Warren's Abstract Machine

A gradual WAM implementation in Clojure following Hassan Aït-Kaci's tutorial reconstruction.

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Language ℒ₀ – Unification

Exercise 2.1 (pg. 9)

Verify that the effect of executing the sequence of instructions shown in Figure 2.3 (starting with H = 0) does indeed yield a correct heap representation for the term p(Z, h(Z, W), f(W)) — the one shown earlier as Figure 2.1, in fact.

See ℳ₀ machine instructions for implementation details

  (use 'wam.instruction-set)
  (use 'wam.store)
  (use 'table.core)

  (def context (make-context))

  (->
    context
    (put-structure 'h|2, 'X3)
    (set-variable 'X2)
    (set-variable 'X5)
    (put-structure 'f|1, 'X4)
    (set-value 'X5)
    (put-structure 'p|3, 'X1)
    (set-value 'X2)
    (set-value 'X3)
    (set-value 'X4)
    heap
    (table :style :unicode))

Produces:

┌──────┬────────────┐
│ key  │ value      │
├──────┼────────────┤
│ 1000 ╎ [STR 1001] │
│ 1001 ╎ h|2        │
│ 1002 ╎ [REF 1002] │
│ 1003 ╎ [REF 1003] │
│ 1004 ╎ [STR 1005] │
│ 1005 ╎ f|1        │
│ 1006 ╎ [REF 1003] │
│ 1007 ╎ [STR 1008] │
│ 1008 ╎ p|3        │
│ 1009 ╎ [REF 1002] │
│ 1010 ╎ [STR 1001] │
│ 1011 ╎ [STR 1005] │
└──────┴────────────┘

EBNF ℒ₀ Grammar & Parser Combinators

The simplistic EBNF grammar rules for ℒ₀ below have been implemented using a parser monad.

<Digit> ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
<Number> ::= <Digit> <Digit>*
<LowerAlpha> ::= 'a' .. 'z'
<UpperAlpha> ::= 'A' .. 'Z'
<AlphaNum> ::= <LowerAlpha> | <UpperAlpha> | <Digit>
<Predicate> ::= <LowerAlpha> <AlphaNum>*
<Constant> ::= <Number>
<Variable> ::= <UpperAlpha> <AlphaNum>* | '_'
<Structure> ::= <Predicate> | <Predicate> '(' <List> ')'
<List> ::= <Element> | <Element> ',' <List>
<Element> ::= <Variable> | <Constant> | <Structure>

Parsing the term p(Z, h(Z, W), f(W)) with:

(use 'wam.grammar)
(use 'jasentaa.parser)
(parse-all structure "p(Z, h(Z, W), f(W))")

yields a structure as follows:

#Structure{:functor p|3,
           :args (#Variable{:name Z}
                  #Structure{:functor h|2,
                             :args (#Variable{:name Z}
                                    #Variable{:name W}})}
                  #Structure{:functor f|1,
                             :args (#Variable{:name W})})}

Compiling ℒ₀ queries

Now that the term p(Z, h(Z, W), f(W)) parses into a hierarchical data structure, a breadth-first search is employed to allocate registers on a least available index basis:

(use 'wam.compiler)
(use 'wam.grammar)
(use 'jasentaa.parser)
(use 'table.core)

(def term (parse-all structure "p(Z, h(Z, W), f(W))"))
(table (register-allocation term) :style :unicode)

evaluates as:

┌──────────────────┬───────┐
│ key              │ value │
├──────────────────┼───────┤
│ p(Z h(Z W) f(W)) ╎ X1    │
│ Z                ╎ X2    │
│ h(Z W)           ╎ X3    │
│ f(W)             ╎ X4    │
│ W                ╎ X5    │
└──────────────────┴───────┘

Inspecting the structures, and indeed it matches as follows:

X1 = p(X2, X3, X4)
X2 = Z
X3 = h(X2, X5)
X4 = f(X5)
X5 = W

Next, given that we have a linear register allocation, walking the query term structures in depth-first post-order means that instructions can be assembled as follows:

(use 'wam.compiler)
(use 'wam.grammar)
(use 'table.core)

(table
  (cons
    ["instr" "arg1" "arg2"]
    (emit-instructions query-builder term (register-allocation term)))
  :style :unicode)

Which returns a list of instructions, which corresponds to Figure 2.3 in the tutorial:

