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PCM20230124_SICP_3.2.1_TheRulesForEvaluation.jl
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### A Pluto.jl notebook ###
# v0.19.12
using Markdown
using InteractiveUtils
# ╔═╡ d8605b7e-3cfa-42b9-bfd2-ae0fa8afe8fa
using Plots
# ╔═╡ eeebdde0-9c08-11ed-1bee-89bc2518d37a
md"
====================================================================================
#### SICP: [3.2.1 The Rules for Evaluation](https://sarabander.github.io/sicp/html/3_002e2.xhtml#g_t3_002e2_002e1)
##### file: PCM20230124\_SICP\_3.2.1\_TheRulesForEvaluation.jl
##### Julia/Pluto.jl-code (1.8.3/0.19.14) by PCM *** 2023/02/21 ***
====================================================================================
"
# ╔═╡ 78539779-7135-43c9-ad94-f53d8789ba66
md"
*- The environment model of evaluation **replaces** the substitution model in specifying what it means to apply a compound procedure to arguments.*
*- ... a procedure is always a **pair** consisting of some code and a pointer to an environment.*
*- Procedures are **created** in one way only: by evaluataing a $$\lambda$$-expression.*
*- This produces a procedure whose **code** is obtained from the text of the $$\lambda$$-expression and whose **environment** is the environment in which the $$\lambda$$-expression was evaluated to produce the procedure* (SICP, 1996, p.238)
"
# ╔═╡ a224ee70-9a3c-471f-aec6-5a7bcb3b5666
md"
---
###### *Global* environment *E0*
(simulated by a $$let$$-expression)
"
# ╔═╡ 6d49451f-46d8-4d1a-9d4d-d794b246e276
md"
We are not very satisfied by environment *diagrams* as introduced by Weizenbaum (1968) and presented by Allen (1978, p. 143). Unfortunately their semantics could not be explored in simulation runs. Instead we represent the environments by *nested* $let$-expressions. These are syntactic sugar for nested $\lambda$-expressions. Thus simulations in Julia are easy possible.
"
# ╔═╡ 85508544-c61f-4c0c-b7e8-d86b4504c85f
rectangleObj(x, y, w, h) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])
# ╔═╡ 36700724-6802-441f-9170-fc1e59d2b1f2
squareObj(x, y, w) = rectangleObj(x, y, w, w) # square(x-coord, y-coord, width)
# ╔═╡ cd7a0889-ce50-47d9-b083-982f60f2eeaf
# adapted from LazarA in https://discourse.julialang.org/t/plot-a-circle-with-a-given-radius-with-plots-jl/23295/4
circleShape(x, y, r) =
let θ = LinRange(0, 2π, 100)
xs = x .+ r*sin.(θ)
ys = y .+ r*cos.(θ)
xs, ys
end # let
# ╔═╡ 28acbc1a-9a7a-452a-b4a0-8f96485837ad
let
#-----------------------------------------------------------------------------
plot(title="Structure of Environment Frames", xlims=(0, 15), ylims=(-0.5, 14), scale=:same, legend=:no, showaxis=:yes, titlelocation = :center)
#-----------------------------------------------------------------------------
# draw gloabal environment
function drawGlobalEnvironment(x, y, w, h)
plot!(rectangleObj(x, y, w, h),fillcolor=plot_color(:cornflowerblue, 0.2), line=:blue) # E0
annotate!(x+3.5, y+2.3, ("E0", 11, :blue)) # E0
annotate!(x+1.2, y+1.7, ("others:...", 9, :blue)) # E0
annotate!(x+1.0, y+0.7, ("square:", 9, :blue)) # E0
end # function drawGlobalEnvironment
drawGlobalEnvironment(4.5, 9, 4, 3)
#-----------------------------------------------------------------------------
# lambda-expression of square
function drawLambdaSquare(x, y, w, h)
plot!(rectangleObj(x, y, w, h),fillcolor=plot_color(:cornflowerblue,0.2), line=(:dash, :blue)) # E0'
annotate!(x+w/3, y+w/2.25, ("parm: x", 9, :blue)) # E0'
annotate!(x+w/2.15, y+w/4, ("body: *(x, x)", 9, :blue)) # E0'
end # function drawLambdaSquare
drawLambdaSquare(2.5, 2.3, 3, 2) # lambda-expression of square
#-----------------------------------------------------------------------------
function drawArrowDashDownLeft(x, y, w, h)
# dash downline
plot!([(x, y), (x, y-h)], line = (1.3, :red), linestyle=:dash)
# dashed arrowToTheLeft
plot!([(x, y-h),(x-1.1, y-h)],line=(1.3, :red), linestyle=:dash, arrow=:head)
