dummy_pattern", T)) used = wenzelm@24850: let val [x] = Name.invents used Name.uu 1 wenzelm@24733: in (Free (Name.internal x, T), Name.declare x used) end wenzelm@24733: | free_dummy_patterns (Abs (x, T, b)) used = wenzelm@24733: let val (b', used') = free_dummy_patterns b used wenzelm@24733: in (Abs (x, T, b'), used') end wenzelm@24733: | free_dummy_patterns (t $ u) used = wenzelm@24733: let wenzelm@24733: val (t', used') = free_dummy_patterns t used; wenzelm@24733: val (u', used'') = free_dummy_patterns u used'; wenzelm@24733: in (t' $ u', used'') end wenzelm@24733: | free_dummy_patterns a used = (a, used); wenzelm@24733: wenzelm@24762: fun replace_dummy Ts (Const ("dummy_pattern", T)) i = wenzelm@24762: (list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)), i + 1) wenzelm@24762: | replace_dummy Ts (Abs (x, T, t)) i = wenzelm@24762: let val (t', i') = replace_dummy (T :: Ts) t i wenzelm@24762: in (Abs (x, T, t'), i') end wenzelm@24762: | replace_dummy Ts (t $ u) i = wenzelm@24762: let wenzelm@24762: val (t', i') = replace_dummy Ts t i; wenzelm@24762: val (u', i'') = replace_dummy Ts u i'; wenzelm@24762: in (t' $ u', i'') end wenzelm@24762: | replace_dummy _ a i = (a, i); wenzelm@11903: wenzelm@11903: val replace_dummy_patterns = replace_dummy []; wenzelm@9536: wenzelm@10552: fun is_replaced_dummy_pattern ("_dummy_", _) = true wenzelm@10552: | is_replaced_dummy_pattern _ = false; wenzelm@9536: wenzelm@16035: fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T) wenzelm@16035: | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u wenzelm@16035: | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t) wenzelm@16035: | show_dummy_patterns a = a; wenzelm@16035: wenzelm@13484: wenzelm@20100: (* display variables *) wenzelm@20100: wenzelm@15986: val show_question_marks = ref true; berghofe@15472: wenzelm@14786: fun string_of_vname (x, i) = wenzelm@14786: let wenzelm@15986: val question_mark = if ! show_question_marks then "?" else ""; wenzelm@15986: val idx = string_of_int i; wenzelm@15986: val dot = wenzelm@15986: (case rev (Symbol.explode x) of wenzelm@15986: _ :: "\\<^isub>" :: _ => false wenzelm@15986: | _ :: "\\<^isup>" :: _ => false wenzelm@15986: | c :: _ => Symbol.is_digit c wenzelm@15986: | _ => true); wenzelm@14786: in wenzelm@15986: if dot then question_mark ^ x ^ "." ^ idx wenzelm@15986: else if i <> 0 then question_mark ^ x ^ idx wenzelm@15986: else question_mark ^ x wenzelm@14786: end; wenzelm@14786: wenzelm@14786: fun string_of_vname' (x, ~1) = x wenzelm@14786: | string_of_vname' xi = string_of_vname xi; wenzelm@14786: clasohm@1364: end; clasohm@1364: wenzelm@4444: structure BasicTerm: BASIC_TERM = Term; wenzelm@4444: open BasicTerm;