┌──────────────────────────────────────────────┬──────┬──────┐
│ instr                                        │ arg1 │ arg2 │
├──────────────────────────────────────────────┼──────┼──────┤
│ #function[wam.instruction-set/put-structure] ╎ h|2  ╎ X3   │
│ #function[wam.instruction-set/set-variable]  ╎ X2   ╎      │
│ #function[wam.instruction-set/set-variable]  ╎ X5   ╎      │
│ #function[wam.instruction-set/put-structure] ╎ f|1  ╎ X4   │
│ #function[wam.instruction-set/set-value]     ╎ X5   ╎      │
│ #function[wam.instruction-set/put-structure] ╎ p|3  ╎ X1   │
│ #function[wam.instruction-set/set-value]     ╎ X2   ╎      │
│ #function[wam.instruction-set/set-value]     ╎ X3   ╎      │
│ #function[wam.instruction-set/set-value]     ╎ X4   ╎      │
└──────────────────────────────────────────────┴──────┴──────┘

The instructions are not directly executable as yet, as a context must be supplied in the first argument to each instruction, but they are however in a suitable format for returning a function that can execute them given a context:

(use 'wam.compiler)
(use 'wam.grammar)
(use 'wam.store)
(use 'table.core)

(def context (make-context))

(def query0
  (->>
    "p(Z, h(Z, W), f(W))"
    (parse-all structure)
    (compile-term query-builder)))

(-> context query0 heap table)

This produces the same heap representation as earlier, but significantly, was instead generated automatically from executing emitted WAM instructions, which were derived from hierarchical data structures, which in turn were parsed from a string representation "p(Z, h(Z, W), f(W))".

┌──────┬────────────┐
│ key  │ value      │
├──────┼────────────┤
│ 1000 ╎ [STR 1001] │
│ 1001 ╎ h|2        │
│ 1002 ╎ [REF 1002] │
│ 1003 ╎ [REF 1003] │
│ 1004 ╎ [STR 1005] │
│ 1005 ╎ f|1        │
│ 1006 ╎ [REF 1003] │
│ 1007 ╎ [STR 1008] │
│ 1008 ╎ p|3        │
│ 1009 ╎ [REF 1002] │
│ 1010 ╎ [STR 1001] │
│ 1011 ╎ [STR 1005] │
└──────┴────────────┘

Compiling ℒ₀ programs

Compiling a program term follows a similar vein to query term construction: registers are allocated breadth-first, but instead of walking the tree in post-order, a program is walked in pre-order. The rules for emitting instructions are also subtly different. Assuming the same helper methods as before:

(use 'wam.compiler)
(use 'wam.grammar)
(use 'table.core)

; Assume the same helper functions as before

(def term (parse-all structure "p(f(X), h(Y, f(a)), Y)"))

(table
  (cons
    ["instr" "arg1" "arg2"]
    (emit-instructions program-builder term (register-allocation term)))
  :style :unicode)

Which returns a list of instructions, which corresponds to Figure 2.4 in the tutorial:

┌───────────────────────────────────────────────┬──────┬──────┐
│ instr                                         │ arg1 │ arg2 │
├───────────────────────────────────────────────┼──────┼──────┤
│ #function[wam.instruction-set/get-structure]  ╎ p|3  ╎ X1   │
│ #function[wam.instruction-set/unify-variable] ╎ X2   ╎      │
│ #function[wam.instruction-set/unify-variable] ╎ X3   ╎      │
│ #function[wam.instruction-set/unify-variable] ╎ X4   ╎      │
│ #function[wam.instruction-set/get-structure]  ╎ f|1  ╎ X2   │
│ #function[wam.instruction-set/unify-variable] ╎ X5   ╎      │
│ #function[wam.instruction-set/get-structure]  ╎ h|2  ╎ X3   │
│ #function[wam.instruction-set/unify-value]    ╎ X4   ╎      │
│ #function[wam.instruction-set/unify-variable] ╎ X6   ╎      │
│ #function[wam.instruction-set/get-structure]  ╎ f|1  ╎ X6   │
│ #function[wam.instruction-set/unify-variable] ╎ X7   ╎      │
│ #function[wam.instruction-set/get-structure]  ╎ a|0  ╎ X7   │
└───────────────────────────────────────────────┴──────┴──────┘

Exercise 2.2 (pg. 14)

Give heap representations for the terms f(X, g(X, a)) and f(b, Y). Let a₁ and a₂ be their respective heap addresses, and let a_x and a_y be the heap addresses corresponding to variables X and Y, respectively. Trace the effects of executing unify(a₁, a₂), verifying that it terminates with the eventual dereferenced bindings from a_x and a_y corresponding to X = b and Y = g(b, a).