end # function drawDashDownLeft
drawArrowDashDownLeft(6.6, 9.6, 1.1, 6.2)
#-----------------------------------------------------------------------------
function drawArrowRightUp(x, y, w, h)
# uparrow C
plot!([(x+w, y),(x+w, y+h)], line = (:arrow, 1.3, :red), linestyle=:dash)
# lineToTheRight
plot!([(x, y),(x+w, y)],line=(1.3,:red), linestyle=:dash)
end # function drawArrowRightUp
drawArrowRightUp(5.5, 3, 1.4, 6)
#-----------------------------------------------------------------------------
plot!(circleShape(6.6, 9.6, 0.2), seriestype=[:shape], lw=0.5, c=:red, linecolor=:red, legend=:false)
end # let
# ╔═╡ dfafeb4d-93b6-482d-b025-dc15652f8da5
md"
**Fig. 3.2.1** *Environment diagram E0* after evaluating $$square$$ (cf. SICP, 1996, Fig. 3.2)
---
"
# ╔═╡ 7fad9ca2-bb22-4a56-8bdc-a668d80c4850
md"
*square* evaluates to $$\lambda$$-expression: $$square \Rightarrow \lambda x.*(x, x) \equiv x \rightarrow *(x, x)$$
"
# ╔═╡ 5002c5cb-7cbc-4143-83fc-08e2912aa6f6
let # simulated global environment E0
#-------------------------------------------------------
square = x -> *(x, x)
#-------------------------------------------------------
square # square ==> x -> *(x, x); square evaluates to λ-expression
end # let E0
# ╔═╡ 34407212-d1fa-44d7-aae0-80a49eb922b2
md"
---
###### *Extending* global environment *E0* by *E1*
"
# ╔═╡ c9456bfc-8833-409c-b706-367707be797e
md"
Evaluation of $$square(6)$$ in *E0* and *E1*:
$$square(6) \Longrightarrow 36$$ after parameter-argument binding and extension of E0 to E1.
"
# ╔═╡ 4ed2ff2f-09fa-4079-a375-81ea55766fc5
let
#-----------------------------------------------------------------------------
plot(title="Structure of Environment Frames", xlims=(0, 15), ylims=(-0.5, 14), scale=:same, legend=:no, showaxis=:yes, titlelocation = :center)
#-----------------------------------------------------------------------------
# draw global environment E0
function drawGlobalEnvironment(x, y, w, h)
plot!(rectangleObj(x, y, w, h),fillcolor=plot_color(:cornflowerblue, 0.2), line=:blue) # E0
annotate!(x+w*0.9, y+h*0.77, ("E0", 11, :blue)) # E0
annotate!(x+w*0.28, y+h*0.5, ("others:...", 9, :blue)) # E0
annotate!(x+w*0.25, y+h*0.23, ("square:", 9, :blue)) # E0
end # function drawGlobalEnvironment
drawGlobalEnvironment(4.5, 9, 4, 3)
#-----------------------------------------------------------------------------
# lambda-expression of rectangle
function drawLambdaRectangle(x, y, w, h)
plot!(rectangleObj(x, y, w, h),fillcolor=plot_color(:cornflowerblue,0.2), line=(:dash, :blue)) # E0'
annotate!(x+w/3, y+w/2.25, ("parm: x", 9, :blue)) # E0'
annotate!(x+w/2.15, y+w/4, ("body: *(x, x)", 9, :blue)) # E0'
end # function drawLambdaRectangle
drawLambdaRectangle(2.5, 2.3, 3, 2) # lambda-expression of rectangle
#-----------------------------------------------------------------------------
function drawArrowDashDownLeft(x, y, w, h)
# dash downline
plot!([(x, y), (x, y-h)], line = (1.3, :red), linestyle=:dash)
# dashed arrowToTheLeft
plot!([(x, y-h),(x-1.1, y-h)],line=(1.3, :red), linestyle=:dash, arrow=:head)
end # function drawDashDownLeft
drawArrowDashDownLeft(6.6, 9.6, 1.1, 6.2)
#-----------------------------------------------------------------------------
function drawArrowRightUp(x, y, w, h)
# uparrow C
plot!([(x+w, y),(x+w, y+h)], line = (:arrow, 1.3, :red), linestyle=:dash)
# lineToTheRight
plot!([(x, y),(x+w, y)],line=(1.3,:red), linestyle=:dash)
end # function drawArrowRightUp
drawArrowRightUp(5.5, 3, 1.4, 6)
#-----------------------------------------------------------------------------
plot!(circleShape(6.6, 9.6, 0.2), seriestype=[:shape], lw=0.5, c=:red, linecolor=:red, legend=:false)
#============================================================================#
# draw local environment E1
function drawLocalEnvironment(x, y, w, h)
plot!(rectangleObj(x, y, w, h),fillcolor=plot_color(:cornflowerblue, 0.2), line=:blue) # E1
annotate!(x+w*0.8, y+h*0.75, ("E1", 11, :blue)) # E1