By applying the query terms to an empty context,

(use 'wam.compiler)
(use 'wam.store)
(use 'table.core)

(->
  (make-context)
  (query "f(X, g(X, a))")
  (query "f(b, Y)")
  diag)

Gives the following heap structure. Note that the heap addresses for a₁, a₂, a_x and a_y have been annotated at locations 1006, 1012, 1008 and 1015 respectively.

Heap                   Registers             Variables
------------------------------------------------------------
┌──────┬────────────┐  ┌─────┬────────────┐  ┌─────┬───────┐
│ key  │ value      │  │ key │ value      │  │ key │ value │
├──────┼────────────┤  ├─────┼────────────┤  ├─────┼───────┤
│ 1000 ╎ [STR 1001] │  │ X1  ╎ [STR 1013] │  │ X   ╎ X2    │
│ 1001 ╎ a|0        │  │ X2  ╎ [STR 1011] │  │ Y   ╎ X3    │
│ 1002 ╎ [STR 1003] │  │ X3  ╎ [REF 1015] │  └─────┴───────┘
│ 1003 ╎ g|2        │  │ X4  ╎ [STR 1001] │
│ 1004 ╎ [REF 1004] │  └─────┴────────────┘
│ 1005 ╎ [STR 1001] │
│ 1006 ╎ [STR 1007] │    ← a1
│ 1007 ╎ f|2        │
│ 1008 ╎ [REF 1004] │    ← aX
│ 1009 ╎ [STR 1003] │
│ 1010 ╎ [STR 1011] │
│ 1011 ╎ b|0        │
│ 1012 ╎ [STR 1013] │    ← a2
│ 1013 ╎ f|2        │
│ 1014 ╎ [STR 1011] │
│ 1015 ╎ [REF 1015] │    ← aY
└──────┴────────────┘

Now, calling unify(a₁, a₂), the changed context store is displayed below.

(use 'wam.anciliary)

(defn tee [v func]
  (func v)
  v)

(->
  (make-context)
  (query "f(X, g(X, a))")
  (query "f(b, Y)")
  (unify 1012 1006)
  diag
  (tee #(println "X =" (resolve-struct % (register-address 'X2))))
  (tee #(println "Y =" (resolve-struct % (register-address 'X3)))))

Note that the context failed flag returns as false (not shown), indicating unification was successful.

Heap                   Registers             Variables
------------------------------------------------------------
┌──────┬────────────┐  ┌─────┬────────────┐  ┌─────┬───────┐
│ key  │ value      │  │ key │ value      │  │ key │ value │
├──────┼────────────┤  ├─────┼────────────┤  ├─────┼───────┤
│ 1000 ╎ [STR 1001] │  │ X1  ╎ [STR 1013] │  │ X   ╎ X2    │
│ 1001 ╎ a|0        │  │ X2  ╎ [STR 1011] │  │ Y   ╎ X3    │
│ 1002 ╎ [STR 1003] │  │ X3  ╎ [REF 1015] │  └─────┴───────┘
│ 1003 ╎ g|2        │  │ X4  ╎ [STR 1001] │
│ 1004 ╎ [STR 1011] │  └─────┴────────────┘
│ 1005 ╎ [STR 1001] │
│ 1006 ╎ [STR 1007] │
│ 1007 ╎ f|2        │
│ 1008 ╎ [REF 1004] │
│ 1009 ╎ [STR 1003] │
│ 1010 ╎ [STR 1011] │
│ 1011 ╎ b|0        │
│ 1012 ╎ [STR 1013] │
│ 1013 ╎ f|2        │
│ 1014 ╎ [STR 1011] │
│ 1015 ╎ [STR 1003] │
└──────┴────────────┘

X = b
Y = g(b, a)

Inspecting the heap, and it becomes clear that:

dereferencing a_x, STR 1011 → b|0, so X = b
dereferencing a_y, STR 1015 → STR 1003 → g|2, so Y = g(X, a) = g(b, a)

Exercise 2.3 (pg. 14)

Verify that the effect of executing the sequence of instructions shown in Figure 2.4 right after that in Figure 2.3 produces the MGU of the terms p(Z, h(Z, W), f(W)) and p(f(X), h(Y, f(a)), Y). That is, the (dereferenced) bindings corresponding to W = f(a), X = f(a), Y = f(f(a)), Z = f(f(a)).

MGU = Most General Unifier

(->
  (make-context)

  ; fig 2.3: compiled code for ℒ₀ query ?- p(Z, h(Z, W), f(W)).
  (put-structure 'h|2, 'X3)
  (set-variable 'X2)
  (set-variable 'X5)
  (put-structure 'f|1, 'X4)
  (set-value 'X5)
  (put-structure 'p|3, 'X1)
  (set-value 'X2)
  (set-value 'X3)
  (set-value 'X4)

  ; fig 2.4: compiled code for ℒ₀ query ?- p(f(X), h(Y, f(a)), Y).
  (get-structure 'p|3, 'X1)
  (unify-variable 'X2)
  (unify-variable 'X3)
  (unify-variable 'X4)
  (get-structure 'f|1, 'X2)
  (unify-variable 'X5)
  (get-structure 'h|2, 'X3)
  (unify-value 'X4)
  (unify-variable 'X6)
  (get-structure 'f|1, 'X6)
  (unify-variable 'X7)
  (get-structure 'a|0, 'X7)

  diag

  (tee #(println "W =" (resolve-struct % (register-address 'X5))))
  (tee #(println "X =" (resolve-struct % (register-address 'X5))))
  (tee #(println "Y =" (resolve-struct % (register-address 'X4))))
  (tee #(println "Z =" (resolve-struct % (register-address 'X2)))))

Prints:

Heap                   Registers             Variables
------------------------------------------------------
┌──────┬────────────┐  ┌─────┬────────────┐  ┌───────┐
│ key  │ value      │  │ key │ value      │  │ value │
├──────┼────────────┤  ├─────┼────────────┤  ├───────┤
│ 1000 ╎ [STR 1001] │  │ X1  ╎ [STR 1008] │  └───────┘
│ 1001 ╎ h|2        │  │ X2  ╎ [REF 1002] │
│ 1002 ╎ [STR 1013] │  │ X3  ╎ [STR 1001] │
│ 1003 ╎ [STR 1016] │  │ X4  ╎ [STR 1005] │
│ 1004 ╎ [STR 1005] │  │ X5  ╎ [REF 1014] │
│ 1005 ╎ f|1        │  │ X6  ╎ [REF 1003] │
│ 1006 ╎ [REF 1003] │  │ X7  ╎ [REF 1017] │
│ 1007 ╎ [STR 1008] │  └─────┴────────────┘
│ 1008 ╎ p|3        │
│ 1009 ╎ [REF 1002] │
│ 1010 ╎ [STR 1001] │
│ 1011 ╎ [STR 1005] │
│ 1012 ╎ [STR 1013] │
│ 1013 ╎ f|1        │
│ 1014 ╎ [REF 1003] │
│ 1015 ╎ [STR 1016] │
│ 1016 ╎ f|1        │
│ 1017 ╎ [STR 1019] │
│ 1018 ╎ [STR 1019] │
│ 1019 ╎ a|0        │
└──────┴────────────┘

W = f(a)
X = f(a)
Y = f(f(a))
Z = f(f(a))

Exercise 2.4 (pg. 14)

What are the respective sequences of ℳ₀ instructions for ℒ₀ query term ?-p(f(X), h(Y, f(a)), Y) and program term p(Z, h(Z, W), f(W))?

Setting the execution trace to true and running the two terms:

(->
  (make-context)
  (assoc :trace true)
  (query "p(Z, h(Z, W), f(W))")
  (program "p(f(X), h(Y, f(a)), Y)"))

Gives the following instruction list:

put_structure h|2, X3
set_variable X2
set_variable X5
put_structure f|1, X4
set_value X5
put_structure p|3, X1
set_value X2
set_value X3
set_value X4
get_structure p|3, X1
unify_variable X2
unify_variable X3
unify_variable X4
get_structure f|1, X2
unify_variable X5
get_structure h|2, X3
unify_value X4
unify_variable X6
get_structure f|1, X6
unify_variable X7
get_structure a|0, X7

Exercise 2.5 (pg. 14)

After doing Exercise 2.4, verify that the effects of executing the sequence you produced yields the same solution as that of Exercise 2.3.