annotate!(x+w*0.3, y+h*0.35, ("x: 6", 9, :blue)) # E1
end # function drawLocalEnvironment E1
drawLocalEnvironment(9, 4, 2, 2)
#-----------------------------------------------------------------------------
function drawArrowLeftUp(x, y, w, h)
plot!([(x-w, y),(x-w, y+h)], line = (:arrow, 2, :red)) # uparrow C
plot!([(x, y),(x-w, y)],line=(2,:red)) # lineToTheRight
end # function drawArrowLeftUp
drawArrowLeftUp(8.9, 5, 1.4, 4)
#-----------------------------------------------------------------------------
end # let
# ╔═╡ 25fac027-1ee6-4488-9d69-cf57b23600f9
md"
**Fig. 3.2.2** *Extended* environment diagram after evaluating '$$square2(6)$$' (cf. SICP, 1996, Fig. 3.3)
"
# ╔═╡ 109f49c7-c120-4854-acd0-a10bca16ab1c
let # simulated global environment E0
square = x -> *(x, x)
let # parameter-argument binding, extending E0 by E1
#--------------------------------------------------------
x = 6
#--------------------------------------------------------
square(x) # ==> (x -> *(x, x))(x)
(x -> *(x, x))(x) # ==> (x -> *(x, x))(6)
(x -> *(x, x))(6) # ==> *(6, 6)
*(6, 6) # ==> 36, evaluation in E1
end # let E1
end # let E0
# ╔═╡ 43da2893-dd3a-45ee-a775-7cd43c343996
md"
---
##### Environment model of procedure application
- **Rule 1**: A procedure object is applied to a set of arguments by:
(1) constructing a frame,
(2) binding the formal parameters of the procedure to the arguments of the call,
(3) and then evaluating the body of the procedure in the context of the new (extended) environment constructed.
The *new* frame has as its enclosing environment the environment part of the procedure object being applied.(cf. SICP, 1996, ch.3.2.1, p.240f)
"
# ╔═╡ 4d2bd09b-3de7-487d-abc8-03511e3fd9cc
md"
- **Rule 2**: A procedure is created by evaluating a λ-expression relative to a given environment. The resulting procedure object is a *pair* consisting of the text of the λ-expression and a pointer to the environment in which the procedure was created.(cf. SICP, 1996, ch.3.2.1, p.240f)
"
# ╔═╡ 98ed3edc-b7ce-47bb-8c91-cdb7b5a4a894
md"
- **Rule 3**: Defining a symbol with 'function' or '=' creates a binding in the current environment frame and assigns to the symbol the indicated value.(cf. SICP, 1996, ch.3.2.1, p.240f)
"
# ╔═╡ 9c34669d-2ad6-4255-bd24-4c0080a4fc22
md"
- **Rule 4**: Evaluating the expression '<symbol> = <value>' in some environment locates the binding of the variable in the environment and changes that binding to indicate the new value. That is, one finds the first frame in the environment that contains a binding for the variable and modifies that frame.
"
# ╔═╡ 5ffc8937-ca71-4ffa-b876-7e0c4b6642d6
md"
---
##### References
- **Allen, J.**, The Anatomy of Lisp, New York: McGraw Hill, 1978
- **Weizenbaum, J.**, [*The FUNARG Problem*](https://en.wikipedia.org/wiki/Funarg_problem) *Explained*, [unpublished memorandum](https://www.softwarepreservation.org/projects/LISP/MIT/Weizenbaum-FUNARG_Problem_Explained-1968.pdf), MIT, Cambridge Mass., 1968
- **Wikipedia**, [*The FUNARG Problem*](https://en.wikipedia.org/wiki/Funarg_problem), last visit 2023/02/21
"
# ╔═╡ 453908cd-138d-459d-80ab-52c2e69ff86a
md"
---
##### end of ch. 3.2.1
"
# ╔═╡ 47829574-dbc0-4c68-9cad-fd5564e3ec99
md"
====================================================================================
This is a **draft** under the Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license. Comments, suggestions for improvement and bug reports are welcome: **claus.moebus(@)uol.de**
====================================================================================
"
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
[compat]
Plots = "~1.38.3"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
julia_version = "1.8.5"
manifest_format = "2.0"
project_hash = "4aa5240c0625a5c9fb53ded0ddfcbc6926f9c61c"
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deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
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