Executing:

(->
  (make-context)
  (assoc :trace true)
  (query "p(Z, h(Z, W), f(W))")
  (program "p(f(X), h(Y, f(a)), Y)")
  diag

  (tee #(println "W =" (resolve-struct % (register-address 'X5))))
  (tee #(println "X =" (resolve-struct % (register-address 'X5))))
  (tee #(println "Y =" (resolve-struct % (register-address 'X4))))
  (tee #(println "Z =" (resolve-struct % (register-address 'X2)))))

This gives the same output as exercise 2.3 (albeit with extra register allocations):

Heap                   Registers             Variables
------------------------------------------------------------
┌──────┬────────────┐  ┌─────┬────────────┐  ┌─────┬───────┐
│ key  │ value      │  │ key │ value      │  │ key │ value │
├──────┼────────────┤  ├─────┼────────────┤  ├─────┼───────┤
│ 1000 ╎ [STR 1001] │  │ X1  ╎ [STR 1008] │  │ W   ╎ X5    │
│ 1001 ╎ h|2        │  │ X2  ╎ [REF 1002] │  │ X   ╎ X5    │
│ 1002 ╎ [STR 1013] │  │ X3  ╎ [STR 1001] │  │ Y   ╎ X4    │
│ 1003 ╎ [STR 1016] │  │ X4  ╎ [STR 1005] │  │ Z   ╎ X2    │
│ 1004 ╎ [STR 1005] │  │ X5  ╎ [REF 1014] │  └─────┴───────┘
│ 1005 ╎ f|1        │  │ X6  ╎ [REF 1003] │
│ 1006 ╎ [REF 1003] │  │ X7  ╎ [REF 1017] │
│ 1007 ╎ [STR 1008] │  └─────┴────────────┘
│ 1008 ╎ p|3        │
│ 1009 ╎ [REF 1002] │
│ 1010 ╎ [STR 1001] │
│ 1011 ╎ [STR 1005] │
│ 1012 ╎ [STR 1013] │
│ 1013 ╎ f|1        │
│ 1014 ╎ [REF 1003] │
│ 1015 ╎ [STR 1016] │
│ 1016 ╎ f|1        │
│ 1017 ╎ [STR 1019] │
│ 1018 ╎ [STR 1019] │
│ 1019 ╎ a|0        │
└──────┴────────────┘

W = f(a)
X = f(a)
Y = f(f(a))
Z = f(f(a))

Language ℒ₁ – Argument Registers

Exercise 2.6 (pg. 18)

Verify that the effect of executing the sequence of ℳ₁ instructions shown in Figure 2.9 produces the same heap representation as that produced by the ℳ₀ code of Figure 2.3 (see Exercise 2.1).

Assuming the same imports and initial context as perviously:

(->
  (make-context)
  (put-variable 'X4, 'A1)
  (put-structure 'h|2, 'A2)
  (set-value 'X4)
  (set-variable 'X5)
  (put-structure 'f|1, 'A3)
  (set-value 'X5)
  heap
  table)

gives:

┌──────┬────────────┐
│ key  │ value      │
├──────┼────────────┤
│ 1000 ╎ [REF 1000] │
│ 1001 ╎ [STR 1002] │
│ 1002 ╎ h|2        │
│ 1003 ╎ [REF 1000] │
│ 1004 ╎ [REF 1004] │
│ 1005 ╎ [STR 1006] │
│ 1006 ╎ f|1        │
│ 1007 ╎ [REF 1004] │
└──────┴────────────┘

Apart from the term root, the heap is layed out similarly to that of Figure 2.3 as below, albeit with different references:

                         ┌──────┬────────────┐
┌──────┬────────────┐    │ key  │ value      │
│ key  │ value      │    ├──────┼────────────┤
├──────┼────────────┤    │ 1000 ╎ [REF 1000] │
│ 1000 ╎ [STR 1001] │    │ 1001 ╎ [STR 1002] │
│ 1001 ╎ h|2        │    │ 1002 ╎ h|2        │
│ 1002 ╎ [REF 1002] │    │ 1003 ╎ [REF 1000] │
│ 1003 ╎ [REF 1003] │    │ 1004 ╎ [REF 1004] │
│ 1004 ╎ [STR 1005] │    │ 1005 ╎ [STR 1006] │
│ 1005 ╎ f|1        │    │ 1006 ╎ f|1        │
│ 1006 ╎ [REF 1003] │    │ 1007 ╎ [REF 1004] │
│ 1007 ╎ [STR 1008] │    └──────┴────────────┘
│ 1008 ╎ p|3        │
│ 1009 ╎ [REF 1002] │
│ 1010 ╎ [STR 1001] │
│ 1011 ╎ [STR 1005] │
└──────┴────────────┘

Exercise 2.7 (pg. 18)

Verify that the effect of executing the sequence of ℳ₁ instructions shown in Figure 2.10 right after that in Figure 2.9 produces the MGU of the terms p(Z, h(Z, W), f(W)) and p(f(X), h(Y, f(a)), Y). That is, the binding W = f(a), X = f(a), Y = f(f(a)), Z = f(f(a)).

Defining p/3 as:

(def p|3
  (list
    [get-structure 'f|1, 'A1]
    [unify-variable 'X4]
    [get-structure 'h|2, 'A2]
    [unify-variable 'X5]
    [unify-variable 'X6]
    [get-value 'X5, 'A3]
    [get-structure 'f|1, 'X6]
    [unify-variable 'X7]
    [get-structure 'a|0, 'X7]
    [proceed]))

Then, executing the program term directly after the query term:

(->
  ctx
  (put-variable 'X4, 'A1)
  (put-structure 'h|2, 'A2)
  (set-value 'X4)
  (set-variable 'X5)
  (put-structure 'f|1, 'A3)
  (set-value 'X5)
  (load 'p|3 p|3)
  (call 'p|3)
  diag
  (tee #(println "W =" (resolve-struct % (register-address 'X4))))
  (tee #(println "X =" (resolve-struct % (register-address 'X4))))
  (tee #(println "Y =" (resolve-struct % (register-address 'A3))))
  (tee #(println "Z =" (resolve-struct % (register-address 'X5)))))

gives:

Heap                   Registers             Variables
------------------------------------------------------
┌──────┬────────────┐  ┌─────┬────────────┐  ┌───────┐
│ key  │ value      │  │ key │ value      │  │ value │
├──────┼────────────┤  ├─────┼────────────┤  ├───────┤
│ 1000 ╎ [STR 1009] │  │ X1  ╎ [REF 1000] │  └───────┘
│ 1001 ╎ [STR 1002] │  │ X2  ╎ [STR 1002] │
│ 1002 ╎ h|2        │  │ X3  ╎ [STR 1006] │
│ 1003 ╎ [REF 1000] │  │ X4  ╎ [REF 1010] │
│ 1004 ╎ [STR 1012] │  │ X5  ╎ [REF 1000] │
│ 1005 ╎ [STR 1006] │  │ X6  ╎ [REF 1004] │
│ 1006 ╎ f|1        │  │ X7  ╎ [REF 1013] │
│ 1007 ╎ [REF 1004] │  └─────┴────────────┘
│ 1008 ╎ [STR 1009] │
│ 1009 ╎ f|1        │
│ 1010 ╎ [REF 1004] │
│ 1011 ╎ [STR 1012] │
│ 1012 ╎ f|1        │
│ 1013 ╎ [STR 1015] │
│ 1014 ╎ [STR 1015] │
│ 1015 ╎ a|0        │
└──────┴────────────┘

W = f(a)
X = f(a)
Y = f(f(a))
Z = f(f(a))

Exercise 2.8 (pg. 18)

What are the respective sequences of ℳ₁ instructions for ℒ₁ query term ?-p(f(X), h(Y, f(a)), y) and ℒ₁ program term p(Z, h(Z, W), f(W))?

There is a bit of a leap here in the tutorial, and I'm not sure if I fully understand, but the query term ?-p(f(X), h(Y, f(a)), y) is now build from the following instructions:

put-structure f|1, A1
set-variable X4)
put-structure h|2, A2
set-variable A3)
put-structure f|1, X5
put-structure a|0, X6
set-value A3
call p|3

And the program term p(Z, h(Z, W), f(W)) is comprised of:

unify-variable A1
get-structure h|2, A2
unify-value A1
unify-variable X4
get-structure f|1, A3
unify-value X4
proceed

Exercise 2.9 (pg. 19)

After doing Exercise 2.8, verify that the effect of executing the sequence you produced yields the same solution as that of Exercise 2.7.

Executing the program against the query term does give the same unification result as previously:

(def p|3
  (list
    [unify-variable 'A1]
    [get-structure 'h|2, 'A2]
    [unify-value 'A1]
    [unify-variable 'X4]
    [get-structure 'f|1, 'A3]
    [unify-value 'X4]
    [proceed]))

(->
  ctx
  (put-structure 'f|1, 'A1)
  (set-variable 'X4)
  (put-structure 'h|2, 'A2)
  (set-variable 'A3)
  (put-structure 'f|1, 'X5)
  (put-structure 'a|0, 'X6)
  (set-value 'A3)
  (load 'p|3 p|3)
  (call 'p|3)
  (diag)
  (tee #(println "W =" (resolve-struct % (register-address 'X4))))
  (tee #(println "X =" (resolve-struct % (register-address 'X4))))
  (tee #(println "Y =" (resolve-struct % (register-address 'A3))))
  (tee #(println "Z =" (resolve-struct % (register-address 'A1)))))

Outputs:

Heap                   Registers             Variables
------------------------------------------------------
┌──────┬────────────┐  ┌─────┬────────────┐  ┌───────┐
│ key  │ value      │  │ key │ value      │  │ value │
├──────┼────────────┤  ├─────┼────────────┤  ├───────┤
│ 1000 ╎ [STR 1001] │  │ X1  ╎ [STR 1001] │  └───────┘
│ 1001 ╎ f|1        │  │ X2  ╎ [STR 1004] │
│ 1002 ╎ [STR 1007] │  │ X3  ╎ [REF 1005] │
│ 1003 ╎ [STR 1004] │  │ X4  ╎ [STR 1007] │
│ 1004 ╎ h|2        │  │ X5  ╎ [STR 1007] │
│ 1005 ╎ [STR 1001] │  │ X6  ╎ [STR 1009] │
│ 1006 ╎ [STR 1007] │  └─────┴────────────┘
│ 1007 ╎ f|1        │
│ 1008 ╎ [STR 1009] │
│ 1009 ╎ a|0        │
│ 1010 ╎ [REF 1005] │
└──────┴────────────┘

W = f(a)
X = f(a)
Y = f(f(a))
Z = f(f(a))

Language ℒ₂ – Flat Resolution

TODO

Language ℒ₃ – Prolog

TODO

References

License

The MIT License (MIT)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Name		Name	Last commit message	Last commit date
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src/wam		src/wam
test/wam		test/wam
.editorconfig		.editorconfig
.gitignore		.gitignore
.travis.yml		.travis.yml
LICENSE.md		LICENSE.md
README.md		README.md
project.clj		project.clj

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Warren's Abstract Machine

Language ℒ₀ – Unification

Exercise 2.1 (pg. 9)

EBNF ℒ₀ Grammar & Parser Combinators

Compiling ℒ₀ queries

Compiling ℒ₀ programs

Exercise 2.2 (pg. 14)

Exercise 2.3 (pg. 14)

Exercise 2.4 (pg. 14)

Exercise 2.5 (pg. 14)

Language ℒ₁ – Argument Registers

Exercise 2.6 (pg. 18)

Exercise 2.7 (pg. 18)

Exercise 2.8 (pg. 18)

Exercise 2.9 (pg. 19)

Language ℒ₂ – Flat Resolution

Language ℒ₃ – Prolog

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Warren's Abstract Machine

Language ℒ₀ – Unification

Exercise 2.1 (pg. 9)

EBNF ℒ₀ Grammar & Parser Combinators

Compiling ℒ₀ queries

Compiling ℒ₀ programs

Exercise 2.2 (pg. 14)

Exercise 2.3 (pg. 14)

Exercise 2.4 (pg. 14)

Exercise 2.5 (pg. 14)

Language ℒ₁ – Argument Registers

Exercise 2.6 (pg. 18)

Exercise 2.7 (pg. 18)

Exercise 2.8 (pg. 18)

Exercise 2.9 (pg. 19)

Language ℒ₂ – Flat Resolution

Language ℒ₃ – Prolog

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